伊藤随机马尔可夫跳变奇异系统控制设计

Control design for Ιtô stochastic Markovian jump singular systems

研究一类具有时变转移率的连续时间伊藤随机马尔可夫跳变奇异系统的随机容许性及H性能,并设计了一种静态输出反馈控制器。首先,运用随机李雅普诺夫函数和矩阵分解技术建立闭环系统正则、无脉冲、随机稳定及具有H性能的充分条件;其次,运用Finsler引理将非线性矩阵不等式条件转化为线性形式,得到新的保守性较小的充分条件,并设计一种使闭环系统满足H性能的静态输出反馈控制器;最后,通过数值算例验证了所提方法的有效性。

This paper is concerned with the problems of stochastic admissibility and H∞ performance as well as static output feedback controller design for a class of continuous-time Ιtô stochastic Markovian jump singular systems with time-varying transition rates. Firstly, a sufficient condition of stochastic admissibility and H∞ performance of the systems under consideration is established in terms of the stochastic Lyapunov function and matrix decoupling method. In light of Finsler lemma, the nonlinear matrix inequality condition is decoupled and a new sufficient condition in linear form is obtained with less conservative. Thus, the static output feedback controller is developed to guarantee the closed-loop system satisfying stochastic admissibility and H∞ performance. Finally, a practical example is provided to illustrate the effectiveness of the proposed method.