Modified Looped Functional for Sampled-Data Control of T-S Fuzzy Markovian Jump Systems

• Published in: IEEE transactions on fuzzy systems Vol. 29; no. 9; pp. 2543 - 2552
• Main Authors: Guan, Chaoxu, Fei, Zhongyang, Park, PooGyeon
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.09.2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Closed loop systems; Control stability; Control systems design; Delays; Feedback control; Fuzzy control; Fuzzy systems; Looped functional; sampled-data control; Stability criteria; Stochastic processes; Symmetric matrices; Takagi–Sugeno (T–S) fuzzy Markovian jump systems
• ISSN: 1063-6706; 1941-0034
• DOI: 10.1109/TFUZZ.2020.3003498

This article investigates the sampled-data control for a class of Takagi-Sugeno (T-S) fuzzy Markovian jump systems via a novel looped functional approach. By refining the fractional delayed state concept, the looped functional is established to include more sampling information of the intervals not only from <inline-formula><tex-math notation="LaTeX">x(t_{k})</tex-math></inline-formula> to <inline-formula><tex-math notation="LaTeX">x(t)</tex-math></inline-formula> but also from <inline-formula><tex-math notation="LaTeX">x(t)</tex-math></inline-formula> to <inline-formula><tex-math notation="LaTeX">x(t_{k+1})</tex-math></inline-formula>, which would contribute to a reduction in the conservatism. Then, a sufficient criterion is presented to ensure the stochastic stability of the resulting closed-loop system, based on which the sampled-data controller is further designed for the T-S fuzzy Markovian jump system under the influence of asynchronous premise variables. Finally, the obtained theorems are applied to a numerical example and a practical application to show the effectiveness and superiority of the proposed method.