Regional anti-windup compensation for linear systems with input saturation

In this paper we propose LMI methods for designing dynamic/static anti-windup compensators to improve regional performance and stability of linear control systems with saturating actuators. Algorithms are developed for minimizing the upper bound on the regional L₂ gain for exogenous inputs with L₂ norm bounded by a given value, and for minimizing 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 stability and finite L₂ gain for exogenous inputs with L₂ norm hounded 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.