Periodically time-varying memory state-feedback controller synthesis for discrete-time linear systems

• Published in: Automatica (Oxford) Vol. 47; no. 1; pp. 14 - 25
• Main Authors: Ebihara, Yoshio, Peaucelle, Dimitri, Arzelier, Denis
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01-01-2011; Elsevier
• Subjects: Applied sciences; Computer science; control theory; systems; Control system analysis; Control system synthesis; Control theory. Systems; Discrete-time linear systems; Exact sciences and technology; Linear matrix inequalities; Periodic controllers; Polytopic uncertainties; Robust control; Robust control; Periodic controllers; Linear matrix inequalities; Discrete-time linear systems; Polytopic uncertainties; Polytope; State feedback; Feedback regulation; Control synthesis; Periodic control; Time varying system; Linear time invariant system; Uncertain system; Discrete time; Linear matrix inequality; Invarying system
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/j.automatica.2010.10.004

In this paper, we deal with discrete-time linear periodic/time-invariant systems with polytopic-type uncertainties and propose a new linear matrix inequality (LMI)-based method for robust state-feedback controller synthesis. In stark contrast with existing approaches that are confined to memoryless static controller synthesis, we explore dynamical controller synthesis and reveal a particular periodically time-varying memory state-feedback controller (PTVMSFC) structure that allows LMI-based synthesis. In the context of robust controller synthesis, we prove rigorously that the proposed design method encompasses the well-known extended-LMI-based static controller synthesis methods as particular cases. Through numerical experiments, we demonstrate that the suggested design method is indeed effective in achieving less conservative results, under both periodic and time-invariant settings. We finally derive a viable test to verify that the designed robust PTVMSFC is “exact” in the sense that it attains the best achievable robust performance. This exactness verification test works fine in practice, and we will show via a numerical example that exact robust control is indeed attained by designing PTVMSFCs, even for such a problem where the standard memoryless static state-feedback fails.