Fuzzy Time-delay Systems Research Articles

Admissible control for a singular T-S fuzzy time-delay system: application to a truck-trailer system

Admissible control for a singular T-S fuzzy time-delay system: application to a truck-trailer system

Stability and Stabilization of T–S Fuzzy Time-Delay Systems Under Sampled-Data Control via New Asymmetric Functional Method

This paper studies the stability and stabilization of Takagi-Sugeno (T-S) fuzzy time-delay systems under sampleddata control via a new asymmetric Lyapunov-Krasovskii functional (LKF) method. The method improves the common symmetric basic functional term. Besides, we improve the loopedfunctional term and the discontinuous functional term through combining the integral about time delay and each sampling interval, respectively. Based on the above new approaches, we present the stability and stabilization results with less conservativeness than the literature through linear matrix inequalities (LMIs). In the process, we introduce a simplification approach for stabilization of sampled-data control, which effectively reduces the computational complexity of results. At last, we provide three examples to verify the effects and advantages of our results.

Dynamic event-triggered fuzzy non-fragile control of DC microgrids

This paper studies the event-triggered fuzzy non-fragile control of uncertain DC microgrids subject to false data injection (FDI) attacks, controller saturation, network delays and premise mismatching. Firstly, a dynamic event-triggered mechanism (ETM) is proposed, which can save more communication bandwidth than the static ETMs, and remove the complex Zeno-free computation required by the continuous-time ETMs. Secondly, a fuzzy time-delay closed-loop system model is established, which provides a unified framework to study the effects of the dynamic ETM, FDI attacks, uncertainties, saturation, delays and premise mismatching. Thirdly, mean-square exponential stability criteria are established, and co-design method for the saturated fuzzy non-fragile (SFNF) controller and the dynamic ETM is presented. Simulation results confirm that the SFNF controller can stabilize the unstable DC microgrid, while the dynamic ETM significantly reduces the triggering rate by 84.98%. Comparisons show that the proposed controller performs better than the non-fragile controller, fuzzy controller and robust linear controller, and the dynamic ETM achieves a lower triggering rate than the static ETMs.

Finite-time stability of mild solution to time-delay fuzzy fractional differential systems under granular computing

Finite-time stability of mild solution to time-delay fuzzy fractional differential systems under granular computing

Cooperative Fault Diagnosis of Fuzzy Fractional Order Time-Varying Multi-Agent System With Directed Networks

This brief focuses on the cooperative fault diagnosis of fuzzy time-delay fractional order multi-agent system (FOMAS) over directed networks, whose fractional order belongs to (0, 1). Due to the interconnections, for each agent’s estimator, when estimating the local state and error parameters, whose purpose is to further consider faulty effects on others. Firstly, by the interconnection relationships between each agent, a new formulation scheme is proposed so that the shared signals are achieved by correctly constructing auxiliary graphs of a directed network. Then, unlike the existed papers dealing with normal fuzzy multi-agent systems, new admissible criteria of fuzzy FOMASs are proposed with time-varying. Finally, to illustrate the method proposed above is available, a practical application example of unmanned aerial vehicles is given.

An exponential stabilization criterion for switched delayed interval type-2 fuzzy systems under admissible edge-dependent average dwell time mechanism

This paper addresses the exponential stabilization of the switched interval type-2 fuzzy (IT-2F) time-delay systems under admissible edge-dependent average dwell time (AEDADT) scheme with a non-fragile memory state feedback controller. The IT-2F model depicts uncertain nonlinear systems where the lower and upper membership functions characterize the uncertain parameters. Unlike the previous works that relied on average dwell time (ADT), this work employs the concepts of slow switching and fast switching based on the AEDADT property for both stable and unstable modes. The main reason behind the integration is that fast switching has a great feature in restricting the unstable subsystems. Furthermore, in most nonlinear systems, the feedback control rate is realized by memoryless state feedback control. However, a time lag occurs between system state and control response. Therefore, a non-fragile memory state feedback controller is chosen to ensure the globally uniformly exponential stability condition for proposed nonlinear systems through the linear matrix inequalities (LMI) approach. A mode-dependent average dwell time (MDADT) switching scheme is compared with the described switching rule and derived the superiority of obtained results. The results demonstrate that the AEDADT switching rule is more flexible and achieves tighter bounds than the MDADT property. Finally, numerical simulations and comparisons are provided to illustrate the capability of proposed theoretical results.

Interval type-2 fuzzy decentralised event-triggered H ∞ control for nonlinear interconnected systems with time delays

This paper studies the interval type-2 fuzzy decentralised event-triggered control design problem for the nonlinear time-delay interconnected systems. The considered plant is first represented by an interval type-2 Takagi-Sugeno (IT2 T-S) fuzzy time-delay interconnected system and then an event-triggered mechanism is established through using the sampled states. By using the PDC algorithm, a fuzzy decentralised event-triggered controller is developed. Furthermore, the asymptotic stable conditions with a performance of closed-loop system are obtained, which are formulated in the form of linear matrix inequalities. Finally, an example of the nonlinear Tuned Mass Damper system with time delays is given to illustrate the effectiveness of the proposed fuzzy decentralised controller.

Stability Analysis and Robust Stabilization of Uncertain Fuzzy Time-Delay Systems

New sufficient conditions for delay-independent and delay-dependent robust stability of uncertain fuzzy time-delay systems based on uncertain fuzzy Takagi-Sugeno (T-S) models are presented by using the properties of matrix and norm measurements. Further sufficient conditions are formulated, in terms of the linear matrix inequalities (LMIs) of robust stabilization, and are developed via the technique of parallel distributed compensation (PDC), and then the simplification of the conditions for the controller design of uncertain fuzzy time-delay systems. The proposed methods are simple and effective. Some examples below are presented to illustrate our results.

Fault-tolerant control for delayed interval type-2 fuzzy systems with nonlinear fault input

This paper addresses the stabilization of Takagi-Sugeno (T-S) fuzzy systems with time delay. In particular, the control system with parameter uncertainties are modeled through an interval type-2 (IT2) T-S fuzzy model, in which the uncertainties are handled via lower and upper membership functions. By developing some new techniques, a fault-tolerant controller is designed to ensure that the closed-loop fuzzy time-delay system is asymptotically stable with nonlinear fault input. Finally, a numerical example that demonstrate the effectiveness of the proposed conditions are provided.

One scheme of stabilization and sample-data control for T-S fuzzy time-delay systems

In this article, a refined Lyapunov functional is proposed to study the stabilization problem for Takagi-Sugeno (T-S) fuzzy systems with time delays. Considering both the time-varying delays of the system and the constant delays of the part of sample-data control loop, the refined Lyapunov function in this paper makes it more practical in actual sampling control pattern compared with some existing research. Some techniques of dealing the linear matrix inequalities (LMIs) are used to derive the less conservative criteria and an example is presented in the end to prove the availability of the work.

Consensus-Based Estimation for Type-2 Fuzzy Time-Delay Systems Under Deception Attacks and Partial Information Exchange

This paper addresses the problem of consensus-based state estimation for interval type-2 Takagi–Sugeno (T–S) fuzzy time-delay systems over a wireless sensor network under deception attacks, partial information exchange and switching sensor-network topologies. The switching-topology-dependent estimators are constructed using interval type-2 fuzzy models considering the cases where the premise variables are available and unavailable. By means of the mode-dependent dwell time approach, sufficient conditions are established such that the estimation error system is exponentially and ultimately bounded. In addition, a fuzzy Lyapunov functional is utilized to derive the existence conditions of estimators for the case that the premise variable are unavailable. Two illustrative examples are provided to verify the effectiveness of the proposed method.

Stabilization of T-S fuzzy fractional rectangular descriptor time-delay system

This paper focuses on the stabilization of the T-S fuzzy fractional rectangular descriptor time-delay system. To convert the fuzzy rectangular time-delay system into the fuzzy square time-delay system, a suitable dynamic compensator of proportional and derivative type is constructed, and the admissibility of the resultant square closed-loop system is enough to guarantee the stabilization of the nonlinear rectangular descriptor time-delay system. A sufficient condition is derived to ensure the stabilization for the considered system and the dynamic compensator parameters can be computed by solving the corresponding linear matrix inequalities (LMIs). A numerical example is provided to manifest the theoretical result.

Fault Detection and Isolation of T–S Fuzzy Systems with Time-Delay Using Geometric Approach

This paper investigates the fault detection and isolation problem for Takagi–Sugeno fuzzy time-delay systems under the framework of geometric method. First, the geometric concept of unobservability subspace is introduced and the algorithm for constructing the subspace is presented. Then, based on the above algorithm, the faults are divided into the different unobservability subspaces, and the reduced-order subsystems set corresponding to the fault set is constructed according to the geometrical properties of factor space and canonical projection. Finally, a set of structured residuals which are sensitive to a single fault and decoupled from other faults is established by designing an observer for the subsystems. In addition, $$H_\infty$$ performance is introduced to attenuate the effects of disturbances and error signals caused by a time-varying delay on the residual. Simulation example verifies the effectiveness of the proposed method.

Stability and control of fuzzy time delay systems with unmatched preconditions

The stability and control of nonlinear time-delay systems of Takagi-Sugeno (T-S) fuzzy model are studied in this paper. The integral inequality of a free weight matrix is chosen to give a less conservative delay-dependent stability criterion in the form of linear matrix inequalities (LMIs). The premise mismatch strategy is applied, it is combined with Finsler lemma, a more flexible design method of fuzzy state feedback controller is proposed. This method does not require the controller and system to share the common premise membership function and the number of rules. The controller design strategy proposed in this paper can effectively solve the control problem of fuzzy systems when the number of state variables is not equal to the number of input variables (r≠c), or mi⁢(x⁢(t))≠hi⁢(x⁢(t)),i=1,2,…,r. Finally, two simulation examples are given to prove the advancement and effectiveness of the proposed theory.

Passive control of a class of fuzzy time-delay systems

In this paper, it is studied the passive control of a class of fuzzy systems with state uncertainty and time-delay. First, a class of nonlinear systems is described by using T-S fuzzy model with uncertain items and time-delay ; Secondly, by using the linear matrix inequality technique(LMI) and designing the state feedback controller, we can obtain the feedback gain matrix , the robust stability of the closed-loop system is achieved by using Lyapunov’s stability theory, at the same time, it is realized the sufficient conditions for passive control of the system. Finally, the feasibility and validity of the results are verified by simulation examples.

Stability and Stabilization of T–S Fuzzy Time-Delay System via Relaxed Integral Inequality and Dynamic Delay Partition

This article investigates delay-dependent stability analysis and stabilization for continuous Takagi–Sugeno fuzzy systems with a time-varying delay. By employing dynamic delay partition, the delay interval <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$[0, d(t)]$</tex-math></inline-formula> is partitioned into some variable subintervals so that much more information of time-varying delay can be utilized. Moreover, a novel relaxed integral inequality is applied to estimate the derivative of Lyapunov–Krasovskii functionals for achieving reduction of estimation gap. As a result, several further robust stability and stabilization criteria with less conservativeness are proposed. Finally, three examples are provided to demonstrate the effectiveness and advantages of the presented methods.

Non-fragile sampled-date dissipative analysis for uncertain T–S fuzzy time delay system with actuator saturation

In this paper, non-fragile fuzzy sampled-data control is used to analyze the dissipation of uncertain time-varying delay T–S fuzzy system under actuator saturation. First, this paper builds a novel augmented Lyapunov–Krasovskii functional that is more flexible. It involves complete information about the relevant sampled-data patterns. Second, the use of Wirtinger-based integral inequality and Newton–Leibniz formulas yields less conservative results. Next, we discuss the sufficient conditions of the dissipative performance for T–S model, then use the linear matrix inequality (LMI) to give the non-fragile fuzzy sampled-data controller with actuator saturation. Finally, the routine examples show that the advanced approach is effective and feasible and has certain advantages.

Finite-Time Control for Nonlinear Systems with Time-Varying Delay and Exogenous Disturbance

This paper is concerned with the problem of finite-time control for nonlinear systems with time-varying delay and exogenous disturbance, which can be represented by a Takagi–Sugeno (T-S) fuzzy model. First, by constructing a novel augmented Lyapunov–Krasovskii functional involving several symmetric positive definite matrices, a new delay-dependent finite-time boundedness criterion is established for the considered T-S fuzzy time-delay system by employing an improved reciprocally convex combination inequality. Then, a memory state feedback controller is designed to guarantee the finite-time boundness of the closed-loop T-S fuzzy time-delay system, which is in the framework of linear matrix inequalities (LMIs). Finally, the effectiveness and merits of the proposed results are shown by a numerical example.

Improved Delay-Range-Dependent Stability Condition for T–S Fuzzy Systems with Variable Delays Using New Extended Affine Wirtinger Inequality

In this paper, a new integral inequality lemma along with an appropriate Lyapunov–Krasovskii functional (LKF) is proposed for fuzzy time-delay system to enhance the delay upper bound estimate. The proposed lemma is referred to hereafter as Extended Affine Wirtinger inequality. The novelty of the lemma is twofold, it has the ability to integrate uncertain delay information utilizing the convex combination of certain and uncertain delay intervals involved in the proposed LKF, and it is compatible to derive delay-range-dependent (DRD) stability conditions for continuous time Takagi–Sugeno (T–S) fuzzy time-delay system. One noteworthy advantage of the proposed stability condition in a linear matrix inequality (LMI) framework is that it requires less number of matrix variables compared to the existing integral inequalities of the similar type, thus reducing the computational burden too. The efficacy of the proposed DRD stability condition over existing conditions is validated numerically by solving three examples related to fuzzy time-delay system.

Design of an Observer-based Controller for the T-S Fuzzy Time-delay Systems under the Imperfect Premise Matching

Design of an Observer-based Controller for the T-S Fuzzy Time-delay Systems under the Imperfect Premise Matching