Two types of fuzzy switching sliding surfaces are presented, which combines an event-triggered (ET) method to investigate a fuzzy switching sliding mode control problem of T-S fuzzy systems. Different from the existing ET sliding mode control method, the fuzzy membership functions (FMFs) as well as their derivatives are fully employed for devising the fuzzy integral switching function. To reduce the frequency of controller updates, a corresponding triggering instant integral sliding variable is constructed, which is merely composed of variables related to the triggering instant. Meanwhile, a mixed ET mechanism is consist of fuzzy state variables errors and integral sliding variables errors, which serves as a critical element for ensuring the existence of a practical sliding mode (PSM). A bounded stability criteria of the sliding motion are derived using a fuzzy Lyapunov method, in which the linear decoupling strategies are applied to address a bilinear matrix inequality problem. Furthermore, a switching approach is employed to design the ET fuzzy switching SMC (ETFSSMC) law, which effectively utilizes the characteristics of the FMFs and their derivatives. According to the proposed ETFSSMC method, the existence of a PSM and no Zeno phenomenon can be guaranteed. In the end, the validity as well as the benefits of the methodology can be illustrated via two simulation examples.

This article investigates the integral sliding-mode control (SMC) problem for T-S fuzzy systems via the periodic event-triggered method. First, in order to remove the assumption that the inter-execution time has a uniform upper bound, a novel sliding variable error function is added into the event-triggering mechanism. Second, in order to avoid the extra information transmission, a new sliding-mode switching function consisting of the triggering state information is proposed to design the event-triggered integral SMC (ISMC) law. In addition, the ultimate boundedness of sliding motion can be ensured via using a designed event-triggered ISMC law. A sufficient condition of boundedness is given in the form of linear matrix inequality, which is employed to solve the controller gain matrix. Finally, the effectiveness of theoretical results can be illustrated via three illustrative examples.

This article investigates the stability analysis and stabilization problems for fractional-order T–S fuzzy systems via fuzzy Lyapunov function method. A membership-function-dependent fuzzy Lyapunov function instead of the general quadratic Lyapunov function is employed to obtain the stability and stabilization criteria. Different from the general quadratic Lyapunov function, the fuzzy Lyapunov functions contain the product of three term functions. Since the general Leibniz formula cannot be satisfied for fractional derivative, the current results on the fractional derivative for the quadratic Lyapunov functions cannot be extended to the fuzzy Lyapunov functions. Therefore, to estimate the fractional derivative of fuzzy Lyapunov functions, the fractional derivative rule for the product of three term functions is proposed. Based on the proposed fractional derivative rule, the corresponding stability and stabilization criteria are established, which extend the existing results. Finally, two simulation examples are presented to illustrate the effectiveness of the proposed theoretical analysis.

An event-triggered sliding-mode control problem is investigated for a class of multiple-input Takagi-Sugeno (T-S) fuzzy systems via designing a linear switching function. An assumption that all local linear systems share a common input matrix is removed. Then, a novel event-triggered sliding-mode controller with asynchronous premise variables is designed, which can ensure that the trajectory of multiple-input T-S fuzzy systems can be driven onto the region near the sliding surface after finite time. A sufficient condition is established to guarantee the stability of sliding motion, and the sliding-mode controller gain is obtained by solving a set of linear matrix inequalities. The positive lower bound of the interexecution time can be ensured, which means that there is no Zeno phenomenon. In the end, the advantages and effectiveness of the theoretical results are illustrated by two examples.

This paper is centered upon the state estimation for delayed genetic regulatory networks. Our aim is at estimating the concentrations of mRNAs and proteins by designing reduced-order and full-order state observers based on available network outputs. We introduce a Lyapunov-Krasovskii functional including quadruplicate integrals, and estimate its derivative by employing the Wirtinger-type integral inequalities, reciprocal convex technique, and convex technique. From which, delay-dependent sufficient conditions, in the form of linear matrix inequalities (LMIs), are investigated to ensure that the resultant error system is asymptotically stable. One can verify these conditions by utilizing the MATLAB Toolboxes LMI or YALMIP. In addition, the gains of reduced-order and full-order observers are represented by the feasible solutions of the LMIs, and thereby, the concrete expressions of the desired reduced-order and full-order state observers are presented. Finally, the simulation results of a numerical example are demonstrated, which explains the validity of the proposed method.

This paper is concerned with the finite-time stability problem of the delayed genetic regulatory networks (GRNs) with reaction-diffusion terms under Dirichlet boundary conditions. By constructing a Lyapunov-Krasovskii functional including quad-slope integrations, we establish delay-dependent finite-time stability criteria by employing the Wirtinger-type integral inequality, Gronwall inequality, convex technique, and reciprocally convex technique. In addition, the obtained criteria are also reaction-diffusion-dependent. Finally, a numerical example is provided to illustrate the effectiveness of the theoretical results.