Fuzzy Time-delay Systems Research Articles

Design of an Observer-Based Controller for T-S Fuzzy Time-Delay Systems under Imperfect Premise Matching

Design of an Observer-Based Controller for T-S Fuzzy Time-Delay Systems under Imperfect Premise Matching

Finite-time Control for Takagi-Sugeno Fuzzy Systems with Time-varying Delay

This paper focuses on the problem of finite-time control for Takagi-Sugeno (T-S) fuzzy systems with time-varying delay and norm-bounded disturbance. By constructing a new augmented Lyapunov-Krasovskii functional, a delay-dependent finite-time boundedness criterion is derived for the T-S fuzzy time-delay system by aid of the auxiliary function-based integral inequalities and the reciprocally convex combination technique. Then, based on the parallel distributed compensation scheme, a state feedback controller is designed to ensure finite-time boundness of the closed-loop T-S fuzzy system, which can be obtained by solving a set of linear matrix inequalities (LMIs). Finally, two numerical examples are given to demonstrate the effectiveness and advantages of the proposed results.

Observer-Based Sliding Mode Control for Uncertain Fuzzy Systems via Event-Triggered Strategy

This paper investigates the problem of sliding mode observer design for a class of uncertain fuzzy time-delay systems based on an event-triggered strategy. The objective is to design an event-triggered mechanism by utilizing the information of system output and observer function. Based on the delay partitioning method and the Lyapunov–Krasovskii function approach, delay-dependent sufficient conditions are proposed to guarantee the overall system, including sliding mode dynamics and error dynamics, to be asymptotically stable with an $\mathcal {H}_{\infty }$ performance. Furthermore, an event-triggered sliding mode controller is synthesized to ensure that the system dynamics can be driven to the sliding region near the equilibrium point in finite time. Finally, a verification example is provided to demonstrate the feasibility and efficiency of the theoretical results presented.

Robust fuzzy stabilization of nonlinear time-delay systems subject to impulsive perturbations

This paper is concerned with robust stabilization problem of Takagi–Sugeno (T-S) fuzzy time-delay systems subject to impulsive perturbations. New results on robust stabilization via parallel distributed compensation (PDC) control are derived. First, based on the impulse-type Razumikhin–Lyapunov method combined with the use of an impulse-time-dependent Lyapunov function, a new exponential stability criterion for T-S fuzzy time-delay system with impulsive effects is obtained. The proposed stability criterion removes the restrictive condition on the relationship between the size of time-delay and lower bound of impulse intervals imposed by the previous results. Then, by employing a convex relaxation technique, a sufficient condition for the constructing the PDC controllers is presented, which is expressed in terms of linear matrix inequalities (LMIs). Next, the robust stabilization problem for the T-S system with slowly time-varying delay is studied. A different stabilization condition is derived via an impulse-time-dependent Lyapunov functional, which is less conservative than the former when the state delay is constant. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed analysis and design techniques.

Improved Delay-Dependent Stability and Stabilization Conditions of T-S Fuzzy Time-Delay Systems via an Augmented Lyapunov-Krasovskii Functional Approach

This paper develops some improved stability and stabilization conditions of T-S fuzzy system with constant time-delay and interval time-varying delay with its derivative bounds available, respectively. These conditions are presented by linear matrix inequalities (LMIs) and derived by applying an augmented Lyapunov-Krasovskii functional (LKF) approach combined with a canonical Bessel-Legendre (B-L) inequality. Different from the existing LKFs, the proposed LKF involves more state variables in an augmented way resorting to the form of the B-L inequality. The B-L inequality is also applied in ensuring the positiveness of the constructed LKF and the negativeness of derivative of the LKF. By numerical examples, it is verified that the obtained stability conditions can ensure a larger upper bound of time-delay, the larger number of Legendre polynomials in the stability conditions can lead to less conservative results, and the stabilization condition is effective, respectively.

Event-Triggered Control for Networked Switched Fuzzy Time-Delay Systems with Saturated Inputs

For a class of fuzzy networked switched time-delay systems, event-triggered control approach is given. The saturated controllers are developed. By using Lyapunov–Krasovskii functional method and linear matrix inequalities (LMIs) theory, the exponential stability of fuzzy networked time-delay systems is proved. To obtain the control gain matrices and observe gain matrices, a separate design principle is proposed. At last, two numerical examples prove the feasibility of the proposed approach and conditions.

Local stability conditions for T-S fuzzy time-delay systems using a homogeneous polynomial approach

Local stability conditions for time-delay T-S fuzzy systems are proposed by use of a homogeneous polynomial approach. Lesser conservatism can be expected based on the derived stability criteria due to the following three factors: a) a new fuzzy Lyapunov-Krasovskii functional is constructed, which contains a homogeneous polynomially parameter-dependent matrix of degree 2; b) the off-diagonal matrix in Reciprocal Convexity lemma is extended to a homogeneous polynomially parameter-dependent matrix; and c) local stability conditions for time-delay T-S fuzzy systems are proposed to overcome the difficulty of dealing with the time derivative of membership functions. Finally, two numerical examples illustrate the effectiveness of the proposed methods.

Finite-time control for interval type-2 fuzzy time-delay systems with norm-bounded uncertainties and limited communication capacity

This paper investigates the finite-time stabilization problem for interval type-2 T-S fuzzy systems with norm-bounded uncertainties and time-varying delays. A static output feedback controller is designed to guarantee the finite-time stability of closed-loop fuzzy control systems. Data packet loss is assumed to exist in the feedback transmission channel, and a novel delay product-type Lyapunov–Krasovskii function is constructed for deriving the delay-dependent stabilization conditions. These conditions can be denoted by linear matrix inequalities, according to matrix decoupling techniques and inequality constriction methods. The information of the upper and lower membership functions is integrated into the stabilization conditions using a membership function-dependent analysis method to reduce conservativeness. The simulation results demonstrate the effectiveness of the proposed finite-time control method.

Robust mixed performance for uncertain Takagi-Sugeno fuzzy time-delay systems with linear fractional perturbations

The robust mixed H2/H∞ performance for Takagi-Sugeno (T-S) fuzzy systems with time delay and linear fractional perturbations is considered in this paper. Some delay-dependent conditions have been proposed to guarantee the mixed performance of uncertain fuzzy time-delay systems. The LMI optimisation approach is used to find the minimisation of H2 performance measure. Some numerical simulations are illustrated to show the significant improvement over some previous results.

Robust mixed performance for uncertain Takagi-Sugeno fuzzy time-delay systems with linear fractional perturbations

The robust mixed H2/H∞ performance for Takagi-Sugeno (T-S) fuzzy systems with time delay and linear fractional perturbations is considered in this paper. Some delay-dependent conditions have been proposed to guarantee the mixed performance of uncertain fuzzy time-delay systems. The LMI optimisation approach is used to find the minimisation of H2 performance measure. Some numerical simulations are illustrated to show the significant improvement over some previous results.

Sampled-data Robust H∞ Control for T-S Fuzzy Time-delay Systems with State Quantization

This paper investigates the sampled-data robust H∞ control for T-S fuzzy time-delay systems with state quantization. Based on a modified Lyapunov-Krasovskii function(LKF), which is fully considered the characteristics of sample-data and state quantization, a sample-data and state quantized controller is designed. By introducing the free weighting matrices, some integral techniques and modified inequalities, the results in this paper are less conservative than other existing results. At the end of the paper, two examples are given to show the effectiveness and superiority of the proposed methods.

Delay-Dependent Admissibility Analysis and Dissipative Control for T-S Fuzzy Time-Delay Descriptor Systems Subject to Actuator Saturation

In this paper, a delay-dependent admissibility analysis method and dissipative controller design are developed for a class of nonlinear time-delay descriptor systems subject to actuator saturation and L 2 -disturbances via a Takagi-Sugeno (T-S) fuzzy model. A less conservative admissible condition is first derived under which the system is not only regular, impulse free but also stable under certain initial conditions. The method can eliminate the impulsive behavior of a descriptor system so as to ensure the existence and uniqueness of solutions. The estimate of attraction domain is also determined in which the admissible initial states converge asymptotically to the origin. The disturbance attenuation capability is studied by designing the dissipative fuzzy controller such that the closed-loop system is admissible and holds the dissipative performance for the prescribed disturbance attenuation level and L 2 -disturbances. The method is more suitable for admissibility analysis and robust control synthesis. Moreover, H ∞ control processes can be achieved in the same design process, which shows that the cost and time may potentially be reduced when a controller is designed for an actual physical system. Simulations are performed to validate the proposed methods and illustrate the decrease in conservativeness for a classic nonlinear system based on the T-S fuzzy time-delay descriptor model under actuator saturation and L 2 -disturbances. The study seeks to establish a foundation for investigating the control synthesis of T-S fuzzy time-delay descriptor systems subject to actuator saturation.

H<sub>∞</sub> disturbance attenuation of nonlinear networked control systems via Takagi-Sugeno fuzzy model

H∞ disturbance attenuation of nonlinear networked systems which are described by the Takagi-Sugeno fuzzy time-delay systems is concerned. In the networked control system, the control signal is delayed and the closed-loop system with the controller can be modeled as a fuzzy system with time-varying delays in sensor and actuator nodes. The system often encounters the external noises that disturb its behaviors. For such a nonlinear system with delays, the H∞ disturbance attenuation problem is considered. Multiple Lyapunov-Krasovskii function with multiple integral functions allows us to obtain less conservative conditions for a networked control system to satisfy the disturbance attenuation criterion. Based on this approach, a novel control design method for a networked control system is proposed. An illustrative example is given to show the effectiveness of the proposed method.

Delay dependent stability analysis of Takagi-Sugeno fuzzy time-delays system

Generally, nonlinearities and time-delays are inherent characters for the Takagi-Sugeno fuzzy system. There has been a lot of research works dealing with this type of systems. Most of these researches are based on measurable states but not all states are available in many physical systems. When such case happens, an observer is designed to estimate the system unavailable states. This work addresses the problem of stability analyses and stabilisation for the Takagi-Sugeno fuzzy system with time-delays. Motivated by recent concerns in stability issues, a stabilisation observer controller for Takagi-Sugeno fuzzy time-delay systems is re-evaluated in this paper. Based on the fuzzy weighting dependent Lyapunov-Krasovskii function approach, we provided, in terms of linear matrix inequalities, the sufficient conditions for the existence of a robust state feedback parallel distributed compensation controller that guarantees stability and finding the maximum delay bounds. The effectiveness and the applicability of the designed stabilisation controller are illustrated via the truck trailer systems.

Delay dependent stability analysis of Takagi-Sugeno fuzzy time-delays system

Generally, nonlinearities and time-delays are inherent characters for the Takagi-Sugeno fuzzy system. There has been a lot of research works dealing with this type of systems. Most of these researches are based on measurable states but not all states are available in many physical systems. When such case happens, an observer is designed to estimate the system unavailable states. This work addresses the problem of stability analyses and stabilisation for the Takagi-Sugeno fuzzy system with time-delays. Motivated by recent concerns in stability issues, a stabilisation observer controller for Takagi-Sugeno fuzzy time-delay systems is re-evaluated in this paper. Based on the fuzzy weighting dependent Lyapunov-Krasovskii function approach, we provided, in terms of linear matrix inequalities, the sufficient conditions for the existence of a robust state feedback parallel distributed compensation controller that guarantees stability and finding the maximum delay bounds. The effectiveness and the applicability of the designed stabilisation controller are illustrated via the truck trailer systems.

Local stabilization for discrete-time T–S fuzzy time-delay systems with sensor fault

This paper focuses on a local stabilization problem for discrete-time T–S fuzzy time-delay systems with sensor fault and external disturbances. The main purpose is to synthesize a controller such that the state can be restricted into a pre-specified region even when the system is subject to sensor fault and external disturbance. First, by restricting the reachable set into an ellipsoid set which is contained in the objective domain, the system state is restricted into the objective area such that the local stabilization can be achieved. Second, the differential mean value theorem is used to determine the bound of the deviation between the membership function of the system and that of the controller. Then, the information of the deviation is employed for designing the controller. Different from some existing methods, in the proposed method, the influence of the sensor fault on the membership function of the controller has been fully considered and the information of aforementioned deviation is made full use of such that a less conservative stability criterion can be derived. Meanwhile, due to the use of the differential mean value theorem, the deviation bound can be calculated. Then, the requirement, where the deviation bound of is assumed to be previously known, is removed. Finally, an example is presented to verify the effectiveness of the proposed method.

<inline-formula> <tex-math notation="LaTeX">$H_{\infty }$</tex-math> </inline-formula> Stabilization for Polynomial Fuzzy Time-Delay System: A Sum-of-Squares Approach

The $H_{\infty }$ stabilization problem for polynomial fuzzy time-delay system (PFTDS) is investigated in this paper. First, a polynomial fuzzy controller is proposed to stabilize the PFTDS. Based on Euler's homogeneity relation, homogeneous polynomial Lyapunov–Krasovskii functional, and the developed polynomial slack variable matrices, a novel stabilization condition without the assumption in common use is presented in terms of sum-of-squares (SOS). In order to reduce the conservative and implementation cost, the property of membership function, and the right-hand side technique are adopted. Also, two relaxed $H_{\infty }$ stabilization conditions for PFTDS, which may or may not share the same fuzzy rules, are proposed. To illustrate the feasibility and merit of the proposed result, three examples are provided. In the first example, a well-known Takagi–Sugeno fuzzy time-delay system is demonstrated to show that the proposed SOS-based methods can provide a longer allowable delay time than do some existing linear matrix inequality based methods. The second and third examples show the validity and feasibility of the proposed results for PFTDS with the same or fewer rule numbers of the polynomial fuzzy controller.

Membership-Function-Dependent Stability and Stabilization Conditions for T–S Fuzzy Time-Delay Systems

ABSTRACTIn this paper, the stability analysis and stabilization of time-delay nonlinear systems represented by a Takagi–Sugeno fuzzy model are investigated. Combining with a recently developed integral inequality, relaxed delay-dependent stability conditions are derived by means of linear matrix inequalities. To obtain the further relaxed stability criteria, the membership-function-dependent method is applied via the piecewise membership functions (PMFs) and some slack variables. The PMFs are selected to approximate the membership functions (MFs), and then the characteristics of the MFs are taken into consideration adequately. Under the imperfect premise matching design scheme, this paper also proposes a flexible fuzzy controller design strategy that the fuzzy controllers do not employ the identical MFs and the number of rules as the fuzzy models. Finally, this proposed approach is tested successfully and its effectiveness is validated by the simulation examples.

Further studies on robust H∞ control for a class of Takagi–Sugeno fuzzy time-delay systems with application to continuously stirred tank reactor problems

This article is concerned with the problem of robust [Formula: see text] control for a class of Takagi–Sugeno fuzzy systems with parameter uncertainties and time-varying delays. By constructing a novel Lyapunov–Krasovskii functional and utilizing some integral inequalities, a new bounded real lemma is proposed in terms of linear matrix inequalities. Also, the robust [Formula: see text] state feedback control design conditions are obtained on the basis of the cone complementarity linearization algorithm. Moreover, The controller guarantees the robust asymptotic stability of the closed-loop fuzzy system and the [Formula: see text] performance of the system from the exogenous signals to the measurement output below a prescribed level. Finally, as an illustrative example, a continuously stirred tank reactor is employed to show the effectiveness of the theoretical results.

Passivity control for uncertain singular discrete T–S fuzzy time-delay systems subject to actuator saturation

ABSTRACTThis paper deals with passivity control for uncertain singular discrete T–S (Takagi-Sugeno) fuzzy time-delay systems subject to actuator saturation. Primarily, a sufficient condition is derived which guarantees that the uncertain singular discrete T–S (Linear matrix inequality) constraints is formulated to estimate the domain of attraction for the discrete T–S closed-loop system. At last, we show the applicability and superiority of obtained theoretical results through three simulations.