Stability analysis of switched systems using variational principles: An introduction

Michael Margaliot*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Many natural and artificial systems and processes encompass several modes of operation with a different dynamical behavior in each mode. Switched systems provide a suitable mathematical model for such processes, and their stability analysis is important for both theoretical and practical reasons. We review a specific approach for stability analysis based on using variational principles to characterize the "most unstable" solution of the switched system. We also discuss a link between the variational approach and the stability analysis of switched systems using Lie-algebraic considerations. Both approaches require the use of sophisticated tools from many different fields of applied mathematics. The purpose of this paper is to provide an accessible and self-contained review of these topics, emphasizing the intuitive and geometric underlying ideas.

Original languageEnglish
Pages (from-to)2059-2077
Number of pages19
Issue number12
StatePublished - Dec 2006


FundersFunder number
Israel Science Foundation199/03


    • Absolute stability
    • Bang-bang control
    • Bilinear systems
    • Differential inclusions
    • Dynamic programming
    • Geometric control theory
    • Global asymptotic stability
    • Hamilton-Jacobi-Bellman equation
    • Hybrid systems
    • Lie algebra
    • Lie bracket
    • Maximum principle
    • Nilpotent control systems
    • Reachability with nice controls
    • Stability under arbitrary switching
    • Switched controllers


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