Nonfragile and Nonsynchronous Synthesis of Reachable Set for Bernoulli Switched Systems

• Published in: IEEE transactions on systems, man, and cybernetics. Systems Vol. 50; no. 2; pp. 726 - 731
• Main Authors: Che, Wei-Wei, Su, Hongye, Shi, Peng, Wu, Zheng-Guang
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.02.2020; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Bounded disturbances; Closed loop systems; Computer simulation; Control systems design; Cybernetics; Estimation; Feedback control; Mathematical models; nonfragile controller; nonsynchronous controller; reachable set; Switched systems; Switches; Switching; Symmetric matrices; Synthesis; System effectiveness
• ISSN: 2168-2216; 2168-2232
• DOI: 10.1109/TSMC.2017.2773480

In this paper, the problems of nonfragile and nonsynchronous synthesis for Bernoulli switched systems are studied. The disturbances in the systems are assumed to have bounded peak in the sense of mean square. With the interval additive gain variations consideration, a nonfragile and nonsynchronous controller is designed subject to a nonsynchronous assumption that the switching signals of the system are not accurately gained for synthesis. A sufficient condition that is dependent on the known sojourn probabilities of switching signals is proposed to ascertain the reachable set of the closed-loop system, which is a hidden Bernoulli model, mean square contained in an ellipsoid-like set. Several nonfragile and nonsynchronous controllers are parameterized to guarantee the corresponding requirements to be satisfied for the closed-loop systems. The effectiveness and advantages of the proposed new design techniques are illustrated by a numerical simulation example.