Energy analysis of a class of state-dependent switched systems with all unstable subsystems

In this paper, we investigate the stability and periodicity of a class state-dependent switched systems with all unstable subsystems by means energy analysis. We firstly transform reversibly into form second order mechanical systems, then construct functions calculating sum kinetic potential energies each subsystem. After that, two switching lines, derived from lines largest smallest drops, make stable phase trajectory approach to equilibrium point at fastest speed. addition, explore possible dynamic behaviors system under pair line including asymptotic stability, instability periodicity. Furthermore, based on bisection method nested intervals theorem, design law, which makes periodic initiated law. Finally, numerical simulation examples are provided illustrate effectiveness less conservativeness proposed practical significance.