Design of dynamic output feedback H _∞ controller for common singular discrete systems

A method to design a strictly proper dynamic output feedback H_∞ controller for common discrete singular system is given. First, an auxiliary singular discrete system is constructed and its state feedback H_∞ controller is designed, and then by means of two groups of matrix inequalities, a sufficient condition for the existence of the dynamic output feedback H_∞ controller is presented, such that the resulting closed-loop system is admissible with its transfer function satisfying H_∞ norm constraint. By solving the two groups of matrix inequalities, the desired controller can be obtained. The condition for the solvability of the controllers is expressed by using the coefficient matrices of the whole system. The design procedure involves no decomposition of the system, which can avoid some numerical problems arising from the decomposition of matrices. A numerical example is given to demonstrate the application of the proposed method.