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Robust output-feedback stabilization of a class of nonlinear systems with the nonlinearities of varied form
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作者 Sun Xiping Wang Yongji 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2006年第3期629-634,共6页
The back-stepping designs based on confine functions are suggested for the robust output-feedback global stabilization of a class of nonlinear continuous systems; the proposed stabilizer is efficient for the nonlinear... The back-stepping designs based on confine functions are suggested for the robust output-feedback global stabilization of a class of nonlinear continuous systems; the proposed stabilizer is efficient for the nonlinear continuous systems confined by a bound function, the nonlinearities of the systems may be of varied forms or uncertain; the designed stabilizer is robust means that a class of nonlinear continuous systems can be stabilized by the same output feedback stabilization schemes; numerical simulation examples are given. 展开更多
关键词 nonlinear systems robust output-feedback control back-stepping design bound function
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Observer-based Output-feedback Stabilization Control Design for a Class of Nonlinear Uncertain Systems 被引量:3
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作者 ZHANG Yun LIU Yun-Gang LI Yan-Fang 《自动化学报》 EI CSCD 北大核心 2006年第1期101-106,共6页
The output-feedback stabilization control problem is investigated for a class of nonlinear uncertain systems. Based on the multivariable analog of circle criterion, an observer is designed to estimate the system state... The output-feedback stabilization control problem is investigated for a class of nonlinear uncertain systems. Based on the multivariable analog of circle criterion, an observer is designed to estimate the system states and hence the dynamical equations that the estimation error satisfies are derived first. Then, by using integral backstepping approach together with completing square technique, the output-feedback stabilization control is constructively designed such that the closed-loop system is asymptotically stable. Finally, an example is given to illustrate the main results of this paper. 展开更多
关键词 非线性系统 不确定性 输出反馈 稳定性 误差估计
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Output-feedback Stabilization for Stochastic High-order Nonlinear Systems with a Ratio of Odd Integers Power 被引量:4
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作者 LIU Liang DUAN Na XIE Xue-Jun 《自动化学报》 EI CSCD 北大核心 2010年第6期858-864,共7页
关键词 反馈系统 稳定性 自动化 研究
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Synergistic effect of nitrocellulose coating on structural and reactivity stabilization of ammonium nitrate oxidizer 被引量:1
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作者 Amir Abdelaziz Djalal Trache +5 位作者 Ahmed Fouzi Tarchoun Hani Boukeciat Yash Pal Sourbh Thakur Weiqiang Pang Thomas M.Klapötke 《Defence Technology(防务技术)》 2025年第1期35-43,共9页
The present work aims to stabilize the room temperature allotropic transition of ammonium nitrate(AN)particles utilizing a microencapsulation technique,which involves solvent/non-solvent in which nitrocellulose(NC)has... The present work aims to stabilize the room temperature allotropic transition of ammonium nitrate(AN)particles utilizing a microencapsulation technique,which involves solvent/non-solvent in which nitrocellulose(NC)has been employed as a coating agent.The SEM micrographs revealed distinct features of both pure AN and NC,contrasting with the irregular granular surface topography of the coated AN particles,demonstrating the adherence of NC on the AN surface.Structural analysis via infrared spectroscopy(IR)demonstrated a successful association of AN and NC,with slight shifts observed in IR bands indicating interfacial interactions.Powder X-ray Diffraction(PXRD)analysis further elucidated the structural changes induced by the coating process,revealing that the NC coating altered the crystallization pattern of its pure form.Thermal analysis demonstrates distinct profiles for pure and coated AN,for which the coated sample exhibits a temperature increase and an enthalpy decrease of the room temperature allotropic transition by 6℃,and 36%,respectively.Furthermore,the presence of NC coating alters the intermolecular forces within the composite system,leading to a reduction in melting enthalpy of coated AN by~39%compared to pure AN.The thermal decomposition analysis shows a two-step thermolysis process for coated AN,with a significant increase in the released heat by about 78%accompanied by an increase in the activation barrier of NC and AN thermolysis,demonstrating a stabilized reactivity of the AN-NC particles.These findings highlight the synergistic effect of NC coating on AN particles,which contributed to a structural and reactive stabilization of both AN and NC,proving the potential application of NC-coated AN as a strategically advantageous oxidizer in composite solid propellant formulations. 展开更多
关键词 Ammonium nitrate NITROCELLULOSE stabilization COATING Thermolysis kinetics
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Output-feedback adaptive stochastic nonlinear stabilization using neural networks
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作者 Weisheng Chen 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2010年第1期81-87,共7页
For the first time, an adaptive backstepping neural network control approach is extended to a class of stochastic non- linear output-feedback systems. Different from the existing results, the nonlinear terms are assum... For the first time, an adaptive backstepping neural network control approach is extended to a class of stochastic non- linear output-feedback systems. Different from the existing results, the nonlinear terms are assumed to be completely unknown and only a neural network is employed to compensate for all unknown nonlinear functions so that the controller design is more simplified. Based on stochastic LaSalle theorem, the resulted closed-loop system is proved to be globally asymptotically stable in probability. The simulation results further verify the effectiveness of the control scheme. 展开更多
关键词 neural network output-feedback nonlinear stochastic systems backstepping.
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Design and implementation of disturbance sliding mode observer for enhancing the dynamic control precision of inertial stabilization platform
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作者 ZHANG Zhidong YANG Gongliu +2 位作者 CAI Qingzhong FAN Jing LI Tao 《Journal of Systems Engineering and Electronics》 2025年第3期791-802,共12页
In order to enhance the dynamic control precision of inertial stabilization platform(ISP),a disturbance sliding mode observer(DSMO)is proposed in this paper suppressing disturbance torques inherent within the system.T... In order to enhance the dynamic control precision of inertial stabilization platform(ISP),a disturbance sliding mode observer(DSMO)is proposed in this paper suppressing disturbance torques inherent within the system.The control accuracy of ISP is fundamentally circumscribed by various disturbance torques in rotating shaft.Therefore,a dynamic model of ISP incorporating composite perturbations is established with regard to the stabilization of axis in the inertial reference frame.Subsequently,an online estimator for control loop uncertainties based on the sliding mode control algorithm is designed to estimate the aggregate disturbances of various parameters uncertainties and other unmodeled disturbances that cannot be accurately calibrated.Finally,the proposed DSMO is integrated into a classical proportional-integral-derivative(PID)control scheme,utilizing feedforward approach to compensate the composite disturbance in the control loop online.The effectiveness of the proposed disturbance observer is validated through simulation and hardware experimentation,demonstrating a significant improvement in the dynamic control performance and robustness of the classical PID controller extensively utilized in the field of engineering. 展开更多
关键词 inertial stabilization platform disturbance suppression sliding mode observer robust control
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Semiglobal Stabilization via Output-feedback for a Class of Uncertain Nonlinear Systems 被引量:1
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作者 LIU Meng-Liang LIU Yun-Gang 《自动化学报》 EI CSCD 北大核心 2013年第12期2154-2159,共6页
这份报纸为不明确的非线性的系统的一个班经由产量反馈认为 semiglobal 是稳定。与存在结果不同,在调查下面的系统拥有更严肃的非线性和实质地增加产量反馈的困难的未知控制系数控制器设计。联合 backstepping 方法和产量反馈支配途径... 这份报纸为不明确的非线性的系统的一个班经由产量反馈认为 semiglobal 是稳定。与存在结果不同,在调查下面的系统拥有更严肃的非线性和实质地增加产量反馈的困难的未知控制系数控制器设计。联合 backstepping 方法和产量反馈支配途径,稳定控制器的 semiglobal 明确地被给,它能保证靠近环的系统在设计参数的适当选择下面完成 semiglobal asymptotic 稳定性。一个模拟例子验证理论结果和建议途径。 展开更多
关键词 不确定非线性系统 输出反馈控制器 半全局镇定 全局渐近稳定性 全局稳定 控制系数 参数选用 闭环系统
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Adaptive NN stabilization for stochastic systems with discrete and distributed time-varying delays
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作者 Jing Li Junmin Li Yuli Xiao 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2011年第6期954-966,共13页
A new adaptive neural network(NN) output-feedback stabilization controller is investigated for a class of uncertain stochastic nonlinear strict-feedback systems with discrete and distributed time-varying delays and ... A new adaptive neural network(NN) output-feedback stabilization controller is investigated for a class of uncertain stochastic nonlinear strict-feedback systems with discrete and distributed time-varying delays and unknown nonlinear functions in both drift and diffusion terms.First,an extensional stability notion and the related criterion are introduced.Then,a nonlinear observer to estimate the unmeasurable states is designed,and a systematic backstepping procedure to design an adaptive NN output-feedback controller is proposed such that the closed-loop system is stable in probability.The effectiveness of the proposed control scheme is demonstrated via a numerical example. 展开更多
关键词 distributed delay output-feedback stabilization nonlinear observer stochastic nonlinear strict-feedback system adaptive neural network control(ANNC).
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Stabilization and trajectory tracking of autonomous airship's planar motion 被引量:7
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作者 Zhang Yan Qu Weidong +1 位作者 Xi Yugeng Cai Zili 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2008年第5期974-981,共8页
The stabilization and trajectory tracking problems of autonomous airship's planar motion are studied. By defining novel configuration error and velocity error, the dynamics of error systems are derived. By applying L... The stabilization and trajectory tracking problems of autonomous airship's planar motion are studied. By defining novel configuration error and velocity error, the dynamics of error systems are derived. By applying Lyapunov stability method, the state feedback control laws are designed and the close-loop error systems are proved to be uniformly asymptotically stable by Matrosov theorem. In particular, the controller does not need knowledge on system parameters in the case of set-point stabilization, which makes the controller robust with respect to parameter uncertainty. Numerical simulations illustrate the effectiveness of the controller designed. 展开更多
关键词 AIRSHIP planar motion stabilization trajectory tracking ROBUSTNESS Lyapunov stability Matrosov theorem.
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Stability analysis and stabilization for discrete-time singular delay systems 被引量:3
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作者 Xin Sun Qingling Zhang +1 位作者 Chunyu Yang Zhan Su 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2011年第3期482-487,共6页
Stability analysis and stabilization for discrete-time singular delay systems are addressed,respectively.Firstly,a sufficient condition for regularity,causality and stability for discrete-time singular delay systems i... Stability analysis and stabilization for discrete-time singular delay systems are addressed,respectively.Firstly,a sufficient condition for regularity,causality and stability for discrete-time singular delay systems is derived.Then,by applying the skill of matrix theory,the state feedback controller is designed to guarantee the closed-loop discrete-time singular delay systems to be regular,casual and stable.Finally,numerical examples are given to demonstrate the effectiveness of the proposed method. 展开更多
关键词 discrete-time singular systems DELAY stabilITY stabilization.
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Delay-dependent stability and stabilization of a class of linear switched time-varying delay systems 被引量:3
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作者 Zhang Lixian Wang Changhong Gao Huijun 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2007年第2期320-326,共7页
The stability and stabilization of a class of linear switched time-varying delay systems are investigated. A piecewise quadratic Lyapunov function (PWQLF) is constructed and is used to obtain the stability condition... The stability and stabilization of a class of linear switched time-varying delay systems are investigated. A piecewise quadratic Lyapunov function (PWQLF) is constructed and is used to obtain the stability conditions based on the linear matrix inequalities (LMIs). The stabilizing controller for this class of system is then designed and the solution of the desired controller can be obtained by a cone complementary linearization algorithm. Numerical examples are provided to illustrate the less conservativeness of the new stability and the validity of the controller design procedures. 展开更多
关键词 Linear switched systems Time-varying delay Delay-dependent stability stabilization LMIs.
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Advances in phase stabilization techniques of AN using KDN and other chemical compounds for preparing green oxidizers 被引量:4
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作者 Pratim Kumar 《Defence Technology(防务技术)》 SCIE EI CAS CSCD 2019年第6期949-957,共9页
Research and development of green oxidizers and green fuels as a possible replacement for ammonium perchlorate(NH4ClO4,AP) and hydrazine(N2H4) respectively has been increased considerably in the recent years.AP and hy... Research and development of green oxidizers and green fuels as a possible replacement for ammonium perchlorate(NH4ClO4,AP) and hydrazine(N2H4) respectively has been increased considerably in the recent years.AP and hydrazine are the oxidizer and fuel entities,and used in solid and liquid rocket motors respectively.AP is highly toxic and led to adverse health effects,while hydrazine is carcinogenic in nature.AP is in use from the last several decades for rocket and space shuttle propulsion,while hydrazine is used in upper stage liquid propelled rocket motors.It’s a tough task to replace AP with the currently available green oxidizers;since their ballistic properties are weaker when compared to AP and also they can’t be successfully deployed in a solid rocket motor at present Some important available solid green oxidizers are ammonium nitrate(AN),ammonium dinitramide(ADN),hydroxyl ammonium nitrate(HAN),and hydrazinium nitroformate(HNF).However,AN is one of the cheap and readily available oxidizer,and has great potential to use in solid/liquid rocket motors.Tremendous progress has been envisaged till now,and more progress will be there in the coming future over the development of AN based green energetic materials(GEM’s).A concise overview has been presented over the development of phase stabilized ammonium nitrate(PSAN) and AN/KDN based green oxidizers in the present review paper. 展开更多
关键词 Green oxidizers Ammonium nitrate(AN) Phase stabilized ammonium nitrate(PSAN) Dinitramide anion(DA) Potassium dinitramide(KDN) Phase stabilizers
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Electronic image stabilization system based on global feature tracking 被引量:7
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作者 Zhu Juanjuan Guo Baolong 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2008年第2期228-233,共6页
A new robust electronic image stabilization system is presented, which involves feature-point, tracking based global motion estimation and Kalman filtering based motion compensation. First, global motion is estimated ... A new robust electronic image stabilization system is presented, which involves feature-point, tracking based global motion estimation and Kalman filtering based motion compensation. First, global motion is estimated from the local motions of selected feature points. Considering the local moving objects or the inevitable mismatch, the matching validation, based on the stable relative distance between the points set is proposed, thus maintaining high accuracy and robustness. Next, the global motion parameters are accumulated for correction by Kalman filteration. The experimental result illustrates that the proposed system is effective to stabilize translational, rotational, and zooming jitter and robust to local motions. 展开更多
关键词 electronic image stabilization global motion estimation feature tracking Kalman filter.
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Robust stability and stabilization for uncertain discrete-time switched singular systems with time-varying delays 被引量:2
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作者 Jinxing Lin Shumin Fei Jiong Shen 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2010年第4期650-657,共8页
The problems of robust stability and stabilization via memoryless state feedback for a class of discrete-time switched singular systems with time-varying delays and linear fractional uncertainties are investigated.By ... The problems of robust stability and stabilization via memoryless state feedback for a class of discrete-time switched singular systems with time-varying delays and linear fractional uncertainties are investigated.By constructing a novel switched Lyapunov-Krasovskii functional,a delay-dependent criterion for the unforced system to be regular,causal and uniformly asymptotically stable is established in terms of linear matrix inequalities(LMIs).An explicit expression for the desired memoryless state feedback stabilization controller is also given.The merits of the proposed criteria lie in their less conservativeness and relative simplicity,which are achieved by considering additionally useful terms(ignored in previous methods) when estimating the upper bound of the forward difference of the Lyapunov-Krasovskii functional and by avoiding utilizing any model augmentation transformation.Some numerical examples are provided to illustrate the validity of the proposed methods. 展开更多
关键词 discrete-time switched singular system time-varying delay delay-dependent criterion switched Lyapunov-Krasovskii functional robust stability stabilization.
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New delay-dependent robust stability and stabilization for uncertain T-S fuzzy time-delay systems under imperfect premise matching 被引量:4
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作者 张泽健 黄显林 +1 位作者 班晓军 高晓智 《Journal of Central South University》 SCIE EI CAS 2012年第12期3415-3423,共9页
To alleviate the conservativeness of the stability criterion for Takagi-Sugeno (T-S) fuzzy time-delay systems, a new delay-dependent stability criterion was proposed by introducing a new augmented Lyapunov function ... To alleviate the conservativeness of the stability criterion for Takagi-Sugeno (T-S) fuzzy time-delay systems, a new delay-dependent stability criterion was proposed by introducing a new augmented Lyapunov function with an additional triple-integral term, which was firstly u3ed to derive the stability criterion for T-S fuzzy time-delay systems. By the same approach, the robust stability issue for fuzzy time-delay systems with uncertain parameters was also considered. On the other hand, in order to enhance the design flexibility, a new design approach for uncertain fuzzy time-delay systems under imperfect premise matching was also proposed, which allows the fuzzy controller to employ different membership functions from the fuzzy time-delay model. By the numerical examples, the proposed stability conditions are less conservative in the sense of getting larger allowable time-delay and obtaining smaller feedback control gains. For instance, when the allowable time-delay increases from 7.3 s to 12 s for an uncertain T-S fuzzy control system with time-delay, the norm of the feedback gains decreases from (34.299 2, 38.560 3) to (10.073 3, 11.349 0), respectively. Meanwhile, the effectiveness of the proposed design method was illustrated by the last example with the robustly stable curves of system state under the initial condition of x(0) = [3 -1]. 展开更多
关键词 T-S fuzzy systems time-delay systems imperfect premise matching stability robust stability linear matrix inequality(LMI) stabilization
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Molecular simulation study of the stabilization process of NEPE propellant 被引量:3
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作者 Ling-ze Kong Ke-hai Dong +3 位作者 Ai-min Jiang Chuan-lu Yang Yan-hui Tang Yun-dong Xiao 《Defence Technology(防务技术)》 SCIE EI CAS CSCD 2023年第7期220-230,共11页
In this reported study, the density functional theory(DFT) was used at the(U)B3LYP/6-311G(d,p) level to investigate the stabilization process of the nitrate ester plasticized polyether propellant(NEPE). Molecular simu... In this reported study, the density functional theory(DFT) was used at the(U)B3LYP/6-311G(d,p) level to investigate the stabilization process of the nitrate ester plasticized polyether propellant(NEPE). Molecular simulations were conducted of the reaction that generates NO_(2), the autocatalytic and aging reaction triggered by the NO_(2), and the nitrogen dioxide absorption reaction of the stabilizers during the propellent stabilization process. These simulations were derived using the transition-state theory(TST)and variational transition-state theory(VTST). The simulation results suggested that the stabilization of the NEPE propellant consisted of three stages. First, heat and NO_(2) were generated during the denitrification reaction of nitroglycerine(NG) and 1,2,4-butanetriol trinitrate(BTTN) in the NEPE propellant.Second, nitroso products were generated by the reactions of N-Methyl-4-nitroaniline(MNA) and 2-nitrodiphenylamine(2NDPA) with NO_(2). Third, the stabilizers were exhausted and the autocatalytic reaction of NG and BTTN and the aging reaction of polyethylene glycol(PEG) were triggered by the heat and NO_(2)generated in the first stage. By comparing the energy barriers of the various reactions, it was found that the NO_(2)generated from the denitrification reaction significantly reduced the reaction energy barrier to 105.56-126.32 kJ/mol, also increased the reaction rate constant, and decreased the thermal stability and energetic properties of the NEPE propellant. In addition, the NO_(2)also weakened the mechanical properties of the NEPE propellant by attacking the-CH2groups and the O atoms in the PEG molecular chain. The energy barriers of the reactions of MNA and 2NDPA with NO_(2)(94.61-133.61 k J/mol) were lower than those of the autocatalytic and decomposition reactions of NG, BTTN, and the aging reactions of PEG(160.30-279.46 kJ/mol). This indicated that, by eliminating NO_(2), the stabilizer in the NEPE propellant can effectively prevent NO_(2)from reacting with the NG, BTTN, and PEG in the NEPE propellant. Consequently, this would help maintain the energy and mechanical properties of the NEPE propellant, thereby improving its thermal stability. 展开更多
关键词 NEPE propellant stabilIZER stabilization process Molecular simulation DFT VTST
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A novel stabilization approach for small signal disturbance of power system with time-varying delay 被引量:4
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作者 杨波 孙元章 《Journal of Central South University》 SCIE EI CAS 2013年第12期3522-3527,共6页
Small signal instability may cause severe accidents for power system if it can not be dear correctly and timely. How to maintain power system stable under small signal disturbance is a big challenge for power system o... Small signal instability may cause severe accidents for power system if it can not be dear correctly and timely. How to maintain power system stable under small signal disturbance is a big challenge for power system operators and dispatchers. Time delay existing in signal transmission process makes the problem more complex. Conventional eigenvalue analysis method neglects time delay influence and can not precisely describe power system dynamic behaviors. In this work, a modified small signal stability model considering time varying delay influence was constructed and a new time delay controller was proposed to stabilize power system under disturbance. By Lyapunov-Krasovskii function, the control law in the form of nonlinear matrix inequality (NLMI) was derived. Considering synthesis method limitation for time delay controller at present, both parameter adjustment method by using linear matrix inequality (LMI) solver and iteration searching method by solving nonlinear minimization problem were suggested to design the controller. Simulation tests were carried out on synchronous-machine infinite-bus power system. Satisfactory test results verify the correctness of the proposed model and the feasibility of the stabilization approach. 展开更多
关键词 power system stability small signal disturbance time-varying delay power system stabilizer
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Adaptive stabilization for cascade nonlinear systems 被引量:1
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作者 ChenLanping WangHongyuan WuBo 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2004年第2期179-183,共5页
An adaptive controller of full state feedback for certain cascade nonlinear systems achieving input-to-state stability with respect to unknown bounded disturbance is designed using backstepping and control Lyapunov fu... An adaptive controller of full state feedback for certain cascade nonlinear systems achieving input-to-state stability with respect to unknown bounded disturbance is designed using backstepping and control Lyapunov function (CLF) techniques. We show that unknown bounded disturbance can be estimated by update laws, which requires less information on unknown disturbance, as a part of stabilizing control. The design method achieves the desired property: global robust stability. Our contribution is illustrated with the example of a disturbed pendulum. 展开更多
关键词 input-to-state stability control Lyapunov function CASCADE BACKSTEPPING state feedback control update law robust stability.
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Stabilization of saline silty sand using lime and micro silica 被引量:17
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作者 R.Z.Moayed E.Izadi S.Heidari 《Journal of Central South University》 SCIE EI CAS 2012年第10期3006-3011,共6页
Many construction and post-construction problems have been reported in the literature when saline soils have been used without understanding of their abnormal behavior,especially their inferior bearing capacity in the... Many construction and post-construction problems have been reported in the literature when saline soils have been used without understanding of their abnormal behavior,especially their inferior bearing capacity in the natural condition.The strength of these soils further decreases on soaking.Saline soil deposits cover extensive areas in central Iran and are associated with geotechnical problems such as excessive differential settlement,susceptibility to strength loss and collapse upon wetting.Because of these characteristics,some of the roads constructed on saline soils in Taleghan area have exhibited deterioration in the form of raveling,cracking and landslides.The main objective of this work is to improve the load-bearing capacity of pavements constructed on Taleghan saline soils using lime and micro silica.Soil samples from Hashtgerd-Taleghan road were collected and tested for improving their properties using lime and micro silica at different dosages ranging from 0 to 6%.The load-bearing capacity of stabilized soil mixtures was evaluated using California Bearing Ratio(CBR) and unconfined compressive strength tests.The test results indicate that the lime improves the performance of soil significantly.The addition of 2% lime with 3% micro silica has satisfied the strength-deformation requirements.Therefore,improved soil can be used as a good subbase in flexible pavements. 展开更多
关键词 lime stabilization saline soil micro silica bearing capacity compressive strength flexible pavements
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Guaranteed Quadratic Stabilization of Certain Time-Varying Large-Scale Delay It Stochastic Systems 被引量:1
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作者 Jin Yansheng & Xu Yumin (Dept. of Mathematics and Physics, Yanshan University, Qinhuangdao 066004, P. R. China) Deng Feiqi (Dept. of Automatic Control Engineering, South China University of Technology, Guangzhou 510641, P. R. China) 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2000年第3期35-39,共5页
In this paper, we investigate the decentralized stabilization of some time-varying uncertain large-scale stochastic systems with delays under matching conditions. A type of decentralized controllers with guaranteed s... In this paper, we investigate the decentralized stabilization of some time-varying uncertain large-scale stochastic systems with delays under matching conditions. A type of decentralized controllers with guaranteed stabilization and sub-optimality are also given. 展开更多
关键词 Stochastic systems Uncertainty stabilization.
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