切换系统的鲁棒二次公共Lyapunov函数矩阵寻找算法

摘要

To obtain a searching algorithm for the common quadratic Lyapunov function (CQLF) of an uncertain switched system (SS), the concept of the common robust quadratic Lyapunov function (CRQLF) is proposed. In addi-tion, sufficient conditions for the CRQLF, and its corresponding recurrence search algorithm method in LMI forms, are obtained using a matrix inequality analysis when the stable matrix set is both involuntary and voluntary. These results enable easy computer implementation, and are valuable for making robust stability judgments of uncertain SSs. Further-more, the application simulation test certificates their validity.%为了获得不确定线性切换系统稳定性判别的公共二次Lyapunov函数寻找方法,提出了鲁棒公共二次Lya-punov函数的概念,运用矩阵不等式分析,得到了在鲁棒稳定矩阵集对合和不对合的情况下,鲁棒公共二次Lyapun-ov函数存在的充分性条件以及LMI形式的递推搜寻算法.获得的结果便于计算机实现,对不确定切换系统鲁棒稳定性判别具有一定价值.应用仿真测试验证了其正确性.