Multiple Lyapunov functions and other analysis tools for switched and hybrid systems

1998/04/01 by M.S. Branicky, Michael S. Branicky · 3,266 citations
Engineering · Mathematics · #Advanced Differential Equations and Dynamical Systems #Applied mathematics #Class (philosophy) #Computer science #Control (management) #Control and Stability of Dynamical Systems #Control theory (sociology) #Hybrid system #Iterated function #Limit (mathematics) #Limit cycle #Lipschitz continuity #Lyapunov function #Mathematical analysis #Mathematics #Nonlinear system #Pure mathematics #Stability (learning theory) #Stability and Control of Uncertain Systems

paper · doi:10.1109/9.664150

published in IEEE Transactions on Automatic Control 43(4), 475-482 (Institute of Electrical and Electronics Engineers)

openalex publication_date 1998/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

We introduce some analysis tools for switched and hybrid systems. We first present work on stability analysis. We introduce multiple Lyapunov functions as a tool for analyzing Lyapunov stability and use iterated function systems theory as a tool for Lagrange stability. We also discuss the case where the switched systems are indexed by an arbitrary compact set. Finally, we extend Bendixson's theorem to the case of Lipschitz continuous vector fields, allowing limit cycle analysis of a class of "continuous switched" systems.

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