Nonpathological ISS-Lyapunov Functions for Interconnected Differential Inclusions

• 成果类型: Article
• 署名作者: Della Rossa, Matteo; Tanwani, Aneel; Zaccarian, Luca
• 署名单位: Universite Catholique Louvain; Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse; University of Trento
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3115437
• 发表日期: 2022
• 页码: 3774-3789
• 关键词: Switched systems; Lyapunov methods; switches; asymptotic stability; Stability criteria; Robustness; Sufficient conditions; Cascade connection; feedback stabilization; generalized gradient; input-to-state stability (ISS); nonpathological function; set-valued derivative; small-gain theorem

摘要

This article concerns robustness analysis for interconnections of two dynamical systems (described by upper semicontinuous differential inclusions) using a generalized notion of derivatives associated with locally Lipschitz Lyapunov functions obtained from a finite family of differentiable functions. We first provide sufficient conditions for input-to-state stability for differential inclusions, using a class of nonsmooth (but locally Lipschitz) candidate Lyapunov functions and the concept of Lie generalized derivative. In general our conditions are less conservative than the more common Clarke derivative-based conditions. We apply our result to state-dependent switched systems, and to the interconnection of two differential inclusions. As an example, we propose an observer-based controller for certain nonlinear two-mode state-dependent switched systems.