区间矩阵的稳定性

来源期刊：中南大学学报(自然科学版)2003年第5期

论文作者：张先明 吴敏 何勇

文章页码：590 - 592

关键词：区间矩阵;稳定性;Riccati不等式;H_∞范数

Key words：interval matrices; stability; Riccati inequality; H-infinite norm

摘    要：利用Lyapunov方法及Riccati不等式方法讨论了区间矩阵[A^m,A^M]的稳定性.首先将区间矩阵的稳定性问题等价地转化为一个代数Riccati不等式A^T₀P+PA₀+PEE^TP+F^TF<0正定解的存在性问题,然后利用H_∞范数理论,获得了区间矩阵稳定的充要条件为A₀稳定且‖F(sI-A₀)^-1E‖_∞<1.

Abstract: This paper discusses the stability of interval matrices [A^m,A^M]by the Lyapunov and Riccati inequality methods. First, the problem of interval matrices stability is converted into a solvable problem of a Riccati inequality, i.e A^T₀P+PA₀+PEE^TP+F^TF<0. Then, by using theH-infinity norm theory, the necessary and sufficient condition of the stability of interval matrices is obtained which is A₀ stable and ‖F(sI-A₀)^-1E‖_∞<1.At last, four examples are given as the application of the results.