An extension of LaSalle's invariance principle for switched systems

非自治切换系统中的不变性结果

Invariance-like results for Nonautonomous Switched Systems

本文将Lasalle-Yoshizawa定理推广到非光滑切换系统中，通过分析Filippov和Krasovskii正则化，证明了切换系统的正则化包含在子系统的正则化凸包中，并展示了具有负半定导数的候选Lyapunov函数如何用于建立切换系统的LaSalle-Yoshizawa结果。

LaSalle不变性原理在离散时间动力系统中的应用：一份简洁且自包含的教程

LaSalle Invariance Principle for Discrete-time Dynamical Systems: A Concise and Self-contained Tutorial

本文研究问题是如何在离散时间动力系统中应用LaSalle不变性原理；核心方法是自包含地整理了相关概念、引理和定理；主要贡献是提供了LaSalle不变性原理在离散时间系统中的证明和扩展。

由极大单调算子控制的微分包含的定位定理

Locating Theorems of Differential Inclusions Governed by Maximally Monotone Operators

针对极大单调算子控制的微分包含的渐近行为研究中LaSalle不变性原理失效的问题，提出改进版不变性原理与扩展方法，借助非光滑Lyapunov对型函数实现ω-极限集的更精确定位。

Uniform asymptotic stability of switched nonlinear time-varying systems and detectability of reduced limiting control systems

This paper is concerned with the study of both, local and global, uniform asymptotic stability for switched nonlinear time-varying (NLTV) systems through the detectability of output-maps. With this aim the notion of reduced limiting control systems for switched NLTV systems whose switchings verify time/state dependent constraints, and the concept of weakly zero-state detectability for those reduced limiting systems are introduced. Necessary and sufficient conditions for the (global)uniform asymptotic stability of families of trajectories of the switched system are obtained in terms of this det…

Invariance principles for switched systems with restrictions

In this paper we consider switched nonlinear systems under average dwell time switching signals, with an otherwise arbitrary compact index set and with additional constraints in the switchings. We present invariance principles for these systems and derive by using observability-like notions some convergence and asymptotic stability criteria. These results enable us to analyze the stability of solutions of switched systems with both state-dependent constrained switching and switching whose logic has memory, i.e., the active subsystem only can switch to a prescribed subset of subsystems.

切换系统不变性控制合成：区间分析方法

Invariance Control Synthesis for Switched Systems: An Interval Analysis Approach

本文研究离散时间切换非线性系统不变性控制问题，提出基于区间分析的方法，通过有限次迭代计算受控不变集并直接生成基于分区的不变控制器，无需子系统有共同平衡点。