Necessary and sufficient conditions of stability for switched nonlinear systems

This paper investigates stability/asymptotic stability of switched nonlinear systems with potentially unstable subsystems. At first, switched nonlinear Hamiltonian systems are considered and several necessary and sufficient conditions of stability/asymptotic stability are developed via the maximum energy function based method. Based on the new stability results obtained and the method of Hamiltonian realization, several necessary and sufficient conditions of stability/asymptotic stability are then presented for ordinary switched nonlinear systems with potentially unstable subsystems. A numerical example of an ordinary switched nonlinear system with all unstable subsystems illustrates the effectiveness of the obtained stability results.