On the existence and uniqueness of solutions of switched Hamiltonian systems

This paper investigates the elementary issue of existence and uniqueness of solutions of switched Hamiltonian systems. By means of Banach fixed point theorem, we propose a sufficient condition of existence and uniqueness of solutions of switched Hamiltonian systems. The property of existence and uniqueness of solutions shows that for a switched system, one of the multiple equilibria of subsystems may not be an equilibrium point of the whole switched system. That is, the equilibrium of a switched system is not equivalent to that of its´ subsystems.