Anti-windup design with guaranteed regions of stability: an LMI-based approach

This paper addresses the design 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 modeled by a linear system with a deadzone nonlinearity. A modified sector condition is then used to obtain stability conditions based on quadratic Lyapunov functions. Different from previous works, these conditions are directly in LMI form. Several examples illustrate the effectiveness of the proposed design technique when compared with the previous ones.