A Switching Anti-windup Design Using Multiple Lyapunov Functions

• Published in: IEEE transactions on automatic control Vol. 55; no. 1; pp. 142 - 148
• Main Authors: Lu, Liang, Lin, Zongli
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.01.2010; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Actuator saturation; Actuators; Anti-windup; Applied sciences; Attraction; composite Lyapunov functions; Computer science; control theory; systems; Control system analysis; Control systems; Control theory. Systems; Design engineering; domain of attraction; Ellipsoids; Exact sciences and technology; Expansion; Feedback; Gain; Invariants; Level set; Linear matrix inequalities; Lyapunov functions; Lyapunov method; Mathematical analysis; Mathematics; Ordinary differential equations; Sciences and techniques of general use; Stability analysis; Studies; Switched systems; Switching; Switching systems; Multimodel control; Invariant; Saturation; Switching function; Invariant set; Actuator saturation; Closed feedback; Anti windup; anti-windup; Domain of attraction; composite Lyapunov functions; Actuator; Lyapunov function; Quadratic function; switching systems
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2009.2033753

This technical note proposes a switching anti-windup design, which aims to enlarge the domain of attraction of the closed-loop system. Multiple anti-windup gains along with an index function that orchestrates the switching among these anti-windup gains are designed based on the min function of multiple quadratic Lyapunov functions. In comparison with the design of a single anti-windup gain which maximizes a contractively invariant level set of a single quadratic Lyapunov function as a way to enlarge the domain of attraction, the use of multiple Lyapunov functions and switching in the proposed design allows the union of the level sets of the multiple Lyapunov functions, each of which is not necessarily contractively invariant, to be contractively invariant and within the domain of attraction. As a result, the resulting domain of attraction is expected to be significantly larger than the one resulting from a single anti-windup gain and a single Lyapunov function. Indeed, simulation results demonstrate such a significant improvement.