Stabilization of positive constrained T–S fuzzy systems: Application to a Buck converter

This paper deals with the problem of constrained stability and tracking of Takagi–Sugeno (T–S) fuzzy positive systems. Linear programming (LP) is used to insert the constraints in the design phase while imposing positivity in closed-loop. The theoretical results are applied to the buck DC–DC converter which is widely used in the photovoltaic generators. Based on the simulation results success of the method is shown for this application.     

T–S fuzzy control for dithered nonlinear singularly perturbed systems with multiple time delays

This paper is concerned with the stability problem of nonlinear multiple time-delay singularly perturbed (NDSP) systems. To overcome the effect of modeling error between the reduced-order model of the NDSP plant and Takagi–Sugeno (T–S) fuzzy models, a robustness design of model-based fuzzy control is proposed in this study. A stability criterion in terms of Lyapunov’s direct method is derived to guarantee the asymptotic stability of NDSP systems. According to this criterion, a model-based fuzzy controller is then synthesized via the technique of parallel distributed compensation (PDC) to stabilize the NDSP system. If the designed fuzzy controller cannot stabilize the NDSP system, a high-frequency signal, commonly referred to as dither, is simultaneously introduced to stabilize it. Based on the relaxed method, the NDSP system can be stabilized by regulating appropriately the parameters of dither. If the dither’s frequency is high enough, the output of the dithered reduced system and that of its corresponding mathematical model – the relaxed reduced system – can be made as close as desired. This makes it possible to obtain a rigorous prediction of the stability of the dithered reduced system based on the one of the relaxed reduced system.     

Exponential stabilization and sampled-date H∞ control for uncertain T–S fuzzy systems with time-varying delay

In this paper, the exponential stabilization problem of uncertain T–S fuzzy systems with time-varying delay is emulated by fuzzy sampled-data H_∞ control. Firstly, a novel suitable Lyapunov–Krasovskii function is constructed, which contains all the information about the sampling pattern. Secondly, a less conservative result is achieved by using an extended Jensen inequality, and purposefully using a compact free weighting matrix. In addition, according to the linear matrix inequality (LMI), some sampled-data H_∞ exponential stability sufficient conditions and controller design of T–S fuzzy systems are established. Finally, effectiveness gives some illustrative examples may be used to display the value of the current proposed method as well as a significant improvement.     

Switching PDC control for discrete-time T–S fuzzy system: A membership function ranking approach

In this paper, a new type of switched parallel distributed compensation (PDC) controller is presented, in which a novel switching scheme, namely, membership function ranking (MFR) scheme is proposed. The MFR scheme can be viewed as an improvement and extension of previous results named largest membership function (LMF) scheme concerned with piece-wise quadratic Lyapunov function (PQLF) approach, since it provides a denser subdivision of normalized membership function space and therefore essentially yields less conservative results. Moreover, it shows that MFR scheme covers LMF scheme as a particular case. Based on MFR scheme, a family of _?∞${\mathbf{?}}_{\infty }$ controllers and a switching scheme is designed to ensure the closed-loop system asymptotically stable and has a required _?∞${\mathbf{?}}_{\infty }$ performance. A design example is presented to illustrate the advantages of MFR scheme.     

Actuator saturation control of continuous-time positive switched T–S fuzzy systems

The saturated control problem is investigated for positive switched Takagi–Sugeno (T–S) fuzzy systems with partially controllable subsystems in this paper. Based on the parallel distribution compensation (PDC) algorithm and the convex hull technology, new fuzzy control schemes are proposed for continuous-time positive switched T–S fuzzy systems (PSTSFSs) with actuator saturation. By the multiple linear co-positive Lyapunov function and the slow-fast combined mode-dependent average dwell time (MDADT) approach, sufficient conditions for the stability of continuous-time closed-loop PSTSFSs are developed, which is an extension of the results in previous literature. Furthermore, the least conservative estimation of the attraction domain of PSTSFSs is transformed into an optimization problem. Finally, three simulation examples are given to illustrate the effectiveness of the proposed saturated control schemes.     

Fuzzy quantized sampled-data control for extended dissipative analysis of T–S fuzzy system and its application to WPGSs

This paper investigates the issues of extended dissipativity performance and stabilization for T–S fuzzy model (TSFM) based wind power generation systems (WPGSs). Firstly, the stochastic coupled leakage time-varying delays (CLTVDs) and randomly occurring uncertainty parameters (ROUPs) are firstly introduced for constructing more general TSFM. Second, on basis of the time-delay-product function (TDPF) and looped function strategy, a relaxed Lyapunov–Krasovskii functional (LKF) with the negative definite term and the time-varying matrix is developed, which can get the utmost out of the information of various communication delays. Third, by utilizing the tighter integral inequalities and reciprocally convex combination technique (RCCT), new stabilization criteria are established in terms of the linear matrix inequalities (LMIs). Simultaneously, the desired fuzzy sampled-data control (FSDC) is designed under the state quantization mechanism. Finally, a simulation example is presented to validate the efficiency of the proposed result.     

Quadratically convex combination approach to stability of T–S fuzzy systems with time-varying delay

This paper develops a novel stability analysis method for Takagi–Sugeno (T–S) fuzzy systems with time-varying delay. New delay-dependent stability criteria in terms of linear matrix inequalities for time-varying delayed T–S fuzzy systems are derived by the newly proposed augmented Lyapunov–Krasovski (L–K) functional. This functional contains the cross terms of variables and quadratic terms multiplied by a higher degree scalar function. Different from previous results, our derivation applies the idea of second-order convex combination, and the property of quadratic convex function without resorting to the Jensen's inequality. Two numerical examples are provided to verify the effectiveness of the presented results.     

Robust H∞ persistent dwell time control for switched discrete-time T–S fuzzy systems with uncertainty and time-varying delay

This paper is concerned with the controller synthesis for switched Takagi–Sugeno (T–S) fuzzy systems with time-varying delays, parameter uncertainties and process disturbances. A persistent dwell time (PDT) based control law is mainly proposed for the T–S fuzzy systems in presenting of high-frequency motion switches. Different with the most existing literatures, the dynamics of local subsystems are allowed to be unstable during fast switching time intervals as well as the jump time instants. In addition, the maximal period of persistence time is not limited. Under the influences of the time-varying delays, uncertainties and disturbances, the proposed method ensures the overall closed-loop system to be globally uniformly exponentially stable. Moreover, a pre-given H_∞ performance can be simultaneously guaranteed. Numerical examples are provided to demonstrate the effectiveness of the proposed method.     

ISS control synthesis of T–S fuzzy systems with multiple transmission channels under denial of service

This paper investigates the input-to-state stabilizing (ISS) problem for Takagi–Sugeno (T–S) fuzzy systems with multiple transmission channels under denial-of-service (DoS) attacks. To achieve ISS, time-triggered data update logics on different channels are determined by linear matrix inequalities (LMIs). Under DoS attacks, a switched fuzzy dynamic output feedback controller which takes the security of premise variables into consideration is constructed. A novel time division mechanism is proposed to deal with the uncertainties caused by DoS attacks at different time periods. The proposed mechanism considers all cases of DoS attacks, which is more general compared to the existing method. Then, sufficient conditions are given to ensure the ISS of T–S fuzzy systems under DoS attacks. Finally, two examples are given to illustrate the effectiveness and merits of the proposed method.     

Network-based synchronization of T–S fuzzy chaotic systems with asynchronous samplings

In this paper, we study the problem of network-based synchronization of chaotic systems in Takagi–Sugeno (T–S) fuzzy form, in which the master and slave fuzzy chaotic systems are connected with a continuous-time controller through a network. In all communication channels, asynchronous samplings and external disturbances are considered. The asynchronously sampled state information of the master and slave systems received in the controller is treated by designing an observer for estimating the states of the master system. Then, based on the observation result, the problem of asynchronous samplings between the slave-controller and controller-slave channels is solved in two different cases. Sufficient conditions for the existence of the desired observer and controllers for each asynchronous cases are presented in the form of linear matrix inequalities. An numerical example is given to illustrate the validity and potential of the proposed new design techniques.     

On designing Lyapunov-Krasovskii functional for time-varying delay T–S fuzzy systems

In this work, we have investigated the problem of assessing stability and designing an appropriate feedback control law for T-S fuzzy systems with time-varying delay. By way of designing a new Lyapunov-Krasovskii functional based on Legendre polynomials and membership functions, we have developed conditions for stability assessment and feedback gain synthesis. The resulting algebraic conditions form a set of hierarchical LMIs which, by increasing the order of the Bessel-Legendre polynomial, compete with the sum of squares in both conservatism and complexity. Finally, two examples are provided to demonstrate the effectiveness of the findings.     

The approximation of the T–S fuzzy model for a class of nonlinear singular system with derivative of input

In this paper, the approximation problem of T–S fuzzy linear singular system for a class of nonlinear singular system with derivative of input is considered and the nonlinear singular system has impulses. Consider a numerical example and a two-wheel drive robot, the T–S fuzzy singular systems are calculated for original system with derivative of input. According to solvability and steps of solving of the two examples, the results are extended to more generally nonlinear singular system with derivative of input. The theorem and algorithm that are given if input-state system is bounded impulse-free item and separable impulse item, it can be approximated by T–S fuzzy singular system with arbitrary accuracy. Finally, a numerical simulation is carried out to show the consistency with theoretical analysis and illustrate the effectiveness of approximation.     

Networked H∞ filtering for T–S fuzzy systems with quantization and data dropouts

This paper studies the problem of _H∞$H_{\infty }$ filtering problem for a class of nonlinear time-varying delay systems with unideal communication links. Two defectives are concerned including measurement quantization and packet dropouts. The quantized measurements are transmitted to the filter via network, where the phenomena of packet loss are taken into account. By using Lyapunov–Krasovskii functional, a less conservative delay-dependent stability condition for the closed-loop NCSs is derived. The _H∞$H_{\infty }$ fuzzy controller, which is designed in terms of linear matrix inequalities (LMIs), is developed for the asymptotic stabilization of the closed-loop NCSs. Numerical examples are given to illustrate the effectiveness of the proposed method.     

Adaptive event-triggered H∞ fuzzy filtering for interval type-2 T–S fuzzy-model-based networked control systems with asynchronously and imperfectly matched membership functions

This paper is concerned with the network-based H_∞ fuzzy filtering for non-linear systems with parameter uncertainties under a novel adaptive discrete event-triggered communication scheme (DETCS). Based on interval type-2 (IT2) Takagi–Sugeno (T–S) fuzzy model, the non-linear systems with parameter uncertainties are represented as a class of IT2 T–S fuzzy systems. In the design process, a novel adaptive DETCS is proposed to reduce the usage of system resources and adapt the variation of plant output, and a novel networked IT2 T–S fuzzy filter is applied to improve the flexibility of filter design. By employing the time-delay systems modeling method, the filtering-error-system is modeled as a class of interval time-varying delayed IT2 T–S fuzzy systems with asynchronously and imperfectly matched membership functions, and further conditionally expressed as a favorable form. Then, some relaxed stability criteria are established to determine that this class of delayed IT2 T–S fuzzy systems is asymptotically stable with a prescribed H_∞ disturbance attenuation performance. Also, the co-design of parameter matrices of adaptive DETCS and filter is implemented. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed method.     

Robust fuzzy stabilization of hybrid discrete delay T–S systems

Novel results on robust fuzzy stabilization are developed hereafter for discrete hybrid systems in the (T–S) fuzzy framework. The systems are subject to fractional parametric uncertainties and bounded time-delays. Linear matrix inequalities-based conditions are derived for stability analysis. By optimizing an appropriate performance measure, both stabilizing gains and the switching signal are generated. The analytical findings are validated on a typical water-quality system application to demonstrate the efficacy of the developed techniques.