Hybrid Control for a Class of Switched Singular Systems with State Jumps

The stabilization problem is addressed for a class of switched singular systems with state jumps. Firstly, we introduce a new class of systems, so called switched singular systems with state jumps, by adopting a definition on initial instantaneous jumps of singular systems. Then, multiple Lyapunov function techniques are extended to this class of switched singular systems and a hybrid switching law is designed based on a partition of state space by using S-procedure method. A sufficient condition for the system to be asymptotically stable is formulated by solving a set of LMIs and the state feedback controllers are designed as well. Finally, an example is given to illustrate the effectiveness of our approach for this kind of switched singular systems with state jumps