The slow state variables feedback stabilization problem for semi-Markov jump discrete-time systems with slow sampling singular perturbations is discussed in this work. A new fairly comprehensive system model, semi-Markov jump system with singular perturbations, which is more general than Markov jump model, is employed to describe the phenomena of random abrupt changes in structure and parameters of the systems. Based on a slow state variables feedback control scheme, a novel technique to design the desired controller is presented and the allowed maximum of singular perturbation parameter can be calculated. With the help of the discrete-time semi-Markov kernel approach, some sojourn-time-dependent and less-conservative sufficient conditions are established via a novel matrix decoupling technique to ensure the solvability of the problem to be addressed. Finally, an illustrative example is given to show the superiority and usefulness of the proposed method.

This paper investigates the finite-time event-triggered $\mathcal{H}_\infty$ control problem for Takagi-Sugeno Markov jump fuzzy systems. Because of the sampling behaviors and the effect of network environment, the premise variables considered in this paper are subject to asynchronous constraints. The aim of this work is to synthesize a controller via an event-triggered communication scheme such that not only the resulting closed-loop system is finite-time bounded and satisfies a prescribed $\mathcal{H}_\infty$ performance level, but also the communication burden is reduced. Firstly, a sufficient condition is established for the finite-time bounded $\mathcal{H}_\infty$ performance analysis of the closed-loop fuzzy system with fully considering the asynchronous premises. Then, based on the derived condition, the method of the desired controller design is presented. Two illustrative examples are finally presented to demonstrate the practicability and efficacy of the proposed method.

In this article, a novel hybrid reinforcement $Q$ -learning control method is proposed to solve the adaptive fuzzy $H_{\infty }$ control problem of discrete-time nonlinear Markov jump systems based on the Takagi–Sugeno fuzzy model. First, the core problem of adaptive fuzzy $H_{\infty }$ control is converted to solving fuzzy game coupled algebraic Riccati equation, which can hardly be solved by mathematical methods directly. To solve this problem, an offline parallel hybrid learning algorithm is first designed, where system dynamics should be known as a prior. Furthermore, an online parallel $Q$ -learning hybrid learning algorithm is developed. The main characteristics of the proposed online hybrid learning algorithms are threefold: 1) system dynamics are avoided during the learning process; 2) compared with the policy iteration method, the restriction of the initial stable control policy is removed; and 3) compared with the value iteration method, a faster convergence rate can be obtained. Finally, we provide a tunnel diode circuit system model to validate the effectiveness of the present learning algorithm.

In this article, the sliding mode control issue is investigated for a class of discrete-time Takagi–Sugeno fuzzy networked singularly perturbed systems via an observer-based technique. Moreover, to process the measurement output and schedule the transmission sequence for relieving the communication burden, a logarithmic quantizer and a weighted try-once-discard protocol are synthesized, which can further improve the network bandwidth utilization in networked control systems. Based on the fuzzy observer states, a novel fuzzy sliding surface is established by considering the singularly perturbed parameter properly, and we endeavor to synthesize a sliding mode control law such that the reachability of the prescribed sliding surface could be guaranteed. In addition, by virtue of the convex optimization theory and Lyapunov approach, sufficient conditions are developed to guarantee the asymptotic stability of the sliding mode dynamics as well as the error system with an expected $H_{\infty }$ performance. Finally, a verification example is presented to illustrate the feasibility and effectivity of the proposed method.

In this technical note, the sliding-mode control (SMC) problem is investigated for T-S fuzzy-model-based nonlinear Markovian jump singular systems subject to matched/unmatched uncertainties. To accommodate the model characteristics of such a hybrid system, a novel integral-type fuzzy sliding surface is put forward by taking the singular matrix and state-dependent projection matrix into account simultaneously, which is the key contribution of the note. The designed surface contains two important features: 1) local input matrices for different subsystems in the same system mode are allowed to be different; and 2) the matched uncertainties are completely compensated, and the unmatched ones are not amplified during sliding motion. Sufficient conditions for the stochastic admissibility of the corresponding sliding-mode dynamics are presented, and a fuzzy SMC law is constructed to ensure the reaching condition despite uncertainties. The applicability and effectiveness of our approach are verified by simulations on an inverted pendulum system.

Notice of Violation of IEEE Publication Principles After careful consideration by a duly constituted committee, an author of this article, Hamid Reza Karimi, was found to have acted in violation of the IEEE Principles of Ethical Publishing by artificially inflating the number of citations to this article. This paper is concerned with dissipativity-based fuzzy integral sliding mode control (FISMC) of continuous-time Takagi-Sugeno (T-S) fuzzy systems with matched/unmatched uncertainties and external disturbance. To better accommodate the characteristics of T-S fuzzy models, an appropriate integral-type fuzzy switching surface is put forward by taking the state-dependent input matrix into account, which is the key contribution of the paper. Based on the utilization of Lyapunov function and property of the transition matrix for unmatched uncertainties, sufficient conditions are presented to guarantee the asymptotic stability of corresponding sliding mode dynamics with a strictly dissipative performance. A FISMC law is synthesized to drive system trajectories onto the fuzzy switching surface despite matched/unmatched uncertainties and external disturbance. A modified adaptive FISMC law is further designed for adapting the unknown upper bound of matched uncertainty. Two practical examples are provided to illustrate the effectiveness and advantages of developed FISMC scheme.