Stability and stabilization of switched impulsive systems

Many practical systems in physics, biology, engineering, and information science exhibit impulsive dynamical behaviors due to abrupt changes at certain instants during the dynamical processes. In this paper, stability analysis and stabilization synthesis problems are investigated for switched impulsive systems which consisting of a family of linear constant subsystems and a rule that orchestrates the switching between them. Furthermore, there exist impulses at the switching instants. A switched quadratic Lyapunov function is introduced to check asymptotic stability of such systems. Two equivalent necessary and sufficient conditions for the existence of such a Lyapunov function are established, respectively. The conditions are in linear matrix inequality form and can be used to solve stabilization synthesis problem. The results are extended to the uncertain systems case as well.