多胞型线性切换系统二次稳定的充要条件

A Necessary and Sufficient Condition of the Quadratic Stability for Switched Linear Systems with Polytopic Perturbations

研究了多胞型线性切换系统在任意切换下的二次稳定性问题.首先构造区间矩阵,把多胞型线性切换系统转化为区间系统,利用Riccati不等式给出了在任意切换策略下多胞型线性切换系统二次稳定性的充要条件.这个条件等价于共同二次正定Lyapunov函数判定条件,而且该条件只需找到一组LMI的解就可以判定该系统的二次稳定性,大大降低计算工作量.最后用数值例子对所得结果加以验证,说明了结果的正确性.

The quadratic stability problem of switched linear systems with polytopic perturbations under arbitrary switching laws is presented. First, To construct the interval matrix, switched linear system with polytopic perturbations is translated into interval system. Using Riccati inequality a necessary and sufficient condition for quadratic stability of switched linear systems with polytopic perturbations under arbitrary switching laws is established. This condition is equivalent to common Lyapunov function with quadratic positive-definite for all subsystems. And this condition,only by finding a set of solutions to the LMI, can determine the quadratic stability of switched linear systems. Finally, a numerical example is given to illustrate the effectiveness of the results.