Discrete-time Takagi-Sugeno Research Articles

Input-to-state stabilization of discrete-time delayed fuzzy systems via aperiodically intermittent control

This paper studies input-to-state stabilization of delayed discrete-time Takagi–Sugeno (T-S) fuzzy systems via aperiodically intermittent control. We first consider aperiodically intermittent time-triggered control, where we present sufficient conditions via the mathematical induction under the hypotheses of the quasiperiodicity condition. Based on the derived sufficient conditions, we apply a Lyapunov-Krasovskii (L-K) method together with the descriptor method to derive the explicit linear matrix inequalities (LMIs) that ensure the exponential stability and input-to-state stability (ISS), and show the existence of the aperiodically intermittent time-triggered controller that leads to efficient results with much less numerical complexity. We next consider aperiodically intermittent dynamic event-triggered control with an additional parameter that is larger than one. This strategy allows that the introduced dynamical variable does not remain constant but increases during the control rest interval. As a result, the proposed dynamic event-triggered strategy leads to a smaller number of sent signals than that for the case of the additional parameter which equals to one. Finally, numerical examples including a practical inverted pendulum on a cart are presented to verify the validity of the proposed method.

Fault detection observer design for Takagi–Sugeno fuzzy systems with finite-frequency specifications

This paper addresses robust fault detection observer design for a class of discrete-time Takagi–Sugeno fuzzy systems with finite-frequency specifications. A novel design method is presented based on finite-frequency H−/H∞ indices and peak-to-peak analysis. The finite-frequency H− and H∞ indices are utilized to characterize fault sensitivity and disturbance robustness, respectively. Peak-to-peak analysis is used to derive a dynamic threshold. To further reduce the conservatism caused by predefined parameters, an iterative algorithm is developed. Both theoretical proof and simulation results show that the performance of the proposed method is not worse than the existing works.

Robust [formula omitted] control for LFC of discrete T–S fuzzy MAPS with DFIG and time-varying delays

The H∞ LFC control problem for a class of nonlinear power systems with time-varying delays is under study. Considering uncertainties arising from nonlinear issues such as the generation rate constraint (GRC) and governor dead band (GDB), as well as the high variability of renewable energy sources like wind power, the model is transformed into a discrete-time Takagi–Sugeno (T–S) fuzzy model with parameter uncertainty. By constructing a Lyapunov–Krasovskii functional, and employing difference inequalities and generalized cross-convex matrix inequalities, sufficient conditions for the asymptotic stability of power systems are provided. Based on the obtained conditions, a controller is designed to ensure the asymptotic stability of Multi-Area Power Systems (MAPS), with the performance index being H∞. Finally, simulation results demonstrate the correctness and effectiveness of the theorem.

Asynchronous filtering for discrete-time T–S fuzzy sampled-data systems with improved quantization

This study delves into the asynchronous filtering problem within discrete-time Takagi–Sugeno (T–S) fuzzy sampled-data systems featuring non-periodic sampled measurements. A non-homogeneous Markov chain is utilized to capture the stochastic nature of the sampling period. The transition probability matrix of this non-homogeneous Markov process is time-varying and characterized using a multi-mode structure. To mitigate conservatism, a quantizer associated with the modes is implemented, where the quantization density is defined as the observed modes. Unlike existing approaches, there exists a discrepancy between the quantizer mode and the sampling mode, following a hidden Markov chain process. Additionally, a novel fuzzy asynchronous filter is introduced based on the observed modes to ensure the stochastic stability of the fuzzy system. Ultimately, the effectiveness of the proposed filter strategy is validated via a tunnel diode circuit model.

A membership function-dependent L∞ performance based output interval estimation method for discrete-time Takagi–Sugeno fuzzy systems applied to fault detection

In the design process of traditional L∞ methods, a common performance index is often considered in different fuzzy rules. This may introduce a certain conservatism when most of the whole fuzzy system operates under a certain fuzzy rule or a few fuzzy rules. Therefore, this paper focuses on robust interval estimation problems for discrete-time Takagi–Sugeno fuzzy systems, and a new membership function-dependent L∞ performance index is proposed. The proposed L∞ performance can ensure better results in practical engineering applications by using the priori knowledge that the model works most of the time on some specific fuzzy systems to design performance index. By means of fuzzy basis-dependent Lyapunov functions, a membership function-dependent L∞ performance based interval estimation strategy applied to fault detection is presented. Through simulation analysis, the L∞ index in this paper is better than the conventional one and a tighter interval estimation is obtained leading to more accurate and faster fault detection effects. Meanwhile, the simulation results of this method also reflect the membership function-dependent property well.

WITHDRAWN: Towards robust fault detection for Takagi–Sugeno nonlinear systems

This paper addresses robust fault detection observer design for a class of discrete-time Takagi–Sugeno nonlinear systems. A novel design method is presented based on finite-frequency H−/H∞ indices and peak-to-peak analysis. The finite-frequency H− and H∞ indices are utilized to characterize fault sensitivity and disturbance robustness, respectively. The peak-to-peak analysis is used to derive a dynamic threshold. An iterative algorithm is further developed to reduce conservatism. Theoretical proof shows that the performance of the proposed method is not worse than some existing works. Simulation results demonstrate the validity and viability of the proposed method.

Event-triggered sliding mode control for singular discrete-time fuzzy Markov jump networked systems

In this present paper, the event-triggered sliding mode control (SMC) issue for a type of singular networked Markov jump systems with partly unknown transition probabilities (TPs) is mainly investigated, and it is modeled by discrete-time Takagi–Sugeno fuzzy systems. To save network resources, a mode-dependent event-triggered scheme (ETS) is applied to improve transmission efficiency. Subsequently, a common sliding surface is designed, which can effectively reduce the impact of the jumping process. Therein, the stochastic admissibility criterion for the system with [Formula: see text] performance [Formula: see text] is derived in the sense of partly unknown TPs. Moreover, a novel SMC law that guarantees the reachability of the quasi-sliding mode is given in view of the reaching condition. Finally, the validity of the presented theorems is demonstrated by a numerical example.

An [formula omitted] non-fragile fault detection observer design for discrete-time Takagi–Sugeno fuzzy systems using zonotopic method

In practical engineering applications, as the system becomes complex, the need to ensure its safety and reliability increases, and fault detection technology is the key to determining whether it usually operates. The assumption of precise realization implicit in the design of conventional observers is a significant reason why actual fault detection observers find it difficult to detect faults accurately. False alarms can quickly occur during fault detection due to the observer’s uncertainty. For this reason, a novel fault detection method using zonotopic analysis based on a non-fragile H∞ observer via T-N-L structure is proposed for the discrete-time Takagi–Sugeno (T–S) fuzzy system. The observer proposed in this paper is designed in a two-step form. Firstly, the H∞ technique gives a set of design conditions for the fault detection observer with T-N-L structure, which maintains the robustness of the observation dynamics to disturbances while considering the uncertainties existing in the actual observer. Then, the dynamic fault detection thresholds in the form of intervals are given by zonotopic analysis, which has the advantage of zero false alarm rate when the observer parameter ingress is within the range of design considerations. Simulation results show that the method proposed in this paper provides better safety and reduces the problem of missed false alarms compared with the traditional method. It also reflects that the nature of a non-fragile fault detection observer is a trade-off between safety and speed of fault detection.

Relaxed Resilient Fuzzy Stabilization of Discrete-Time Takagi–Sugeno Systems Based on A New Switching Mechanism

Relaxed Resilient Fuzzy Stabilization of Discrete-Time Takagi–Sugeno Systems Based on A New Switching Mechanism

Decentralized Optimal Passive Control for Discrete-Time Takagi–Sugeno Interconnected Descriptor Systems with Uncertainties

Decentralized Optimal Passive Control for Discrete-Time Takagi–Sugeno Interconnected Descriptor Systems with Uncertainties

Enhanced Resilient Fuzzy Stabilization of Discrete-Time Takagi-Sugeno Systems Based on Augmented Time-Variant Matrix Approach.

In this technical correspondence, the resilient fuzzy stabilization is enhanced in the direction of elevating the feasible stabilization region as large as possible while the same alert threshold is chosen as the recent one. To do this, the switching-type fuzzy state-feedback controller is designed with a set of switch modes so that more groups of gain matrices can be introduced to enhance the degree of freedom. What is far more important is that a novel augmented time-variant matrix approach is proposed in order to collect the proprietary features of normalized fuzzy weighting functions with regard to each switch mode. Then, all the obtained augmented time-variant matrices are split into a set of positive/negative matrices, which can be elaborately assigned into different monomials of our designing conditions under the framework of homogeneous polynomials. Therefore, less conservative results of resilient fuzzy stabilization are obtained even if some higher alert thresholds are chosen for probably ensuring the establishment of the involved precondition. Finally, the superiority of our approach is validated by giving some detailed comparisons on the benchmark example.

Actuator fault-tolerant control for discrete Takagi-Sugeno fuzzy systems using the matrices norms approach

The apparition of faults is a well-known phenomenon in automatic control systems. Faults cause undesired behaviour and disruption of a controlled plant, which can lead to damage. This article addresses the actuator fault problem for nonlinear systems described by a discrete time Takagi–Sugeno fuzzy systems. An active fault-tolerant control based on a fault estimator is designed using the matrices norms approach instead of the usual Lyapunov stability theory. In this work, we consider the case where the premise variables do not depend on the unmeasurable variables. This allows the separate design of the gains of the controller, the observer and the estimator. Two nonlinear systems represented by discrete Takagi–Sugeno fuzzy models are studied to investigate the validity of the proposed method.

Multi-Instant Gain-Scheduling Fuzzy Observer of Discrete-Time Takagi-Sugeno Systems and Its Application: An Efficient Balanced Matrix Approach.

The problem of relaxed state estimation of discrete-time Takagi-Sugeno fuzzy systems is studied by constructing a novel multi-instant gain-scheduling fuzzy observer. First, a multi-instant gain-scheduling mechanism with a single adjustable parameter is given for the first time in order to produce more reasonable switch modes over previous results reported in recent literature. Second, for every switch mode, a batch of specified observer gain matrices is determined by developing an efficient balanced matrix approach so that the updated values of adjacent normalized fuzzy weighting functions can be flexibly exploited. Since the implied information of each specific switch mode is capable of being absorbed and utilized more thoroughly by the aid of the refined higher-order balanced matrices, the conservatism can be prominently reduced at the price of consuming extra computational burden within the allowable range. Finally, two benchmark examples are provided to test and verify the progressiveness of our proposed approach.

Local dynamic output feedback control of saturated discrete-time T-S fuzzy systems with partially measured premise variables

This paper aims to investigate the problem of designing locally stabilizing dynamic output feedback controllers and estimate the domain of attraction for discrete-time Takagi-Sugeno (T-S) fuzzy systems. A realistic scenario is assumed where the control signal is subject to saturation, and the premise variables are partially or completely unmeasured, that is, not available for the control law. As a result, the fuzzy output controller can have a different number of fuzzy rules and a different set of membership functions from the T-S model. To obtain locally stabilizable conditions, we propose modeling the variation rate of the membership functions without using upper bounds, a new contribution in the context of output control of discrete-time T-S systems. The design conditions are expressed as linear matrix inequality relaxations based on fuzzy Lyapunov functions using slack variables introduced by Finsler's lemma. Numerical examples illustrate the effectiveness of the approach.

Security-based dynamic output-feedback model predictive control for nonlinear systems in T-S fuzzy form subject to deception attacks

This paper is concerned with the security-based fuzzy model predictive control (FMPC) problem for a class of discrete-time Takagi-Sugeno (T-S) fuzzy systems with deception attacks on the measured outputs. With respect to the unmeasurable system states, the nonlinearity of the system and the destructiveness of deception attacks, the dynamic output-feedback control in the framework of FMPC is adopted, meanwhile, the worst-case optimization problem over the infinite moving horizon is formulated for the performance analysis and control synthesis. By means of the quadratic function approach and the singular value decomposition technique, the non-convexity caused by couplings between decisive variables is coped with and conditions are derived to suffice the terminal constraint set. In addition, to mitigate the destruction of attacks to the recursive feasibility, the inequality analysis technique is applied with the aid of the introduction of special scalars. Based on the establishments, a certain auxiliary optimization problem with solvability is put forward to find the desired controllers, and sufficient conditions are obtained to guarantee that the underlying system subject to deception attacks under the proposed FMPC-based controllers is mean square secure in H2-sense. Finally, an illustrative example is used to demonstrate the validity of the proposed methods.

Positivity and separation principle for observer-based output-feedback disturbance attenuation of uncertain discrete-time fuzzy models with immeasurable premise variables

We propose a robust observer-based output-feedback (OBOF) controller design method for the positive stabilization of discrete-time Takagi–Sugeno (T–S) fuzzy models subject to immeasurable premise variables, parametric uncertainties, and l∞ disturbances. The results of this paper are as follows. First, a new fuzzy OBOF controller structure is used to improve the possibility that the uncertain closed-loop system is positive. Second, the separation principle is demonstrated for the l∞–l∞ disturbance attenuation. Finally, the stability, positivity, and disturbance attenuation of T–S fuzzy closed-loop models are analyzed in the presence of the perturbation caused by the imperfect premise matching by the immeasurable premise variable.

Nonfragile synchronization control of T-S fuzzy Markovian jump complex dynamical networks

This paper investigates the nonfragile dissipativity synchronization control problem of discrete-time Takagi-Sugeno (T-S) fuzzy Markovian jump complex dynamical networks. Considering the randomly occurring uncertainty, the nonfragile synchronization controller is proposed. According to the strict dissipative performance, a sufficient condition is developed to ensure that the complex network is stochastically stable by using the fuzzy-basis-dependent and mode-dependent Lyapunov function. Then, new design conditions about the nonfragile controller are obtained in the form of linear matrix inequalities. Finally, the validity of the established theoretical results is illustrated by a numerical example.

Nonfragile Guaranteed Cost Control of Discrete-Time Takagi–Sugeno Fuzzy Systems with Multiple Quantizations

Nonfragile Guaranteed Cost Control of Discrete-Time Takagi–Sugeno Fuzzy Systems with Multiple Quantizations

Design of unknown input observer for discrete-time Takagi Sugeno implicit systems with unmeasurable premise variables

In this study, an unknown input observer (UIO) is developed in explicit form to estimate unmeasurable states and unknown inputs (UIs) for nonlinear implicit systems represented by the discrete-time Takagi-Sugeno implicit systems (DTSIS) in the case of unmeasurable premise variables. The method employed is based on singular value decomposition (SVD) and augmenting the state vector, which is formed partly by the system state and partly by the UIs. The convergence of the augmented state estimation error is provided by a Lyapunov function ending with solving the linear matrix inequalities (LMI). An application to a model of the rolling disc is considered to evaluate the effectiveness of the developed approach. It appears that estimated variables converge to the true variables quickly and accurately.

Relaxed Observer Design of Discrete-Time Takagi–Sugeno Fuzzy Systems Based on a Lightweight Gain-Scheduling Law

This study is concerned with proposing much more effective Luenberger-like fuzzy observers than relevant multiinstant observers reported in recent literature, in other words, less conservative results can be given while less computing resource is consumed as an important premise. For the first time, the variation bound of two adjacent time-variant Lyapunov matrices encountered in the synthesis of fuzzy observer is characterized by a contraction factor, and thus the key replacement of the lagged term is developed in order to construct an effective synchronization framework of fuzzy observer synthesis. Since there only exist the current-time normalized fuzzy weighting functions in the obtained synchronization framework, the conservatism caused by the mismatch of different sampling instants can be avoided. Based on this, a lightweight gain-scheduling law is designed in which a large number of redundancy gains in recent multiinstant observers can be condensed in order to save computing resource to the greatest extent. Finally, two benchmark examples are borrowed for validating the superiority of our proposed results.