Stability of Hybrid Dissipative Hamiltonian Systems

This paper investigates the stability of hybrid dissipative Hamiltonian systems under (arbitrary) switching laws, and proposes a number of new results for the problem. For the case that the switching law is an infinite-valued piecewise right-continuous constant function, under a realistic assumption, it is shown that hybrid dissipative Hamiltonian system is stable under arbitrary switching laws. Based on this and by using the dissipative Hamiltonian structural properties and zero-state detectibility/observability, several sufficient conditions are presented for the asymptotical stability of the hybrid dissipative Hamiltonian system. As for the case that the switching law is related only to the state, some new stability results are proposed for the hybrid dissipative Hamiltonian system. Finally, as an application, the results obtained in this paper are applied to investigate the stability of ordinary hybrid nonlinear systems, and several useful corollaries are obtained for the systems. Study on an example and numerical simulations shows that the results obtained in this paper are very practicable in analyzing the stability of explicit hybrid systems.