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This paper presents a new asymmetric Lyapunov-Krasovskii functional (LKF) method on the stability and stabilization of Takagi-Sugeno (T-S) fuzzy systems with time delay. For the reduction of conservativeness, combining the method with membership-function-dependent approach, we propose a novel delay-dependent stability condition in the form of linear matrix inequalities (LMIs). Based on the condition, we further obtain a novel condition of stabilization. At the end, we provide two numerical examples to verify the advantage of the stability and stabilization approaches, respectively.

This paper discusses consensus tracking issue for multi-agent systems (MASs), and the purpose is to develop a fixed-time consensus proposal by fuzzy adaptive method. To this end, we first set up a more general fixed-time stability criterion. By using the proposed stability criterion, a backstepping design procedure is presented to construct the fixed-time fuzzy adaptive controller. The suggested fuzzy adaptive control protocol guarantees that 1) for each agent its closed-loop signals keep bounded; 2) the consensus tracking error tends to a small region around origin in fixed time. In addition, the virtual control signals are constructed to be the piecewise functions to prevent the singularity of their derivatives. Curve fitting method is used such that the designed virtual control signals are derivable at the point of partition. At last, numerical simulation further checks the validity of the suggested control strategy.

This article is aimed at developing a finite-time adaptive fuzzy control strategy for a class of nonlinear strict-feedback systems. For the first time, a fast finite-time practical stability criteria is set up, which provides an effective approach to address the finite-time adaptive fuzzy control design. Furthermore, a systematic finite-time adaptive fuzzy control design procedure is developed by embedding that practical stability criteria. The closed-loop stability analysis shows that the tracking error converges to a small region around the origin in finite time. Meanwhile, all the signals in the closed-loop system are bounded. At last, the presented results are tested by a numerical example.

This article studies the problem of the fuzzy $H_{\infty }$ filter design for nonlinear networked control systems through event-triggered communication (ETC) scheme. First, a novel adaptive ETC scheme is given to determine whether the sampled measurement output should be released to communication network or not. Consequently, less communication resources are occupied under the desired $H_{\infty }$ performance. Second, augmented fuzzy line-integral Lyapunov function is introduced in the $H_{\infty }$ performance analysis of filter error systems, such that the information of time derivative of membership functions are fully considered to reduce the conservativeness of networked fuzzy filter design. Different from the existing results, the upper bounds of time derivative of membership functions need not to be known prior. Third, the resulting filter error system is modeled as time-delay system under ETC mechanism and asynchronous premise in a unified framework. As a result, applying Lyapunov theory and inequality technique, new sufficient condition is obtained to meet the $H_{\infty }$ performance for the filter error systems. Further, the corresponding filter and event-triggering parameters are codesigned and solved by a set of linear matrix inequalities. Finally, two examples are offered to demonstrate the advantage of the proposed method.

This paper considers the problems of designing a robust observer and developing a backstepping-based adaptive fuzzy control scheme for a class of strict-feedback systems, in which the virtual control coefficients are unknown. By using convex combination method, a robust fuzzy observer has been constructed to estimate the unmeasurable system state variables. Further, an observer-based adaptive fuzzy control scheme has been proposed. During the controller design procedure, fuzzy logic systems are used to model the unknown nonlinear functions, adaptive technique and backstepping are combined to construct the ideal virtual and the real laws. The proposed adaptive fuzzy output feedback controller guarantees that the tracking error converges to a small neighborhood of the origin and all the signals in the adaptive closed-loop system are bounded. Simulation results are provided to demonstrate the effectiveness of the presented approach.

This paper addresses the finite-time tracking problem of nonlinear pure-feedback systems. Unlike the literature on traditional finite-time stabilization, in this paper the nonlinear system functions, including the bounding functions, are all totally unknown. Fuzzy logic systems are used to model those unknown functions. To present a finite-time control strategy, a criterion of semiglobal practical stability in finite time is first developed. Based on this criterion, a novel adaptive fuzzy control scheme is proposed by a backstepping technique. It is shown that the presented controller can guarantee that the tracking error converges to a small neighborhood of the origin in a finite time, and the other closed-loop signals remain bounded. Finally, two examples are used to test the effectiveness of proposed control strategy.

Adaptive fuzzy control via command filtering is proposed for uncertain strict-feedback nonlinear systems with unknown nonsymmetric dead-zone input signals in this paper. The command filtering is utilized to cope with the inherent explosion of the complexity problem of the classical backstepping method, and the error compensation mechanism is introduced to overcome the drawback of the dynamics surface approach. In addition, by utilizing the bound information of dead-zone slopes, a new adaptive fuzzy method that does not need to establish the inverse of the dead zone is presented for the unknown nonlinear systems. Compared with existing results, the advantages of the developed scheme are that the compensating signals are designed to eliminate the filtering errors and only one adaptive parameter is required, which will make the proposed control scheme more effective for practical systems. An example of position tracking control for the electromechanical system is given to demonstrate the usefulness and potential of the new design scheme.

This paper focuses on the problem of adaptive fuzzy control for a class of nonlinear systems without a strict-feedback form. A new adaptive fuzzy control scheme is proposed for nonlinear delayed systems with unknown dead-zone nonlinearity. Control design is achieved by introducing a variable separation approach and employing the unique structural property of fuzzy logic systems. The proposed adaptive fuzzy controller guarantees that all the closed-loop signals are semiglobally uniformly ultimately bounded, and the tracking error converges to a small neighborhood of the origin. Two simulation examples illustrate the effectiveness of the proposed approach.

This paper focuses on the fuzzy-H∞-filter-design problem for Takagi-Sugeno (T-S) fuzzy systems with interval time-varying delays. Two cases of the time-varying delays are considered: 1) The delays are differentiable and have both the lower and upper bounds of the delay derivatives, and 2) the delays are bounded but not necessary to be differentiable. Since we employ a new fuzzy Lyapunov-Krasovskii functional (LKF) and estimate a tighter upper bound of its derivative, the proposed delay-derivative-dependent bound-real-lemma (BRL) condition has advantages over some previous results in that it enlarges the application scope but has less conservatism, which is established theoretically. The BRL condition that depends on both the upper and lower bounds of the delay derivatives is derived. Then, based on the aforesaid BRL, a new fuzzy H∞ filter scheme is proposed, and a sufficient condition for the existence of such a filter is established in terms of linear-matrix inequalities (LMIs). Finally, some numerical examples and an application to the truck-trailer system are utilized to demonstrate the effectiveness and reduced conservatism of our results.

This paper focuses on the problem of adaptive control for a class of nonlinear time-delay systems with unknown nonlinearities and strict-feedback structure. Based on the Lyapunov-Krasovskii functional approach, a state-feedback adaptive controller is constructed by backstepping. The proposed adaptive controller guarantees that the system output converges into a small neighborhood of the reference signal, and all the signals of the closed-loop system remain bounded. Compared with the results that exist, the main advantage of the proposed method is that the controller design is independent of the choice of the fuzzy-membership functions; therefore, a priori knowledge of fuzzy approximators is not necessary for control design, and the proposed approach requires only one adaptive law for an nth-order system. Two numerical examples are used to illustrate the effectiveness of the proposed approach.

This paper is concerned with the Hinfin filter design for nonlinear systems with time-varying delay via Takagi-Sugeno fuzzy model approach. Delay-dependent design method is proposed in terms of linear matrix inequalities (LMIs), which forms the main contribution of this paper. The main technique used is the free-weighting matrix method combined with a matrix decoupling approach. The results for rate-independent case, delay-independent case, and delay-free case are also given as easy corollaries. An illustrative example is given to show the effectiveness of the present method.

This paper discusses the stabilization of Takagi-Sugeno (T-S) fuzzy systems with bounded and time-varying input delay. The robust stabilization via state feedback is first addressed, and delay-dependent stabilization conditions are proposed in terms of LMIs. Observer-based feedback stabilization is also discussed for T-S fuzzy input delay systems without uncertainties. A separate design principle is developed. Some illustrative examples are given to show the effectiveness and the feasibility of the proposed methods.

This paper addresses the problem of observer-based Hinfin control for nonlinear systems with time-varying delay represented by Takagi-Sugeno (T-S) fuzzy model. It presents a single-step linear matrix inequality (LMI) method for the fuzzy control design, which overcomes the drawback of the two-step LMI approach often encountered in the literature. The derivation relies mainly on a proposed matrix decoupling technique using which a resultant matrix inequality can be equivalently converted to strict LMIs. When restricted to delay-free fuzzy systems, the present results improve or reduce to existing ones. Illustrative examples show the effectiveness and merits of the present results.

This paper studies a class of fuzzy time-delay descriptor systems in the extended Takagi-Sugeno (T-S) fuzzy model. Sufficient conditions are derived for the stability and stabilization in terms of linear matrix inequalities (LMIs). Illustrative examples are given to show the effectiveness and the advantages of the present results

In view of a recent new application of variable structure control (VSC) to the stabilization problem for Takagi-Sugeno (T-S) fuzzy models, this paper aims to study the stabilization of uncertain fuzzy time-delay systems in T-S fuzzy model via VSC approach. There are mainly two features in this paper: one lies in the incorporation of time-delays (both smooth and nonsmooth delays) in which case Lyapunov functionals and Razumikhin Theorem are required to solve the stabilization problem; the other feature is that not only matched uncertainties but also mismatched uncertainties in the state variables are considered. As a sequence, the contribution of this paper consists of various control schemes proposed for the VSC design and the present results are in terms of linear matrix inequalities (LMIs). An illustrative example is given to show the effectiveness of our various results.