摘要
研究了系统矩阵、时滞矩阵和输入矩阵均含有不确定性的多时滞区间矩阵系统的 Ｈ∞鲁棒控制问题。文中首先针对时滞系统ｘ（ｔ）＝ Ａｘ（ｔ）＋ Δ Ａｘ （ｔ－ τ）在 Ａ 稳定条件下，运用根轨迹法，导出时滞系统稳定的条件；接着运用该条件及 Ｈ∞控制方法和实对称矩阵集合最小上界定理，设计了多时滞区间矩阵系统的 Ｈ∞鲁棒控制器。该设计方法把确定多个矩阵不等式共同解的复杂问题简化为求解单子代数 Ｒｉｃｃａｔｉ矩阵方程，所得多时滞区间矩阵系统的 Ｈ∞控制律，对于所有允许的不确定性，可使闭环系统稳定，且使系统从扰动输入到控制输出的传递函数具有 Ｈ∞范数界。文中算例表明了该方法的有效性。
The problem of H ∞ robust control for multiple time delay systems with system matrix, time delay matrix and input matrix being interval is studied. First supposing that A is stable, the stability condition of the time delay system (t)=Ax(t)+ Δ Ax(t-τ) is obtained by using the method of root locus. Then based on the stability condition, H ∞ control theory and the method for determining the minimum upper bound of the real symmetric matrix set, a design method of robust controller for interval matrix systems with multiple time delay is presented. In this method, the complex problem for determining the solution of matrix inequalities is simplified to solving single algebraic Riccati equation. The H ∞ linear feedback control law obtained not only stabilizes the closed loop system but also makes the H ∞ norm of the system transfer function from the disturbance inputs to control outputs below a given bound over all admissible uncertainties. An illustrative example is given to demonstrate the effectiveness of the design method.
出处
《南京航空航天大学学报》
EI
CAS
CSCD
北大核心
1999年第4期373-380,共8页
Journal of Nanjing University of Aeronautics & Astronautics
基金
国家自然科学基金
关键词
鲁棒控制
时滞系统
区间矩阵系统
H^∞控制
stability
robust control
time delay systems
interval matrix systems
minimum upper bound
H ∞ control
