Takagi-Sugeno Fuzzy Time-delay Systems Research Articles

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.

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.

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.

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.

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.

Hankel norm model approximation of Takagi–Sugeno fuzzy time-delay systems

This paper is concerned with the Hankel norm model approximation for discrete-time Takagi–Sugeno (T–S) fuzzy systems with time delay. For a given stable T–S fuzzy system, our attention is focused on the construction of a reduced-order model which not only approximates the original system well with a Hankel norm performance but is also translated into a lower-dimensional system. By employing the modified delay partitioning method, a delay-dependent sufficient condition is developed for the asymptotic stability with a Hankel norm error performance for the error system. Then, the Hankel norm approximation problem is solved by employing the convex linearization approach, which casts the reduced-order model construction into a convex optimization problem subject to linear matrix inequality constraints. Finally, a numerical example is provided to show the effectiveness of the proposed methods.

New delay-dependent robust stability and stabilization for uncertain T-S fuzzy time-delay systems under imperfect premise matching

To alleviate the conservativeness of the stability criterion for Takagi-Sugeno (T-S) fuzzy time-delay systems, a new delay-dependent stability criterion was proposed by introducing a new augmented Lyapunov function with an additional triple-integral term, which was firstly used to derive the stability criterion for T-S fuzzy time-delay systems. By the same approach, the robust stability issue for fuzzy time-delay systems with uncertain parameters was also considered. On the other hand, in order to enhance the design flexibility, a new design approach for uncertain fuzzy time-delay systems under imperfect premise matching was also proposed, which allows the fuzzy controller to employ different membership functions from the fuzzy time-delay model. By the numerical examples, the proposed stability conditions are less conservative in the sense of getting larger allowable time-delay and obtaining smaller feedback control gains. For instance, when the allowable time-delay increases from 7.3 s to 12 s for an uncertain T-S fuzzy control system with time-delay, the norm of the feedback gains decreases from (34.299 2, 38.560 3) to (10.073 3, 11.349 0), respectively. Meanwhile, the effectiveness of the proposed design method was illustrated by the last example with the robustly stable curves of system state under the initial condition of x(0)=[3 −1]

Novel stability and stabilization criteria for Takagi—Sugeno fuzzy time-delay systems

We study the problems of stability and stabilization for Takagi—Sugeno (T—S) fuzzy time-delay systems. First, by constructing a less-redundant Lyapunov—Krasovskii function and introducing a useful inequality, an innovative stability criterion is obtained, which gives a significant improvement on the performance. Compared with the exiting references, our result can use fewer unknown variables and get better results. Furthermore, based on the derived stability criteria, a new stabilization condition is developed, in which the controller gain and the maximum allowable delay bound can be obtained simultaneously. The conditions are all derived in the form of linear matrix inequality, which are easy to verify. Finally, numerical examples are given to show the effectiveness of the proposed methods.

Model Approximation for Discrete-Time State-Delay Systems in the T–S Fuzzy Framework

This paper is concerned with the problem of H∞ model approximation for discrete-time Takagi-Sugeno (T-S) fuzzy time-delay systems. For a given stable T- S fuzzy system, our attention is focused on the construction of a reduced-order model, which not only approximates the original system well in an H∞ performance but is also translated into a linear lower dimensional system. By applying the delay partitioning approach, a delay-dependent sufficient condition is proposed for the asymptotic stability with an H∞ error performance for the error system. Then, the H∞ model approximation problem is solved by using the projection approach, which casts the model approximation into a sequential minimization problem subject to linear matrix inequality (LMI) constraints by employing the cone complementary linearization algorithm. Moreover, by further extending the results, H∞ model approximation with special structures is obtained, i.e., delay-free model and zero-order model. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed methods.

Delay-Dependent Nonfragile Robust H ∞ Filtering of T–S Fuzzy Time-Delay Systems

The problem of nonfragile robust H∞ filtering for a class of Takagi–Sugeno fuzzy time-delay systems is investigated in the paper. We design a fuzzy filter which can tolerate some level of the filter gain variations while ensuring both the robust stability and a prescribed H∞ performance level of the filtering error system. Delay-dependent sufficient conditions for the existence of such filters are obtained in terms of linear matrix inequalities, and an explicit expression of a desired filter is given.

New Robust Stability Conditions and Design of Robust Stabilizing Controllers for Takagi–Sugeno Fuzzy Time-Delay Systems

In this paper, we consider robust stability and stabilization of uncertain Takagi-Sugeno fuzzy time-delay systems where uncertainties come into the state and input matrices. Some stability conditions and robust stability conditions for fuzzy time-delay systems have already been obtained in the literature. However, those conditions are rather conservative and do not guarantee the stability of a wide class of fuzzy systems. This is true in case of designing stabilizing controllers for fuzzy time-delay systems and it thus leads to a conservative fuzzy controller design as well. We first consider rather relaxed robust stability conditions of uncertain fuzzy systems. To this end, we introduce an auxiliary system to the original fuzzy time-delay system to obtain generalized delay-dependent stability conditions. Such an auxiliary system has some arbitrary matrices that generalize not only the system representation but also delay-dependent stability conditions. Conditions we obtain here are delay-dependent conditions that depend on the upper bound of time-delay, and are given in terms of linear matrix inequalities (LMIs). Then, we compare our delay-dependent stability conditions with other conditions in the literature, and show that our conditions guarantee the stability of a wider class of systems than others. Next, we consider the robust stabilization problem with memoryless and delayed state feedback controllers. Based on our generalized robust stability conditions, we obtain delay-dependent sufficient conditions for the closed-loop system to be robustly stable, and give a design method of robustly stabilizing controllers. Finally, we give three examples that illustrate our results.

New delay-dependent approach to robust stability and stabilization for Takagi–Sugeno fuzzy time-delay systems

In this paper, we consider new generalized delay-dependent stability conditions of Takagi–Sugeno fuzzy time-delay systems. In the literature, both delay-independent stability conditions and delay-dependent stability conditions for fuzzy time-delay systems have already been obtained. However, those conditions are rather conservative and do not guarantee a wide stability region. This is also true in case of the robust stability for uncertain fuzzy time-delay systems. Here we choose a generalized Lyapunov functional and introduce a parameterized model transformation with free weighting matrices to it, in order to obtain generalized delay-dependent stability conditions. In fact, these techniques lead to generalized and less conservative stability conditions that guarantee a wide stability region. Our delay-dependent stability conditions thus obtained are given in terms of linear matrix inequalities (LMIs). We give three examples to illustrate our results. Comparison with other stability conditions in the literature shows our conditions are the most powerful ones to guarantee the widest stability region. We also consider the robust stability of fuzzy time-delay systems with uncertain parameters. Applying the same techniques obtained for the stability conditions, we obtain delay-dependent sufficient conditions for the robust stability of uncertain fuzzy systems. Moreover, we give a design method of robustly stabilizing controllers for uncertain Takagi–Sugeno fuzzy time-delay systems.

Robust stability and stabilization for uncertain Takagi–Sugeno fuzzy time-delay systems

In this paper, we consider robust stability and stabilization of uncertain Takagi–Sugeno fuzzy time-delay systems where uncertainties come into the state and input matrices. Some stability conditions and robust stability conditions for fuzzy time-delay systems have already been obtained in the literature. However, those conditions are rather conservative and do not guarantee the stability and robust stability for a wide class of fuzzy systems. This is true in case of designing stabilizing controllers for fuzzy time-delay systems. We first consider robust stability conditions of uncertain fuzzy systems. Conditions we obtain here are delay-dependent conditions that depend on the upper bound of time delay, and are given in linear matrix inequalities(LMIs). An appropriate selection of Lyapunov–Krasovskii function and introduction of free weighting matrices generalize robust stability conditions. Next, we consider the stabilization problem with memoryless and delayed feedback controllers. Based on our generalized robust stability conditions, we obtain delay-dependent sufficient conditions for the closed-loop system to be robustly stable, and give a design method of robustly stabilizing controllers. Finally, we give two examples that illustrate our results. We compare our conditions with other stability conditions and show our conditions are rather generalized.

Design of H∞-control for fuzzy time-delay systems

In this paper the design problems of H ∞ output feedback controllers for Takagi–Sugeno fuzzy time-delay systems are considered. We first introduce Takagi–Sugeno fuzzy time-delay systems and the H ∞-performance (norm) for stable fuzzy time-delay systems. We consider systems with multiple time-delays in state. We give a sufficient condition for the norm being less than a given number. We then consider the H ∞-problems with output feedback controllers. Both memoryless controller and controller with memory are considered. In the design of output feedback controllers, the selection of the premise variables in the If–Then rules is important. As for the premise variable we consider three cases where the premise variable is a given function, the output and the state of the underlying system. In the first two cases we give a design method of H ∞-controllers and sufficient conditions which guarantee the required H ∞-performance of the closed-loop system. In the last case we give an H ∞-controller for an approximation of the original system. Two examples are given to illustrate the theory.

Design of H$infin;-control for fuzzy time-delay systems

In this paper the design problems of H∞ output feedback controllers for Takagi–Sugeno fuzzy time-delay systems are considered. We first introduce Takagi–Sugeno fuzzy time-delay systems and the H∞-performance (norm) for stable fuzzy time-delay systems. We consider systems with multiple time-delays in state. We give a sufficient condition for the norm being less than a given number. We then consider the H∞-problems with output feedback controllers. Both memoryless controller and controller with memory are considered. In the design of output feedback controllers, the selection of the premise variables in the If–Then rules is important. As for the premise variable we consider three cases where the premise variable is a given function, the output and the state of the underlying system. In the first two cases we give a design method of H∞-controllers and sufficient conditions which guarantee the required H∞-performance of the closed-loop system. In the last case we give an H∞-controller for an approximation of the original system. Two examples are given to illustrate the theory.