Semistability of switched dynamical systems, Part I: Linear system theory

This paper develops semistability and uniform semistability analysis results for switched linear systems. Semistability is the property whereby the solutions of a dynamical system converge to Lyapunov stable equilibrium points determined by the system’s initial conditions. Since solutions to switched systems are a function of the system’s initial conditions as well as the switching signals, uniformity here refers to the convergence rate of the multiple solutions as the switching signal evolves over a given switching set. The main results of the paper involve sufficient conditions for semistability and uniform semistability using multiple Lyapunov functions and sufficient regularity assumptions on the class of switching signals considered.