Stability of limit cycles in hybrid systems using discrete-time Lyapunov techniques

This paper concerns stability analysis of limit cycles in hybrid systems. Continuous-time hybrid systems are modeled in a discrete-time affine framework. The discrete-time approach is shown to be appropriate in order to find a Lyapunov formulation for the stability of a hybrid limit cycle. Multiple Lyapunov functions are associated with the transitions in the hybrid system so that the trajectory is shown to converge to the switch points of the limit cycle. The results are formulated in linear matrix inequalities (LMI) which gives a constructive way to find the Lyapunov functions using efficient algorithms. The results are applied to a two-tank example with discrete valued actuators