Finite-Time L<sub>2</sub>-Gain Asynchronous Control for Continuous-Time Positive Hidden Markov Jump Systems via T–S Fuzzy Model Approach
Chengcheng Ren, Shuping He, Xiaoli Luan, Fei Liu, Hamid Reza Karimi
Abstract
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 L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> 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.