Anti-windup Compensator Gain Design for Time-delay Systems with Constraints

Systems that are subject to both time-delay in state and input saturation are considered. We synthesize the anti-windup gain to enlarge the estimation of domain of attraction while guaranteeing the stability of the closed-loop system. An ellipsoid and a polyhedral set are used to bound the state of the system, which make a new sector condition valid. Other than an iterative algorithm, a direct designing algorithm is derived to compute the anti-windup compensator gain, which reduces the conservatism greatly. We analyze the delay-independent and delay-dependent cases, respectively. Finally, an optimization algorithm in the form of LMIs is constructed to compute the compensator gain which maximizes the estimation of domain of attraction. Numerical examples are presented to demonstrate the effectiveness of our approach.