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

• Published in: Automatica (Oxford) Vol. 156; p. 111179
• Main Authors: Odorico, Elizandra K., Terra, Marco H.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.10.2023
• Subjects: Discrete-time linear system; Markovian jump linear system; Robust linear quadratic regulator; Time-delay system; Discrete-time linear system; Robust linear quadratic regulator; Time-delay system; Markovian jump linear system
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/j.automatica.2023.111179

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.