Design of Saturation-Based Switching Anti-Windup Gains for the Enlargement of the Domain of Attraction

This technical note proposes a saturation-based switching anti-windup design for the enlargement of the domain of attraction of the closed-loop system. A widely adopted method of dealing with an
m
-dimensional saturated linear feedback is to express it as a linear combination of a set of 2
m
auxiliary linear feedbacks. For each value of the state, these auxiliary linear feedbacks form a convex polyhedron of 2
m
vertices in the input space. We propose to divide this convex polyhedron into several convex sub-polyhedrons, each of which is defined as the convex hull of a subset of the auxiliary feedbacks. Whenever the value of the saturated linear feedback falls into a sub-polyhedron, it can be expressed as a linear combination of a subset of the 2
m
auxiliary linear feedbacks that define the sub-polyhedron and thus a less conservative result can be expected. A separate anti-windup gain is designed for each sub-polyhedron by using a common quadratic Lyapunov function and implemented when the value of the saturated linear feedback falls into this sub-polyhedron. Simulation results indicate that such a saturation-based switching anti-windup design has the ability to significantly enlarge the domain of attraction of the closed-loop system.