An improved combined switching strategy for switched linear systems

In this paper, an improved combined switching law is proposed for a class of continuous-time switched linear system with two subsystems. Under this switching law, the Lyapunov-like function is not necessarily to be decreasing in both time-driven and state-driven mechanisms. This remarkably reduces the switching frequency. Under suitable assumptions on the system dynamics, the switched system is exponentially stable. In addition, under this switching law, when the switched system is perturbed by time-varying disturbances, the perturbed systems are bounded for bounded perturbations, convergent for convergent perturbations, and exponentially convergent for exponentially convergent perturbations.