Stability analysis of switched systems using variational principles: An introduction

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.