Exponential stabilization of singular systems by controlled switching

Exponentially stabilizing state dependent switching control for a class of continuous-time singular linear systems is studied. The stabilization approaches employ multiple Lyapunov functions and the switching law selects the active mode as to minimize the Lyapunov function along the trajectories of the system with the switching feedback control. Although the singular systems constituting the system modes may be regular and impulse free the trajectory of the controlled system can still exhibit discontinuities at the switching times. It is shown that under the action of the designed switching feedback the corresponding discontinuities in the value of the Lyapunov function preserve its monotonic decrease hence insuring global exponential stabilization.