Necessary and sufficient conditions for stability of switched Hamiltonian systems with multiple equilibria

This paper investigates the stability of switched Hamiltonian systems with multiple equilibria. We first present the concepts of region stability, asymptotical region stability and exponential region stability for this kind of switched systems. Then, for the case that each subsystem has a unique equilibrium point, under a suitable assumption, several necessary and sufficient conditions are proposed for the global region stability and globally asymptotical region stability of switched Hamiltonian systems with multiple equilibria. Then, a sufficient condition of globally exponential region stability is also presented for switched Hamiltonian system with multiple equilibria. Finally, an illustrative example and numerical simulations are carried out to show that the new stability results obtained in this paper are correct and effective.