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Anti-windup design with guaranteed regions of stability for discrete-time linear systems
Authors:JM Gomes da Silva  Jr  S Tarbouriech  
Affiliation:aUFRGS, Department of Electrical Engineering, Avenue Osvaldo Aranha 103, 90035-190 Porto Alegre-RS, Brazil;bLAAS-CNRS, 7 Avenue du Colonel Roche, 31077 Toulouse cedex 4, France
Abstract:The purpose of this paper is to study the determination of stability regions for discrete-time linear systems with saturating controls through anti-windup schemes. Considering that a linear dynamic output feedback has been designed to stabilize the linear discrete-time system (without saturation), a method is proposed for designing an anti-windup gain that maximizes an estimate of the basin of attraction of the closed-loop system in the presence of saturation. It is shown that the closed-loop system obtained from the controller plus the anti-windup gain can be locally modeled by a linear system with a deadzone nonlinearity. Then, based on the use of a new sector condition and quadratic Lyapunov functions, stability conditions in an LMI form are stated. These conditions are then considered in a convex optimization problem in order to compute an anti-windup gain that maximizes an estimate of the basin of attraction of the closed-loop system. Moreover, considering asymptotically stable open-loop systems, it is shown that the conditions can be slightly modified in order to determine an anti-windup gain that ensures global stability. An extension of the proposed results to the case of dynamic anti-windup synthesis is also presented in the paper.
Keywords:Anti-windup  Control saturation  Stability  Discrete-time systems  Linear matrix inequalities
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