Abstract In this paper, we propose an iterative approach for estimating the domains of attraction for a class of discrete-time switched systems, where the state space is divided into several disjoint regions and each region is described by polynomial inequalities. At first, we introduce the basic concepts of Multi-step state subsequence, Multi-step state subspace, Multi-step basin of attraction and Multi-step multiple Lyapunov-like function. Secondly, beginning with an initial inner estimation, a theoretical framework is proposed for estimating the domain of attraction by iteratively calculating the Multi-step multiple Lyapunov-like functions. Thirdly, notice that the Multi-step state subspaces may be empty sets such that the corresponding constraints in the theoretical framework are redundant, we propose a numerical approach based on the homotopy continuation method to pre-check the non-emptiness of the Multi-step state subspaces, and then under-approximatively realize the framework by using S-procedure and sum of squares programming. At last, we implement our iterative approach and apply it to three discrete-time switched system examples with comparisons to existing methods in the literatures. These computation and comparison results show the advantages of our method.

中文翻译：

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基于多步多类李雅普诺夫函数的离散时间切换系统的内逼近吸引力域

摘要 在本文中，我们提出了一种用于估计一类离散时间切换系统的吸引力域的迭代方法，其中状态空间被划分为几个不相交的区域，每个区域由多项式不等式描述。首先介绍多步状态子序列、多步状态子空间、多步引力盆和多步多类李雅普诺夫函数的基本概念。其次，从初始内部估计开始，提出了通过迭代计算多步多类李雅普诺夫函数来估计吸引力域的理论框架。第三，注意多步状态子空间可能是空集，使得理论框架中的相应约束是多余的，我们提出了一种基于同伦延拓法的数值方法来预检查多步状态子空间的非空性，然后通过使用 S 过程和平方和编程来近似地实现框架。最后，我们实现了我们的迭代方法，并将其应用于三个离散时间切换系统示例，并与文献中的现有方法进行比较。这些计算和比较结果显示了我们方法的优点。