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.     

Event-based weighted residual generator design via non-PDC scheme for fault diagnosis in T–S fuzzy systems

This paper is concerned with the event-based weighted residual generator design via non-parallel distribution compensation (PDC) scheme for fault diagnosis in discrete-time T–S fuzzy systems, under consideration of the imperfect premise matching membership functions. An event-triggered mechanism is firstly introduced to save communication resources, which leads to the premise variables of the system and observer to be asynchronous. Then, a fuzzy diagnostic observer with mismatched premise variables is designed to estimate the unmeasurable states of the system. Moreover, by using non-PDC method, a diagnostic observer-based weighted residual generator is established to improve the fault detection (FD) performance by using the information provided by each local system, in which the membership functions structure of the diagnostic observer and residual generator need not to be the same as the systems, and the L_∞/L₂ and L_∞ FD scheme is used to optimize the FD performance. Finally, two simulation results are provided to show the efficiency of the proposed non-PDC method.     

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.     

Sum-of-squares-based robust H∞ controller design for discrete-time polynomial fuzzy systems

This paper investigates a robust H_∞ controller design for discrete-time polynomial fuzzy systems based on the sum-of-squares (SOS) approach when model uncertainties and external disturbances are simultaneously considered. At the beginning of the controller design procedure, a general discrete-time polynomial fuzzy control system proposed in this paper is used to represent a nonlinear system containing model uncertainties and external disturbances. Subsequently, through use of a nonquadratic Lyapunov function and the H_∞ performance index, the novel SOS-based robust H_∞ stability conditions are derived to guarantee the stability of the entire control system. By solving those stability conditions, control gains of the robust H_∞ polynomial fuzzy controller are obtained. Because the model uncertainties and external disturbances are considered simultaneously in the controller design procedure, the closed-loop control system achieves greater robustness and H_∞ performance against model uncertainties and external disturbances. Moreover, the novel operating-domain-based robust H_∞ stability conditions are derived by considering the operating domain constraint to relax the conservativeness of solving the stability conditions. Finally, simulation results demonstrated the availability and effectiveness of the proposed stability conditions, which are more general than those used in existing approaches.     

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.     

Event-triggered non-fragile H∞ fault detection for discrete time-delayed nonlinear systems with channel fadings

In this paper, the event-triggered non-fragile H_∞ fault detection filter is designed for a class of discrete-time nonlinear systems subject to time-varying delays and channel fadings. The Lth Rice fading model is utilized to reflect the actual received measurement signals, and its channel coefficients own arbitrary probability density functions on interval [0,1]. The event-based filter is constructed to reduce unnecessary data transmissions in the communication channel, which only updates the measurement signal to the filter when the prespecified “event” is triggered. Multiplicative gain variations are utilized to describe the phenomenon of parameter variations in actual implementation of the filter. Based on Lyapunov stability theory, stochastic analysis technology along with linear matrix inequalities (LMIs) skills, sufficient conditions for the existence of the non-fragile fault detection filter are obtained which make the filtering error system stochastically stable and satisfy the H_∞ constraint. The gains of the filter can be calculated out by solving the feasible solution to a certain LMI. A simulation example is given to show the effectiveness of the proposed method.     

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.     

A new delay-range-dependent H∞ filter design for T–S nonlinear systems

This paper focuses on the problem of _H∞$H_{\infty }$ filter design for continuous-time Takagi and Sugeno (T–S) fuzzy systems with time-varying delays. The partitioning time delay technique is used to construct the Lyapunov–Krasovskii functional, furthermore, a novel delay-dependent _H∞$H_{\infty }$ filter design approach is proposed based on the matrix decoupling approach, and the filter parameters can be obtained by solving a set of linear matrix inequalities (LMIs). The numerical examples show that the proposed method is of less conservativeness than the existing methods.     

Networked H∞ filtering for Takagi–Sugeno fuzzy systems under multi-output multi-rate sampling

This paper studies networked H_∞ filtering for Takagi–Sugeno fuzzy systems with multi-output multi-sensor asynchronous sampling. Different output variables in a dynamic system are sampled by multiple sensors with different sampling rates. To estimate the signals of such a system, a continuous multi-rate sampled-data fusion method is proposed to design a novel networked filter. By considering a class of decentralized event-triggered transmission schemes, multi-channel network-induced delays, and the updating modes of the MOMR sampled-data, a networked jumping fuzzy filter is proposed to estimate system signals based on the transmitted multi-rate sampled-data of fuzzy system and the multi-rate sampled states of filter, and the jumping among filter modes is governed by a Markov process which depends on the arrival times of sampled output sub-vectors. To deal with asynchronous membership functions, the networked fuzzy filtering system is modeled as an uncertain fuzzy stochastic system with membership function deviation bounds. Based on stability and H_∞ performance analysis, several membership-function-dependent conditions are presented to co-design the event-triggered transmission schemes and the fuzzy filter such that the filtering error system is robustly mean-square exponentially stable with a prescribed H_∞ attenuation level. Finally, the improvement in estimation performance and comparison with the existing filtering methods are discussed through simulation examples.     

Event-based H∞ filtering for discrete-time Markov jump systems with network-induced delay

The problem of event-based H_∞ filtering for discrete-time Markov jump system with network-induced delay is investigated in this paper. For different jumping modes, different event-triggered communication schemes are constructed to choose which output signals should be transmitted. Through the analysis of network-induced delay’s intervals, the discrete-time system, the event-triggered scheme and network-induced delay are unified into a discrete-time Markov jump filter error system with time-delay. Based on time-delay system analysis method, criteria are derived to guarantee the discrete-time Markov jump error system stochastically stable with an H_∞ norm bound. The correspondent filter and the event-based parameters are also given. A numerical example is given to show that the proposed filter design techniques are effective and event-triggered communication scheme can save limited network resources greatly.     

Observer-based finite-time H∞ control for uncertain discrete-time nonhomogeneous Markov jump systems

The problem of observer-based finite-time H_∞ control for discrete-time Markov jump systems with time-varying transition probabilities and uncertainties is studied in this paper, in which time-varying transition probabilities are modelled as convex polyhedron, and the parameter uncertainty satisfies norm-bounded. First of all, a Luenberger observer is designed to measure the system state. Then, observer-based controller is constructed to ensure the stochastic finite-time boundedness of the resulting closed-loop system with an H_∞ performance. Furthermore, sufficient conditions are derived in light of linear matrix inequalities. In the end, the flexibility and applicability of the developed methods are demonstrated by two illustrative examples.     

H∞ reduced-order observer-based controller synthesis approach for T-S fuzzy systems

For continuous-time nonlinear systems represented by Takagi–Sugeno fuzzy models, a new H_∞ reduced-order-observer based controller synthesis structure is investigated in this paper. By the fuzzy reduced-order observer and fuzzy controller, an augmented error system composed of the estimation and control errors is obtained. The fuzzy modeling residual terms are seen as part of the external disturbance, and an extra design matrix is added to facilitate the design process. The robustness and stability conditions are given based on Lyapunov function approach, then the conditions are transformed into convex form to facilitate the numerical solving process. Finally, by the comparison with existing methods in simulation section, the control performance and conservativeness reduction effects of the proposed methods are verified.     

Finite-time H∞ control for a class of discrete-time nonlinear singular systems

This paper investigates the finite-time control problems for a class of discrete-time nonlinear singular systems via state undecomposed method. Firstly, the finite-time stabilization problem is discussed for the system under state feedback, and a finite-time stabilization controller is obtained. Then, based on which, the finite-time H_∞ boundedness problem is studied for the system with exogenous disturbances. Finally, an example of population distribution model is presented to illustrate the validity of the proposed controller. Because there is no any constraint for singular matrix E in the paper, controllers can be designed for more discrete-time nonlinear singular systems.     

Robust delay-dependent H∞ filtering for uncertain Takagi–Sugeno fuzzy neutral stochastic time-delay systems

This paper addresses the robust H_∞ filter design problem for a class of uncertain fuzzy neutral stochastic system with time-delay through Takagi–Sugeno (T–S) fuzzy model. By constructing an augmented Lyapunov–Krasovskii functional, some novel delay-dependent stability criteria for uncertain fuzzy neutral stochastic system with time varying delay are obtained in terms of linear matrix inequalities. By using the integral inequality in the neutral stochastic setting combined with delay decomposition approach, the H_∞ fuzzy filter is designed to guarantee the corresponding filtering error systems robustly asymptotically stable with a specified H_∞ performance index. At last, two numerical examples are presented to show the less conservatism than the previous results.