关键词: 时滞系统, 线性矩阵不等式, Lyapunov-Krasovskii 泛函, 时滞依赖, 保性能控制率, 最优控制, Schur 补引理

Abstract:

In order to maintain robust stability while meeting certain performance index requirements, the problem of guaranteed cost control for time-varyiong time delay singularly perturbed systems with norm bounded uncertainty parameters is discussed. Using Lyapunov stability theory and matrix analysis method, based on a new quadratic L-Y performance index, the sufficient quadratic stability conditions, state feedback guaranteed cost control rate and the guaranteed cost index is presented by showed LMIs, and the minimum performance indication upper bound is derived. The method of the dissertation can be extended to multi-state delay uncertain systems guaranteed cost control problems, the numerical examples are employed to elaborate that this method is effective.

Key words: time-delay system, linear matrix inequality ( LMI), Lyapunov-Kasovskii functional, delay-dependent, guaranteed cost control law, optimal control, Schur complement Lemma