线性切换系统二次稳定性分析与设计

Analysis and design of quadratic stability for switched linear systems

基于区间矩阵的等价表示方法,把线性切换系统转化为区间系统,利用矩阵不等式得到了在任意的切换策略下线性切换系统二次稳定性的充分条件,给出了控制器的实现算法。这个条件等价于共同二次正定Lyapunov函数判定条件,但共同二次正定Lyapunov函数判定条件需要求解若干个矩阵不等式,当子系统较多时计算量是相当大的,而这个条件只需找到一个Riccati不等式的的正定解就可以判定该系统的二次稳定性,大大降低计算工作量。用数值例子对所得结果加以验证,说明了文中结果的正确性。

Based on the equivalent representation of interval matrices, the switched linear system is converted into the interval system. Using matrix inequality the sufficient condition is established for quadratic stability of switched linear systems under arbitrary switching laws, then, the controller design procedure is presented. This condition is equivalent to common Lyapunov function with quadratic positive-definite for all subsystems, But common Lyapunov function with quadratic positive-definite are required to solve a number of matrix inequality, the computation is quite complex when there are a great many subsystems. And yet this condition only requires to solve a Riccati inequality to determinant quadratic stability of switched linear systems. Finally, a numerical example is given to illustrate the effectiveness of the theoretical results.