This work researches the problem of searching for multiple homogeneous polynomial Lyapunov functions (HPLFs) for heterogeneous switched linear systems. First, a nonconvex optimization condition is constructed to study the stability property of heterogeneous switched systems, where each Lyapunov function candidate reduces dimension to their corresponding matrix eigenvalue. Based on the stability analysis condition, a controller-dependently multiple HPLFs condition is introduced to determine controllers and explores locally minimum mode-dependent average dwell time (LMMDADT). Additionally, the existing properties condition and solvable properties condition of controllers are given in the form of HPLFs. At last, a practical example and a contrast example are both presented to show feasibility of the proposed results.

中文翻译：

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通过齐次多项式 Lyapunov 函数方法的具有模式相关平均停留时间的异构切换系统的稳定性和稳定性

这项工作研究了为异构切换线性系统搜索多个齐次多项式 Lyapunov 函数 (HPLF) 的问题。首先，构造一个非凸优化条件来研究异构切换系统的稳定性特性，其中每个Lyapunov函数候选将维数降低到其对应的矩阵特征值。在稳定性分析条件的基础上，引入了控制器依赖的多重HPLFs条件来确定控制器，并探索了局部最小模式依赖的平均停留时间（LMMDADT）。此外，控制器的现有属性条件和可解属性条件以 HPLF 的形式给出。最后，给出了一个实例和一个对比实例，说明了所提结果的可行性。