Output Feedback Guaranteeing Cost Control by Matrix Inequalities for Discrete-Time Delay Systems

Abstract: This paper investigates the construction of guaranteeing cost dynamic output feedback controller for linear discrete-time delay systems with time-varying parameter uncertainties and with exogenous disturbances. A necessary and sufficient condition for a controller to have the guaranteeing cost property is given by a nonlinear matrix inequality. As a sufficient condition, a linear matrix inequality is derived, the solution of which can be used for constructing a control of the desired type. It is also shown that the resulted trajectory is input-to-state stable. A numerical example illustrates the application of the results. Key–Words: guaranteeing cost control, delay systems, discrete-time systems, matrix inequalities