Smooth Lyapunov Functions for Hybrid Systems—Part I: Existence Is Equivalent to Robustness

DOI10.1109/TAC.2007.900829zbMath1366.93430OpenAlexW2052123991MaRDI QIDQ5282178

Rafal Goebel, Chaohong Cai, Andrew R. Teel

Publication date: 27 July 2017

Published in: IEEE Transactions on Automatic Control (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1109/tac.2007.900829

Mathematics Subject Classification ID

Lyapunov and other classical stabilities (Lagrange, Poisson, (L^p, l^p), etc.) in control theory (93D05) Discrete event control/observation systems (93C65) Control problems involving ordinary differential equations (34H05) Stability of solutions to ordinary differential equations (34D20)

Related Items (26)

A Lyapunov-based small-gain approach on design of triggering conditions in event-triggered control systems ⋮ Smooth patchy control Lyapunov functions ⋮ Stability of periodically time-varying systems: Periodic Lyapunov functions ⋮ A characterization of integral input-to-state stability for hybrid systems ⋮ Model-based event-triggered control for linear plant with threshold variable and model states ⋮ Lyapunov small-gain theorems for networks of not necessarily ISS hybrid systems ⋮ Input-to-state stability for a class of hybrid dynamical systems via averaging ⋮ Output-to-state stability for hybrid systems ⋮ Further results on the construction of strict Lyapunov-Krasovskii functionals for time-varying time-delay systems ⋮ Observer-Based Control of Linear Complementarity Systems ⋮ Stability condition for sampled data based control of linear continuous switched systems ⋮ Robustness of stability through necessary and sufficient Lyapunov-like conditions for systems with a continuum of equilibria ⋮ Stability analysis for stochastic hybrid systems: a survey ⋮ Hybrid models of opinion dynamics with opinion-dependent connectivity ⋮ On existence of oscillations in hybrid systems ⋮ On Lyapunov stability of interconnected nonlinear systems: recursive integration methodology ⋮ Uniform stability and ISS of discrete-time impulsive hybrid systems ⋮ On optimal control problems of a class of impulsive switching systems with terminal states constraints ⋮ On the equivalence between global recurrence and the existence of a smooth Lyapunov function for hybrid systems ⋮ Relaxation results for hybrid inclusions ⋮ Epsilon-Tubes and Generalized Skorokhod Metrics for Hybrid Paths Spaces ⋮ Hybrid online learning control in networked multiagent systems: A survey ⋮ Linear quadratic optimal sampled data control of linear systems with unknown switched modes and stochastic disturbances ⋮ Local exponential stabilization for a class of uncertain nonlinear impulsive periodic switched systems with norm-bounded input ⋮ On uniform controller design for linear switched systems ⋮ Classical converse theorems in Lyapunov's second method

This page was built for publication: Smooth Lyapunov Functions for Hybrid Systems—Part I: Existence Is Equivalent to Robustness