Sufficient Stability Conditions for a Class of Switched Systems with Multiple Steady States

In this paper, we present a novel approach to determine the stability of switched linear and nonlinear systems using Sum Squares optimisation. Particularly, use optimisation search for Lyapunov function that defines an absorbing set confines solution trajectories. For systems, show also implies global asymptotic stability. Using approach, can study broader range particularly, attractor whose dynamics are given by polynomial vector fields which have multiple equilibria or limit cycles.