Robust regulation of discrete-time systems subject to parameter uncertainties and state delay

Abstract

This paper deals with the robust recursive regulation problem of uncertain discrete-time linear systems subject to unknown state delays. The variation rate between two consecutive delays is considered bounded. The parameter matrices are affected by norm-bounded uncertainties. Applying the lifting method and modeling the delay as a Markov chain, systems with state delays are converted to augmented delay-free Markovian jump linear systems. Then, a robust recursive linear quadratic regulator is obtained, solving an optimization problem through robust regularized least-squares approaches. The solution is given in terms of algebraic Riccati equations. We assess the proposed regulator through a numerical example and compare its performance with other robust control approaches.