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Stabilization of constrained switched systems via multiple Lyapunov R-functions
Systems & Control Letters ( IF 2.6 ) Pub Date : 2020-05-01 , DOI: 10.1016/j.sysconle.2020.104686
Feiyue Wu , Jie Lian

Abstract This paper investigates the stabilization problem of switched linear systems subject to state constraints, input saturation and external disturbance. Within the set-theoretic framework of R-function, the multiple Lyapunov R-functions (MLRFs) are presented, and merge both the multiple polyhedral and the multiple quadratic Lyapunov functions. The advantages of the MLRFs are that the external level sets are designed in accordance to the state constraints and inner level sets arbitrary can be made as close as possible to the smooth one. Based on the MLRFs method, stabilization conditions for the constrained switched system under a gradient-based switching law are derived. The union of the invariant truncated ellipsoidal sets is provided as an alternative approximation to the domain of attraction of the constrained switched system. Each truncated ellipsoidal set is the intersection of a polyhedral set and an ellipsoidal set, which come from the polyhedral Lyapunov function and the quadratic Lyapunov function, respectively. The sub-optimality bounds are investigated by a policy iteration. Two examples are simulated to show the benefits of the proposed strategy.

中文翻译:

通过多个李雅普诺夫 R 函数稳定约束切换系统

摘要 本文研究了受状态约束、输入饱和和外部干扰影响的切换线性系统的镇定问题。在 R 函数的集合论框架内,提出了多个李雅普诺夫 R 函数 (MLRF),并合并了多个多面体和多个二次李雅普诺夫函数。MLRFs 的优点是外部水平集是根据状态约束设计的,并且可以使任意的内部水平集尽可能接近平滑的水平集。基于MLRFs方法,推导了基于梯度的切换律下约束切换系统的稳定条件。不变截断椭球集合的并集作为约束切换系统的吸引力域的替代近似提供。每个截断椭球集是多面体集和椭球集的交集,分别来自多面体李雅普诺夫函数和二次李雅普诺夫函数。通过策略迭代研究次优边界。模拟了两个示例以显示所提出策略的好处。
更新日期:2020-05-01
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