Asynchronous control of T‐S fuzzy chaotic systems via a unified model using the hidden Markov model subject to strict dissipativity

• Published in: Optimal control applications & methods Vol. 41; no. 2; pp. 587 - 604
• Main Authors: Xu, Chuancan, Tong, Dongbing, Chen, Qiaoyu, Zhou, Wuneng
• Format: Journal Article
• Language: English
• Published: Glasgow Wiley Subscription Services, Inc 01.03.2020
• Subjects: asynchronous control; Chaos theory; chaotic systems; Control stability; Controllers; Fuzzy control; Fuzzy systems; Linear matrix inequalities; Markov analysis; Markov chains; Markovian jumping parameters; strict dissipativity; T‐S fuzzy approach; unified model
• ISSN: 0143-2087; 1099-1514
• DOI: 10.1002/oca.2560

Summary The asynchronous control for the unified model of chaotic systems with Markovian jumping parameters is considered via the Takagi‐Sugeno (T‐S) fuzzy approach in this paper. According to jumping modes for chaotic systems and modes for the asynchronous controller, a double‐mode process is generated. By introducing the hidden Markov model (HMM), the asynchronization phenomenon is represented between the controller and chaotic systems. By linear matrix inequalities (LMIs), some conditions are received to guarantee the stochastic stability and the strict dissipativity for chaotic systems. Based on the stochastic stability theory and the dissipativity theory, the asynchronous controller is discussed. The proposed method can be applied to the mode‐independent controller and the synchronous controller. Finally, the effectiveness of the proposed controller is illustrated by two examples.