Stabilization of Switched Linear Systems Subject to Actuator Saturation via Invariant Semiellipsoids

• Published in: IEEE transactions on automatic control Vol. 65; no. 10; pp. 4332 - 4339
• Main Authors: Lian, Jie, Wu, Feiyue
• Format: Journal Article
• Language: English
• Published: New York IEEE 01-10-2020; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Actuator saturation; Actuators; Control systems; Feedback control; Invariants; Liapunov functions; Linear systems; Lyapunov methods; region of attraction (ROA); Saturation; semiellipsoidal invariant set; Stabilization; State feedback; switched linear systems; Switched systems; Switches
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2019.2955028

This article presents new stabilization conditions for the state feedback control of switched linear systems subject to actuator saturation. Based on the semiellipsoidal approach and the multiple Lyapunov functions method, state feedback controllers and a state-dependent switching law are designed. The presented stabilization conditions are less conservative than those obtained by the ellipsoidal method and simpler than those established by the polyhedral method. Moreover, the union of all positively invariant semiellipsoids is constructed to approximate the region of attraction. Each semiellipsoidal set is the intersection of a positively invariant ellipsoidal set and a constraint set. Constructive solutions of the presented conditions are obtained based on two different techniques: the sum-of-squares technique and the nonlinear matrix inequality technique. Two illustrative examples are given to demonstrate the effectiveness of the main results.