Anti-windup synthesis for linear control systems with input saturation: Achieving regional, nonlinear performance

In this paper, we present LMI-based synthesis tools for regional stability and performance of linear anti-windup compensators for linear control systems. We consider both static and dynamic compensators. Algorithms are developed that minimize the upper bound on the regional L-2 gain for exouenous inputs with L-2 norm bounded by a given value, and that minimize this upper bound with a guaranteed reachable set or domain of attraction. Based on the structure of the optimization problems, it is shown that for systems whose plants have poles in the closed left-half plane, plant-order dynamic anti-windup can achieve semiglobal exponential stability and finite L-2 gain for exogenous inputs with L-2 norm bounded by any finite value. The problems are studied in a general setting where the only requirement on the linear control system is well-posedness and internal stability. The effectiveness of the proposed techniques is illustrated with an example. (C) 2007 Elsevier Ltd. All rights reserved.