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 L2 gain for exogenous inputs with L2 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 L2 gain for exogenous inputs with L2 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.