The purpose of this paper is to study the use of anti-windup gains for obtaining larger regions of stability for linear systems with saturating inputs. Considering that a linear dynamic output feedback has been designed to stabilize the linear system (without saturation), a method is proposed for designing an anti-windup gain that maximizes the estimation of the basin of attraction of the closed-loop system. 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. From this model, stability conditionsbased on quadratic and Lure type Lyapunov functions are stated. Algorithms based on LMI schemes are proposed for computing both the anti-windup gain and an associated region of stability.
h~u c t i o nStudies on the analysis and control design problems for linear systems with saturating actuators have followed two main approaches in the literature. Either a design is carried out directly taking into account the effect of the saturation or the effect of saturation is dealt with in a second step after a previous design performed disregarding the Saturation tenns.The anti-windup fits this second approach as it consists in introducing control modifications in order to recover, as much as possible, the performance induced by a previous design carried out on the basis of the unsaturated system. In particular, anti-windup schemes have been successfully applied in order to avoid or minimize the windup of the integral action in PID controllers, largely applied in the industry. In this case, most of the related literature focuses on the performance improvement in the sense of avoiding large and oscillatory transient responses (see, among others, [2], VI. W1).More recently, a special attention has been paid to the influence of the anti-windup schemes in the stability and the performances of the closed-loop system (see, for example, 131, [SI, [91, 1121, 1131, [141, [17]). Several results on the anti-windup problem are concemed with achieving global stability properties. Since global results cannot be achieved for open-loop unstable linear system in the presence of actuator saturation, local results have to be develaped. In this context, a key issue is the determination of domains of stability for the closed-loop system. With very few exceptions, most of the local results available in the literature of antiwindup do not provide explicit characterization of the domain of stability. It is worth to notice that the basin of attraction is modified by the anti-windup loop. In particular, if the resulting basin of attraction is not sufficiently large, the system can present a divergent behavior depending on its initialization and the action of disturbances.In this paper we focus on the structure of the obmer-based anti-windup [2,1]. F o d stability conditions for this antiwindup structure have been given in [9] on the basis of passivity arguments. A design algorithm is provided which, under certain conditions, achieves global as...
