Finite-Time L2-Gain Asynchronous Control for Continuous-Time Positive Hidden Markov Jump Systems via T-S Fuzzy Model Approach

• Published in: IEEE transactions on cybernetics Vol. 51; no. 1; pp. 77 - 87
• Main Authors: Ren, Chengcheng, He, Shuping, Luan, Xiaoli, Liu, Fei, Karimi, Hamid Reza
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 01.01.2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Asynchronous control; Feedback control; finite-time bounded; Fuzzy systems; Hidden Markov jump systems (HMJSs); Hidden Markov models; L2 gain; Markov chains; Markov processes; Networked control systems; Nonlinear systems; Performance indices; positive systems; Stability analysis; Takagi–Sugeno (T–S) fuzzy model
• ISSN: 2168-2267; 2168-2275; 2168-2275
• DOI: 10.1109/TCYB.2020.2996743

This article investigates the finite-time asynchronous control problem for continuous-time positive hidden Markov jump systems (HMJSs) by using the Takagi-Sugeno fuzzy model method. Different from the existing methods, the Markov jump systems under consideration are considered with the hidden Markov model in the continuous-time case, that is, the Markov model consists of the hidden state and the observed state. We aim to derive a suitable controller that depends on the observation mode which makes the closed-loop fuzzy HMJSs be stochastically finite-time bounded and positive, and fulfill the given <inline-formula> <tex-math notation="LaTeX">L_{2} </tex-math></inline-formula> performance index. Applying the stochastic Lyapunov-Krasovskii functional (SLKF) methods, we establish sufficient conditions to obtain the finite-time state-feedback controller. Finally, a Lotka-Volterra population model is used to show the feasibility and validity of the main results.