一类非线性离散广义马尔可夫跳跃系统的静态输出反馈镇定

Static output feedback stabilization for a class of nonlinear discrete-time descriptor M arkov jump systems

讨论了一类非线性离散广义马尔可夫跳跃系统的静态输出反馈镇定问题。非线性函数满足二次受限条件。首先给出了保证非线性离散广义马尔可夫跳跃系统正则、因果,在原点的邻域内有惟一解,且随机稳定的一个线性矩阵不等式(linear matrix inequality,LMI)充分条件。然后利用奇异值分解方法,给出了静态输出反馈控制器的设计方法。最后用一个数值算例验证了本文方法的有效性。

The static output feedback stabilization problem for a class of nonlinear discrete-time descriptor Markov jump systems is investigated. The nonlinear function satisfies a quadratic constraint. First, a linear matrix inequality （LMI） sufficient condition is given which guarantees that the nonlinear discrete-time descriptor Markov jump systems are regu- lar, causal, have unique solution in a neighborhood of the origin, and are stochastically stable. Then, based on singular value decomposition approach, the design method of static output feedback controllers is given. Last, a numerical ex- ample is provided to illustrate the effectiveness of the proposed method.