Optimal Guaranteed Cost Controller Design for Uncertain Discrete Switched Singular Systems

The design method of proportional-derivative state feedback (PDSF) guaranteed cost controllers (GCCs) is studied for discrete switched singular systems with uncertainties in the derivative matrices by introducing a generalized cost function. Some sufficient conditions, which can guarantee the existence of GCCs, are obtained by using the multiple Lyapunov function method, and state-dependent switching laws are designed. By introducing some appropriate free-weighting matrices and constructing appropriate transformation matrices, a synchronous design method is proposed to design the gains of PDSF-GCCs. A numerical example is given to demonstrate the feasibility and effectiveness of the proposed methods.