On Enlarging the Domain of Attraction for Linear Systems Subject to Asymmetric Actuator Saturation

In this paper, we revisit the problem of enlarging the domain of attraction for linear systems with asymmetric actuator saturation. We partition the state space into several regions according to the sign of each input and rewrite the linear system subject to asymmetric actuator saturation as an equivalent switched system, each subsystem of which is associated with one partition of the state space and is a linear system subject to symmetric actuator saturation. Based on this equivalent representation of the system, we present a Lyapunov function, which is composed of a set of quadratic functions associated with matrices that are not required to be positive definite. We establish sufficient conditions for regional stability and, based on them, formulate optimization problems to enlarge the estimate of the domain of attraction. Simulation results illustrate the effectiveness of the proposed approach.