PWL and PWA ℋ ∞ controller synthesis for uncertain PWA slab systems: LMI approach

• Published in: International journal of control Vol. 82; no. 3; pp. 482 - 492
• Main Authors: LeBel, Stefan, Rodrigues, Luis
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis Group 01.03.2009; Taylor & Francis
• Subjects: Applied sciences; Computer science; control theory; systems; control; Control system analysis; Control system synthesis; Control theory. Systems; Exact sciences and technology; linear matrix inequalities; piecewise-affine systems; piecewise-linear systems; Systeme affine in control; Uncertain system; H2 control; H infinite control; Linear matrix inequality; Control synthesis; Convex programming; Piecewise linearization
• ISSN: 0020-7179; 1366-5820
• DOI: 10.1080/00207170802144313

This article presents new piecewise-affine (PWA) and piecewise-linear (PWL) ℋ ∞ controller synthesis methods for uncertain PWA slab systems. The synthesis problems are formulated as convex programs subject to a set of Linear Matrix Inequalities (LMIs), which can then be solved efficiently using available software. No other synthesis methods available in the literature can design a PWA controller for an uncertain PWA system using convex optimisation without constraining the controller gain matrix. Therefore this is the main contribution of the article. The proposed controller synthesis methodologies are applied to a circuit example.