参数摄动混杂离散系统的鲁棒稳定性

Robust stability of hybrid discrete systems with parameter perturbation

采用线性矩阵不等式 (LMI)方法研究离散事件状态转移条件为状态依赖的参数摄动线性混杂离散系统的鲁棒稳定性问题 ,提出此类系统全局鲁棒渐近稳定性判定定理 ,基于分段Lyapunov函数给出了一般混杂离散系统在Lyapunov意义下局部稳定的判定定理 ,该定理可将线性混杂离散系统的稳定性问题转化为LMI问题 ,在此基础上提出了参数摄动线性混杂离散系统在Lyapunov意义下局部鲁棒稳定的充分条件 .

With the linear matrix inequality (LMI) method, this paper investigates the robust stability of general linear hybrid discrete systems with parameter perturbation. The sufficient conditions for global robust asymptotic stability are proposed. Based on the multiple Lyapunov functions, the sufficient conditions are presented for local Lyapunov stability of general hybrid discrete systems. By applying the result, the stability problems of the linear hybrid discrete systems can be formulated as the LMI problems. Furthermore, the sufficient conditions are derived for local robust Lyapunov stability of the linear hybrid discrete systems with parameter perturbation.