Design of Switched Linear Systems in the Presence of Actuator Saturation

• Published in: IEEE transactions on automatic control Vol. 53; no. 6; pp. 1536 - 1542
• Main Authors: Lu, Liang, Lin, Zongli
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.07.2008; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Actuator saturation; Actuators; Applied sciences; Attraction; Computer science; control theory; systems; Constraint optimization; Control system analysis; Control system synthesis; Control systems; Control theory; Control theory. Systems; Design engineering; Design optimization; Exact sciences and technology; Feedback; Hydraulic actuators; Linear systems; Lyapunov method; set invariance; Stability; switched linear systems; Switched systems; Switching; set invariance; Multimodel control; Saturation; Feedback regulation; Control synthesis; Invariant set; switched linear systems; Attractor; Actuator saturation; Constrained optimization; Hybrid system; Asymptotic stability; Convex hull; Linear system; Linear motor; Domain of attraction
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2008.921021

For a group of linear systems, each under a saturated linear, not necessarily stabilizing, feedback law, we design a switching scheme such that the resulting switched system is locally asymptotically stable at the origin with a large domain of attraction. By expressing each saturated linear feedback in a convex hull of a group of auxiliary linear feedbacks, we formulate and solve the problem of designing such a switching scheme as a constrained optimization problem with the objective of maximizing an estimate of the domain of attraction. Simulation results indicate that the resulting domain of attraction extends well beyond the linear regions of the actuators.