Robust H∞ control of discrete systems with uncertain parameters and unknown delays

In this paper, we address the problems of robust H-infinity performance analysis and control synthesis for a class of discrete-time systems with norm-bounded parameter uncertainty and unknown constant state delay. Through finite-dimensional algebraic Riccati equations, we provide a necessary and sufficient condition for designing a memoryless state-feedback controller which stabilizes the discrete time-delay system under consideration and guarantees an H-infinity-norm bound constraint on the disturbance attenuation for all admissible uncertainties and unknown delays. An example is worked out to illustrate the developed theory. (C) 2000 Elsevier Science Ltd. All rights reserved.