Stability and stabilization for a class of discrete-time piecewise affine singular systems

The stability and stabilization problems for discrete-time piecewise affine singular systems are discussed. A basic linear matrix inequality (LMI) sufficient condition for the systems to be regular, causal and stable is given. With this condition and some inequalities, a LMI stability condition that makes easier the design of the state feedback controller is proposed, and then the state feedback stabilization problem is solved in terms of LMIs. Finally, a numerical example to illustrate the effectiveness of the method is given.