Non-fragile H∞ control based on dynamic output feedback for a class of linear discrete-time systems with time-varying delay

This paper addresses the problem of non-fragile H_∞ dynamic output feedback control for a class of linear discrete-time systems with time-varying delay. The main contribution of the paper is to provide a delay-dependent sufficient condition on the existence of an asymptotically stabilizing and γ-suboptimal H_∞ dynamic output feedback controller in the presence of multiplicative controller parameter variations. As an extension, based on affine characteristic of linear matrix inequality, the corresponding robust non-fragile H_∞ dynamic output feedback control problem where the system matrices are uncertain but belong to a fixed convex polytope, is also treated. In order to find out the parameters of the controller to be designed, we apply sequentially linear programming matrix method (SLPMM) to solve the matrix inequalities. A numerical example is given to demonstrate the effectiveness and feasibility of the proposed method.