In this contribution we show that under some circumstances the Kalman–Yakubovich–Popov (KYP) lemma can be applied for testing quadratic stability of multi-mode switched linear systems. Based on this observation, we introduce several constructive algorithms which enable us to associate a transfer function matrix to a switched linear system given in general form. The strict positive realness test of the resulting transfer function matrix can be easily achieved by available known algebraic conditions. By means of some examples we illustrate the step-by-step implementation of these algorithms.

中文翻译：

---

基于SPR的多模式开关线性系统二次稳定性的设计条件

在本文中，我们证明了在某些情况下，卡尔曼-雅库波维奇-波波夫（KYP）引理可用于测试多模开关线性系统的二次稳定性。基于这种观察，我们介绍了几种构造算法，这些算法使我们能够将传递函数矩阵与以一般形式给出的开关线性系统相关联。通过可用的已知代数条件，可以轻松实现对所得传递函数矩阵的严格正实性测试。通过一些示例，我们说明了这些算法的分步实现。