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.     

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.     

Probabilistic-constrained control of interval type-2 T–S fuzzy systems under the multi-node round-robin scheduling protocol

This work concentrates on the control design of interval type-2 (IT2) T–S fuzzy systems under probabilistic saturation constraints. The actual control signals are allowed to exceed some preset thresholds with a certain frequency. Meanwhile, the sensors are governed by the multi-node round-robin scheduling protocol, which permits more than one sensors to transmit their information at every moment. The main objective is to synthesize a fuzzy controller such that the closed-loop system is locally stochastically stable under probabilistic saturated constraints and the multi-node round-robin scheduling protocol. To this end, the probabilistic saturation constraints are characterized by a Bernoulli-distributed stochastic process, and the received state at the controller side is formulated based on an updating rule and a compensation strategy. By constructing new membership functions, a token-dependent control law is subsequently designed. The stability analysis is facilitated by a modified sector condition dealing with the saturation nonlinearities. With suitable selection of initial states, sufficient conditions are derived to achieve the local stochastic stability of the closed-loop IT2 T–S fuzzy system. A larger domain of stochastic stability can be obtained via a searching algorithm. Finally, the proposed method is illustrated via a simulation example.     

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.     

Strong γc-γcl H∞ stabilization for networked control systems under denial of service attacks

This paper is concerned with the strong γ_c-γ_cl H_∞ stabilization problem for networked control systems (NCSs) subject to denial of service (DoS) attacks, which are common attack behaviors that affect the packet transmission of measurement or control signals. The purpose of the problem under consideration is to design a stable dynamic output feedback (DOF) controller (strong stabilizing controller) with the prescribed H_∞ performance norm bound γ_c to tolerate multiple packet dropouts caused by DoS attacks, such that, the closed-loop system is mean-square stable and captures the H_∞ disturbance attenuation norm bound γ_cl. Based on the Lyapunov functional and the stochastic control approach, some sufficient conditions with the form of matrix inequalities for the existence of the desired stable DOF controller are established. Then, by an orthogonal complement space technique, the controller gain is parameterized. Next, an iterative linear matrix inequality (LMI) algorithm is developed to obtain the controller gain. Finally, the usefulness of the proposed method is indicated by a numerical simulation example.     

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.     

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.     

Finite-time event-triggered containment control of multiple Euler–Lagrange systems with unknown control coefficients

This paper researches the finite-time event-triggered containment control problem of multiple Euler–Lagrange systems (ELSs) with unknown control coefficients. To realize an accurate convergence time, the settling-time performance function is employed to ensures the steady-state and dynamic properties of the containment errors in the resulting system. Meanwhile, to handle unknown control coefficients, adaptive neural networks (ANNs) with an additional saturated term are designed, which removes the requirement of full rank control coefficients in traditional control methods. By establishing an event-triggered mechanism, a novel finite-time event-triggered containment control law is designed, which yields the semi-global practical finite-time stable (SGPFS) of the resulting closed-loop system without Zeno phenomenon according to the finite-time stability criterion. The effectiveness of the designed methodology is verified by simulation.     

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.     

Stabilization of positive Takagi–Sugeno fuzzy discrete-time systems with multiple delays and bounded controls

This paper deals with the problem of stabilization by state feedback control of Takagi–Sugeno (T–S) fuzzy discrete-time systems with multiple fixed delays while imposing positivity in closed-loop. The obtained results are presented under linear programming (LP) form. In particular, the synthesis of state feedback controllers is first solved in terms of Linear programming for the unbounded controls case. This result is then extended to the stabilization problem by nonnegative controls, and stabilization by bounded controls. The stabilization conditions are derived using the single Lyapunov–Krasovskii functional (LKF). An example of a real plant is studied to show the advantages of the design procedure. A comparison between linear programming and LMI approaches is presented.     

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.     

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.     

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.     

Fault detection of discrete-time T–S fuzzy affine systems based on piecewise Lyapunov functions

This paper investigates the problem of robust fault detection for a class of discrete-time nonlinear systems, which are represented by Takagi–Sugeno (T–S) fuzzy affine dynamic models with norm-bounded uncertainties. The objective is to design an admissible fault detection filter guaranteeing the asymptotic stability of the resulting residual system with prescribed performances. It is assumed that the plant premise variables, which are often the state variables or their functions, are not measurable so that the fault detection filter implementation with state-space partition may not be synchronized with the state trajectories of the plant. Based on a piecewise quadratic Lyapunov function combined with S-procedure and some matrix inequality convexification techniques, the results are formulated in the form of linear matrix inequalities. Finally, a simulation example is provided to illustrate the effectiveness of the proposed approach.