Output Feedback Stabilization for Discrete-time Systems with A Time-varying Delay

The free-weighting matrix approach is employed to investigate the output feedback control of linear discrete-time systems with an interval time-varying delay. First, a delay-dependent stability analysis is carried out using a new method of estimating the upper bound on the difference of a Lyapunov function without ignoring any useful terms; and a design criterion for a static output feedback (SOF) controller is formulated based on that analysis. Since the conditions thus obtained for the existence of admissible controllers are not expressed strictly in terms of linear matrix inequalities, a modified cone complementary linearization (CCL) algorithm is employed to solve the nonconvex feasibility SOF control problem. This enables the problem of designing a dynamic output feedback controller to be reduced to one of designing an SOF controller. Numerical examples demonstrate the effectiveness of the method and its advantage over existing methods.