Non-fragile state-feedback control of uncertain piecewise-affine slab systems with input constraints: a convex optimisation approach

• Published in: IET control theory & applications Vol. 8; no. 8; pp. 626 - 632
• Main Authors: Dadkhah, Navid, Rodrigues, Luis
• Format: Journal Article
• Language: English
• Published: Stevenage The Institution of Engineering and Technology 01.05.2014; John Wiley & Sons, Inc
• Subjects: asymptotic stability; closed loop systems; closed‐loop equilibrium point; continuous time systems; continuous‐time piecewise‐affine systems; control input; control system synthesis; Control systems; controller gains; convex optimisation; convex programming; Design engineering; exponential stability; Gain; input constraints; linear matrix inequalities; LMI conditions; nonfragile state‐feedback control; optimisation; optimisation problem; Optimization; PWA systems; robust control; robust nonfragile PWA controller synthesis; Simulation; Slabs; state feedback; sufficient conditions; system uncertainties; uncertain piecewise‐affine slab systems; uncertain systems; Uncertainty; Upper bounds; asymptotic stability; exponential stability; optimisation problem; sufficient conditions; optimisation; linear matrix inequalities; control input; robust control; nonfragile state-feedback control; continuous time systems; convex optimisation; uncertain piecewise-affine slab systems; input constraints; continuous-time piecewise-affine systems; system uncertainties; uncertain systems; control system synthesis; convex programming; robust nonfragile PWA controller synthesis; closed loop systems; LMI conditions; controller gains; state feedback; PWA systems; closed-loop equilibrium point
• ISSN: 1751-8644; 1751-8652; 1751-8652
• DOI: 10.1049/iet-cta.2013.0202

The main contribution of this work is to propose a design technique for state-feedback control of continuous-time piecewise-affine (PWA) systems that is robust not only to the system uncertainties, but also to variations of the controller gains. More specifically, this study presents sufficient conditions to synthesise a robust non-fragile PWA controller that exponentially stabilises the closed-loop equilibrium point. Furthermore, these conditions are cast as an optimisation problem subject to a set of linear matrix inequalities (LMIs), which can then be solved efficiently. In addition, a set of LMI conditions are derived to ensure that the control input will always meet a pre-assigned upper bound. Simulation results demonstrate the effectiveness of the proposed approach.