一类广义混杂系统的随机稳定性及稳定化

针对切换序列为齐次有限状态Markov链的离散广义混杂系统，采用多Lyapunov函数和随机广义Lyapunov函数相结合的方法，无需对广义系统作受限等价变换，得到了系统随机稳定的充要条件，该条件以耦合广义Lyapunov方程(Coupled Generalized Lyapunov Equation，缩写CGLEs)的形式给出，可化为严格线性矩阵不等式(SLMIs)来进行求解．然后，进一步对系统的稳定化问题进行了分析与设计，给出了状态反馈增益矩阵的求解方法．最后的数值算例说明了该方法的有效性．

Stochastic stability and stabilization for a class of singular hybrid systems

Based on the method combining the techniques of the multiple Lyapunov function and stochastic generalized Lyapunov function, a necessary and sufficient condition is derived for discrete-time singular hybrid systems with the time-homogenous finite state Markov chain without using the restricted equivalent property of singular systems. The condition is given in terms of coupled generalized Lyapunov equations (CGLEs) such that the solution of the systems is stochastically stable. The equations can be solved by changing them into strict linear matrix inequalities (SLMIs). The result is extended to solve the stabilization problem and the design of a state-feedback controller. A numerical example shows the effectiveness of the proposed approach.