Switching Anti-Windup Synthesis for Linear Systems With Asymmetric Actuator Saturation

This article proposes a switching anti-windup strategy for linear, time-invariant (LTI) systems subject to asymmetric actuator saturation and $\mathcal{L}_{2}$ -disturbances, the core idea behind which is to make full use of the available range of control input space by switching among multiple anti-windup gains. The asymmetrically saturated LTI system is converted to a switched system with symmetrically saturated subsystems, and a dwell time switching rule is presented to govern the switching between different antiwindup gains. Based on multiple Lyapunov functions, we derive sufficient conditions for guaranteeing the regional stability and weighted $\mathcal{L}_{2}$ performance of the closed-loop system. The switching anti-windup synthesis that designs a separate anti-windup gain for each subsystem is cast as a convex optimization problem. In comparison with the design of a single anti-windup gain, our method can induce less conservative results since the asymmetric character of the saturation constraint is fully utilized in the switching anti-windup design. Two numerical examples, and an application to aeroengine control (the experiments are conducted on a semiphysical test bench), demonstrate the superiority and practicality of the proposed scheme.