This paper develops the mean-square exponential input-to-state stability（exp-ISS） of the Euler-Maruyama（EM） method for stochastic delay control systems（SDCSs）.The definition of mean-square exp-ISS of numerical m...This paper develops the mean-square exponential input-to-state stability（exp-ISS） of the Euler-Maruyama（EM） method for stochastic delay control systems（SDCSs）.The definition of mean-square exp-ISS of numerical methods is established.The conditions of the exact and EM method for an SDCS with the property of mean-square exp-ISS are obtained without involving control Lyapunov functions or functional.Under the global Lipschitz coefficients and mean-square continuous measurable inputs,it is proved that the mean-square exp-ISS of an SDCS holds if and only if that of the EM method is preserved for a sufficiently small step size.The proposed results are evaluated by using numerical experiments to show their effectiveness.展开更多
The global asymptotical stability for a class of stochastic delayed neural networks （SDNNs） with Maxkovian jumping parameters is considered. By applying Lyapunov functional method and Ito＇s differential rule, new d...The global asymptotical stability for a class of stochastic delayed neural networks （SDNNs） with Maxkovian jumping parameters is considered. By applying Lyapunov functional method and Ito＇s differential rule, new delay-dependent stability conditions are derived. All results are expressed in terms of linear matrix inequality （LMI）, and a numerical example is presented to illustrate the correctness and less conservativeness of the proposed method.展开更多
The problem of delay-dependent exponential stability is investigated for impulsive stochastic systems with time-varying delay. Although the exponential stability of impulsive stochastic delay systems has been discusse...The problem of delay-dependent exponential stability is investigated for impulsive stochastic systems with time-varying delay. Although the exponential stability of impulsive stochastic delay systems has been discussed by several authors, few works have been done on delay-dependent exponential stability of impulsive stochastic delay systems. Firstly, the Lyapunov-Krasovskii functional method combing the free-weighting matrix approach is applied to investigate this problem. Some delay-dependent mean square exponential stability criteria are derived in terms of linear matrix inequalities. In particular, the estimate of the exponential convergence rate is also provided, which depends on system parameters and impulsive effects. The obtained results show that the system will stable if the impulses＇ frequency and amplitude are suitably related to the increase or decrease of the continuous flows, and impulses may be used as controllers to stabilize the underlying stochastic system. Numerical examples are given to show the effectiveness of the results.展开更多
A type of stochastic interval delayed Hopfield neural networks as du(t) = [-AIu(t) + WIf(t,u(t)) + WIτf7τ(uτ(t)] dt +σ(t, u(t), uτ(t)) dw(t) on t≥0 with initiated value u(s) = ζ(s) on - τ≤s≤0 has been studie...A type of stochastic interval delayed Hopfield neural networks as du(t) = [-AIu(t) + WIf(t,u(t)) + WIτf7τ(uτ(t)] dt +σ(t, u(t), uτ(t)) dw(t) on t≥0 with initiated value u(s) = ζ(s) on - τ≤s≤0 has been studied. By using the Razumikhin theorem and Lyapunov functions, some sufficient conditions of their globally asymptotic robust stability and global exponential stability on such systems have been given. All the results obtained are generalizations of some recent ones reported in the literature for uncertain neural networks with constant delays or their certain cases.展开更多
The notions of practical φ0-stability were introduced for stochastic differential equations. Sufficient conditions on such practical properties were obtained by using the comparison principle and the cone-valued Lyap...The notions of practical φ0-stability were introduced for stochastic differential equations. Sufficient conditions on such practical properties were obtained by using the comparison principle and the cone-valued Lyapunov function methods. Based on an extended comparison theorem, a perturbation theory of stochastic differential systems was given.展开更多
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
The problems of robust exponential stability in mean square and delayed state feedback stabilization for uncertain stochastic systems with time-varying delay are studied. By using Jensen＇s integral inequality and com...The problems of robust exponential stability in mean square and delayed state feedback stabilization for uncertain stochastic systems with time-varying delay are studied. By using Jensen＇s integral inequality and combining with the free weighting matrix approach, new delay-dependent stability conditions and delayed state feedback stabilization criteria are obtained in terms of linear matrix inequalities. Meanwhile, the proposed delayed state feedback stabilization criteria are more convenient in application than the existing ones since fewer tuning parameters are involved. Numerical examples are given to illustrate the effectiveness of the proposed methods.展开更多
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
In this paper, stochastic stabilization is investigated by max-plus algebra for a Markovian jump cloud control system with a reference signal. For the Markovian jump cloud control system, there exists framework adjust...In this paper, stochastic stabilization is investigated by max-plus algebra for a Markovian jump cloud control system with a reference signal. For the Markovian jump cloud control system, there exists framework adjustment whose evolution is satisfied with a Markov chain. Using max-plus algebra, a maxplus stochastic system is used to describe the Markovian jump cloud control system. A causal feedback matrix is obtained by exponential stability analysis for a causal feedback controller of the Markovian jump cloud control system. A sufficient condition is given to ensure existence on the causal feedback matrix of the causal feedback controller. Based on the causal feedback controller, stochastic stabilization in probability is analyzed for the Markovian jump cloud control system with a reference signal.Simulation results are given to show effectiveness of the causal feedback controller for the Markovian jump cloud control system.展开更多
In this paper, the problem of state feedback stabilization for stochastic feedforward nonlinear systems with input time-delay is considered for the first time. By introducing a variable transformation, skillfully comb...In this paper, the problem of state feedback stabilization for stochastic feedforward nonlinear systems with input time-delay is considered for the first time. By introducing a variable transformation, skillfully combining the homogeneous domination method, and constructing an appropriate LyapunovKrasovskii functional, a state feedback controller is developed to guarantee the closed-loop system globally asymptotically stable in probability.展开更多
The traditional voltage stability analysis method is mostly based on the deterministic mode1.and ignores the uncertainties of bus loads,power supplies,changes in network configuration and so on.However,the great expan...The traditional voltage stability analysis method is mostly based on the deterministic mode1.and ignores the uncertainties of bus loads,power supplies,changes in network configuration and so on.However,the great expansion of renewable power generations such as wind and solar energy in a power system has increased their uncertainty,and仃aditional techniques are limited in capturing their variable behavior.This leads to greater needs of new techniques and methodologies to properly quan tify the voltage stability of power systems.展开更多
The stochastic convergence of the cubature Kalmanfilter with intermittent observations （CKFI） for general nonlinearstochastic systems is investigated. The Bernoulli distributed ran-dom variable is employed to descri...The stochastic convergence of the cubature Kalmanfilter with intermittent observations （CKFI） for general nonlinearstochastic systems is investigated. The Bernoulli distributed ran-dom variable is employed to describe the phenomenon of intermit-tent observations. According to the cubature sample principle, theestimation error and the error covariance matrix （ECM） of CKFIare derived by Taylor series expansion, respectively. Afterwards, itis theoretically proved that the ECM will be bounded if the obser-vation arrival probability exceeds a critical minimum observationarrival probability. Meanwhile, under proper assumption corre-sponding with real engineering situations, the stochastic stabilityof the estimation error can be guaranteed when the initial estima-tion error and the stochastic noise terms are sufficiently small. Thetheoretical conclusions are verified by numerical simulations fortwo illustrative examples; also by evaluating the tracking perfor-mance of the optical-electric target tracking system implementedby CKFI and unscented Kalman filter with intermittent observa-tions （UKFI） separately, it is demonstrated that the proposed CKFIslightly outperforms the UKFI with respect to tracking accuracy aswell as real time performance.展开更多
To study the design problem of robust reliable guaranteed cost controller for nonlinear singular stochastic systems, the Takagi-Sugeno （T-S） fuzzy model is used to represent a nonlinear singular stochastic system wi...To study the design problem of robust reliable guaranteed cost controller for nonlinear singular stochastic systems, the Takagi-Sugeno （T-S） fuzzy model is used to represent a nonlinear singular stochastic system with norm-bounded parameter uncertainties and time delay. Based on the linear matrix inequality （LMI） techniques and stability theory of stochastic differential equations, a stochastic Lyapunov function method is adopted to design a state feedback fuzzy controller. The resulting closed-loop fuzzy system is robustly reliable stochastically stable, and the corresponding quadratic cost function is guaranteed to be no more than a certain upper bound for all admissible uncertainties, as well as different actuator fault cases. A sufficient condition of existence and design method of robust reliable guaranteed cost controller is presented. Finally, a numerical simulation is given to illustrate the effectiveness of the proposed method.展开更多
The asymptotic and stable properties of general stochastic functional differential equations are investigated by the multiple Lyapunov function method, which admits non-negative up-per bounds for the stochastic deriva...The asymptotic and stable properties of general stochastic functional differential equations are investigated by the multiple Lyapunov function method, which admits non-negative up-per bounds for the stochastic derivatives of the Lyapunov functions, a theorem for asymptotic properties of the LaSal e-type described by limit sets of the solutions of the equations is obtained. Based on the asymptotic properties to the limit set, a theorem of asymptotic stability of the stochastic functional differential equations is also established, which enables us to construct the Lyapunov functions more easily in application. Particularly, the wel-known classical theorem on stochastic stability is a special case of our result, the operator LV is not required to be negative which is more general to fulfil and the stochastic perturbation plays an important role in it. These show clearly the improvement of the traditional method to find the Lyapunov functions. A numerical simulation example is given to il ustrate the usage of the method.展开更多
基金supported by the National Natural Science Foundation of China(6127312660904032)the Natural Science Foundation of Guangdong Province(10251064101000008)
文摘This paper develops the mean-square exponential input-to-state stability（exp-ISS） of the Euler-Maruyama（EM） method for stochastic delay control systems（SDCSs）.The definition of mean-square exp-ISS of numerical methods is established.The conditions of the exact and EM method for an SDCS with the property of mean-square exp-ISS are obtained without involving control Lyapunov functions or functional.Under the global Lipschitz coefficients and mean-square continuous measurable inputs,it is proved that the mean-square exp-ISS of an SDCS holds if and only if that of the EM method is preserved for a sufficiently small step size.The proposed results are evaluated by using numerical experiments to show their effectiveness.
基金Supported by National Natural Science Foundation of China(10571036)the Key Discipline Development Program of Beijing Municipal Commission (XK100080537)
基金supported by the National Natural Science Foundation of China(60874114).
文摘The global asymptotical stability for a class of stochastic delayed neural networks （SDNNs） with Maxkovian jumping parameters is considered. By applying Lyapunov functional method and Ito＇s differential rule, new delay-dependent stability conditions are derived. All results are expressed in terms of linear matrix inequality （LMI）, and a numerical example is presented to illustrate the correctness and less conservativeness of the proposed method.
基金Supported by National Natural Science Foundation of China （60425310, 60574014）, the Doctor Subject Foundation of China （20050533015, 200805330004）, the Program for New Century Excellent Talents in University （NCET-06-0679）, and the Natural Science Foundation of Hunan Province （08JJ1010）
基金supported by the National Natural Science Foundation of China (60874114)the Fundamental Research Funds for the Central Universities, South China University of Technology (SCUT)(2009ZM0140)
文摘The problem of delay-dependent exponential stability is investigated for impulsive stochastic systems with time-varying delay. Although the exponential stability of impulsive stochastic delay systems has been discussed by several authors, few works have been done on delay-dependent exponential stability of impulsive stochastic delay systems. Firstly, the Lyapunov-Krasovskii functional method combing the free-weighting matrix approach is applied to investigate this problem. Some delay-dependent mean square exponential stability criteria are derived in terms of linear matrix inequalities. In particular, the estimate of the exponential convergence rate is also provided, which depends on system parameters and impulsive effects. The obtained results show that the system will stable if the impulses＇ frequency and amplitude are suitably related to the increase or decrease of the continuous flows, and impulses may be used as controllers to stabilize the underlying stochastic system. Numerical examples are given to show the effectiveness of the results.
基金This project was supported by the National Natural Science Foundation of China (60074008, 60274007, 60274026) National Doctor foundaction of China (20010487005).
文摘A type of stochastic interval delayed Hopfield neural networks as du(t) = [-AIu(t) + WIf(t,u(t)) + WIτf7τ(uτ(t)] dt +σ(t, u(t), uτ(t)) dw(t) on t≥0 with initiated value u(s) = ζ(s) on - τ≤s≤0 has been studied. By using the Razumikhin theorem and Lyapunov functions, some sufficient conditions of their globally asymptotic robust stability and global exponential stability on such systems have been given. All the results obtained are generalizations of some recent ones reported in the literature for uncertain neural networks with constant delays or their certain cases.
基金Project (60704007) supported by the National Natural Science Foundation of China
文摘The notions of practical φ0-stability were introduced for stochastic differential equations. Sufficient conditions on such practical properties were obtained by using the comparison principle and the cone-valued Lyapunov function methods. Based on an extended comparison theorem, a perturbation theory of stochastic differential systems was given.
基金This project was supported by the National Natural Science Foundation of China (No. 69874015) and Natural Science Foundation of
文摘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.
基金Supported by National Natural Science Foundation of China （60774010）, Program for New Century Excellent Talents in University of China （NCET-05-0607）, Program for Summit of Six Types of Talents of Jiangsu Province （07-A-020）, and Program for Fundamental Research of Natural Sciences in Universities of Jiangsu Province （07KJB510114）
文摘适应州反馈的稳定为在的高顺序的随机的非线性的系统的一个类被调查函数 fi 的上面的界限(?? 铄吗？？
基金Supported by National Natural Science Foundation of China（60774010 10971256） Natural Science Foundation of Jiangsu Province（BK2009083）+1 种基金 Program for Fundamental Research of Natural Sciences in Universities of Jiangsu Province（07KJB510114） Shandong Provincial Natural Science Foundation of China（ZR2009GM008 ZR2009AL014）
基金supported by the National Natural Science Foundation of China(10971232)the Natural Science Foundation of Guangdong Province(101510090010000398351009001000002)
文摘The problems of robust exponential stability in mean square and delayed state feedback stabilization for uncertain stochastic systems with time-varying delay are studied. By using Jensen＇s integral inequality and combining with the free weighting matrix approach, new delay-dependent stability conditions and delayed state feedback stabilization criteria are obtained in terms of linear matrix inequalities. Meanwhile, the proposed delayed state feedback stabilization criteria are more convenient in application than the existing ones since fewer tuning parameters are involved. Numerical examples are given to illustrate the effectiveness of the proposed methods.
基金supported by the National Natural Science Fundation of China (6080402160974139+3 种基金61075117)the Fundamental Research Funds for the Central Universities (JY10000970001K5051070000272103676)
文摘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.
基金supported by the National Natural Science Foundation of China (61973230)Tianjin Research Innovation Project for Postgraduate Students (2021YJSO2S03)。
文摘In this paper, stochastic stabilization is investigated by max-plus algebra for a Markovian jump cloud control system with a reference signal. For the Markovian jump cloud control system, there exists framework adjustment whose evolution is satisfied with a Markov chain. Using max-plus algebra, a maxplus stochastic system is used to describe the Markovian jump cloud control system. A causal feedback matrix is obtained by exponential stability analysis for a causal feedback controller of the Markovian jump cloud control system. A sufficient condition is given to ensure existence on the causal feedback matrix of the causal feedback controller. Based on the causal feedback controller, stochastic stabilization in probability is analyzed for the Markovian jump cloud control system with a reference signal.Simulation results are given to show effectiveness of the causal feedback controller for the Markovian jump cloud control system.
基金Supported by National Natural Science Foundation of China(61273125,61473171)Program for the Scientific Research Innovation Team in Colleges and Universities of Shandong ProvinceShandong Provincial Natural Science Foundation(ZR2012FM018)
文摘In this paper, the problem of state feedback stabilization for stochastic feedforward nonlinear systems with input time-delay is considered for the first time. By introducing a variable transformation, skillfully combining the homogeneous domination method, and constructing an appropriate LyapunovKrasovskii functional, a state feedback controller is developed to guarantee the closed-loop system globally asymptotically stable in probability.
文摘The traditional voltage stability analysis method is mostly based on the deterministic mode1.and ignores the uncertainties of bus loads,power supplies,changes in network configuration and so on.However,the great expansion of renewable power generations such as wind and solar energy in a power system has increased their uncertainty,and仃aditional techniques are limited in capturing their variable behavior.This leads to greater needs of new techniques and methodologies to properly quan tify the voltage stability of power systems.
基金supported by the National Natural Science Foundation of China(6110418661273076)
文摘The stochastic convergence of the cubature Kalmanfilter with intermittent observations （CKFI） for general nonlinearstochastic systems is investigated. The Bernoulli distributed ran-dom variable is employed to describe the phenomenon of intermit-tent observations. According to the cubature sample principle, theestimation error and the error covariance matrix （ECM） of CKFIare derived by Taylor series expansion, respectively. Afterwards, itis theoretically proved that the ECM will be bounded if the obser-vation arrival probability exceeds a critical minimum observationarrival probability. Meanwhile, under proper assumption corre-sponding with real engineering situations, the stochastic stabilityof the estimation error can be guaranteed when the initial estima-tion error and the stochastic noise terms are sufficiently small. Thetheoretical conclusions are verified by numerical simulations fortwo illustrative examples; also by evaluating the tracking perfor-mance of the optical-electric target tracking system implementedby CKFI and unscented Kalman filter with intermittent observa-tions （UKFI） separately, it is demonstrated that the proposed CKFIslightly outperforms the UKFI with respect to tracking accuracy aswell as real time performance.
基金the National Natural Science Foundation of China (60574088,60274014).
文摘To study the design problem of robust reliable guaranteed cost controller for nonlinear singular stochastic systems, the Takagi-Sugeno （T-S） fuzzy model is used to represent a nonlinear singular stochastic system with norm-bounded parameter uncertainties and time delay. Based on the linear matrix inequality （LMI） techniques and stability theory of stochastic differential equations, a stochastic Lyapunov function method is adopted to design a state feedback fuzzy controller. The resulting closed-loop fuzzy system is robustly reliable stochastically stable, and the corresponding quadratic cost function is guaranteed to be no more than a certain upper bound for all admissible uncertainties, as well as different actuator fault cases. A sufficient condition of existence and design method of robust reliable guaranteed cost controller is presented. Finally, a numerical simulation is given to illustrate the effectiveness of the proposed method.
基金Supported by National Natural Science Foundation of China （60704007 60774038） the Key Scientific and Technological Project of Anhui Province （08010202038） the Science and Technological Fund of Anhui Province for Outstanding Youth
基金supported by the National Natural Science Foundation of China(61273126)the Natural Science Foundation of Guangdong Province(10251064101000008+1 种基金S201210009675)the Fundamental Research Funds for the Central Universities(2012ZM0059)
文摘The asymptotic and stable properties of general stochastic functional differential equations are investigated by the multiple Lyapunov function method, which admits non-negative up-per bounds for the stochastic derivatives of the Lyapunov functions, a theorem for asymptotic properties of the LaSal e-type described by limit sets of the solutions of the equations is obtained. Based on the asymptotic properties to the limit set, a theorem of asymptotic stability of the stochastic functional differential equations is also established, which enables us to construct the Lyapunov functions more easily in application. Particularly, the wel-known classical theorem on stochastic stability is a special case of our result, the operator LV is not required to be negative which is more general to fulfil and the stochastic perturbation plays an important role in it. These show clearly the improvement of the traditional method to find the Lyapunov functions. A numerical simulation example is given to il ustrate the usage of the method.
