Robust H2 performance analysis and synthesis of linear polytopic discrete-time periodic systems via LMIs

• Published in: Systems & control letters Vol. 56; no. 2; pp. 159 - 166
• Main Authors: FARGES, Christophe, PEAUCELLE, Dimitri, ARZELIER, Denis, DAAFOUZ, Jamal
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier 02-02-2007
• Subjects: Applied sciences; Automatic; Computer science; control theory; systems; Control system synthesis; Control theory. Systems; Engineering Sciences; Exact sciences and technology; Polytope; State feedback; Robust stability; X2 performance; Control program; Feedback regulation; Control synthesis; Periodic function; Linear time; LMI; Real time; Optimization; Polytopic uncertainty; Closed feedback; Robust control; Linear periodic discrete-time systems; Uncertain system; Parameter-dependent Lyapunov functions; Discrete time; Linear matrix inequality; Performance analysis; Periodic system; Lyapunov function; Quadratic stability; H2 performance
• ISSN: 0167-6911; 1872-7956
• DOI: 10.1016/j.sysconle.2006.08.006

A particular class of uncertain linear discrete-time periodic systems is considered. The problem of robust stabilization of real polytopic linear discrete-time periodic systems via a periodic state-feedback control law is tackled here, along with H2 performance optimization. Using additional slack variables and the periodic Lyapunov lemma, an extended sufficient condition of robust H2 stabilization is proposed. Based on periodic parameter-dependent Lyapunov functions, this last condition is shown to be always less conservative than the more classic one based on the quadratic stability framework. This is illustrated on a numerical example from the literature.