Takagi-Sugeno Fuzzy Stochastic Systems Research Articles

Dissipativity-Based Intermittent Fault Detection and Tolerant Control for Multiple Delayed Uncertain Switched Fuzzy Stochastic Systems With Unmeasurable Premise Variables.

This study focuses on dissipativity-based fault detection for multiple delayed uncertain switched Takagi-Sugeno fuzzy stochastic systems with intermittent faults and unmeasurable premise variables. Nonlinear dynamics, exogenous disturbances, and measurement noise are also considered. In contrast to the existing study works, there is a wider range of applications. An observer is explored to detect faults. A controller is studied to stabilize the considered system. A piecewise fuzzy Lyapunov function is collected to obtain delay-dependent sufficient conditions by means of linear matrix inequalities. The designed observer has less conservatism. In addition, the strict [Formula: see text]dissipativity performance is achieved in the residual dynamic. Besides, the elaborate H∞ performance and the elaborate H_ performance are also acquired. Finally, the availability of the method in this study is verified through two simulation examples.

Observer-based fault estimation and tolerant control for stochastic Takagi–Sugeno fuzzy systems with Brownian parameter perturbations

In this paper, robust fault estimation and fault tolerant control for stochastic Takagi–Sugeno fuzzy systems, subjected to Brownian parameter perturbations, unknown process uncertainties and unexpected faults, are investigated. Augmented system approach, unknown input observer techniques and sliding mode control strategies are integrated to decouple the influences from the unknown input uncertainties, and drive the trajectories of the estimation error dynamics to enter and subsequently remain within a desired surface of the error space. As a result, a robustly simultaneous estimate of the means of the faults concerned and the full system states can be achieved. In the meanwhile, the actuator/sensor signal compensation techniques are used to formulate the tolerant control strategy to eliminate or offset the influences from the faults to the systems dynamics and ensure the robust stabilization of the closed-loop control system. In terms of linear matrix inequalities, sufficient conditions are proposed to ensure the robust stability of the overall closed-loop system composed of system state and estimation error dynamics, as well as the reachability of the sliding mode surface. Furthermore, the systematic design procedures for the robust fault estimation and fault tolerant control scheme are addressed. Finally, simulation studies on a single-link manipulator and a three-tank system are illustrated to demonstrate the effectiveness of the suggested methodologies.

L2 – L∞ reduced-order filter design for T-S fuzzy stochastic discrete systems

ABSTRACTThis paper investigates the problem of the filtering for discrete-time Takagi–Sugeno fuzzy stochastic systems. The objective is to find new filter design conditions ensuring both the mean square asymptotic stability and prescribed performance of the filtering error system. By means of a fuzzy Lypunov function and by introducing some slack variables through an appropriate use of the projection lemma, new analysis conditions of performance are proposed. Then, the full and reduced-order filter design conditions are proposed in Linear Matrix Inequality form. Finally, to illustrate the proposed approach, simulation and comparison with existing results in the literature are given.

Fault Detection Filtering for Uncertain Itô Stochastic Fuzzy Systems With Time-Varying Delays

This paper considers the problem of robust \(H_{\infty }\) fault detection for a class of Ito stochastic Takagi–Sugeno fuzzy systems with time-varying delays and parameter uncertainties. The purpose is to design fuzzy-rule-independent and fuzzy-rule-dependent fault detection filters, which guarantee the fault detection system is not only mean square asymptotically stable, but also satisfies a prescribed \(H_{\infty }\)-norm level for all admissible uncertainties. Via the application of Lyapunov stability theory and the linear matrix inequality technique, novel delay-dependent solvability conditions are obtained. Weighting fault signal approach is utilized to improve the performance of the fault detection system, and explicit expression of the desired filter parameters is characterized by congruence transformation, matrix decomposition, and convex optimization technique. A numerical example and a mass-spring-damper mechanical system are employed to illustrate the usefulness and effectiveness of the proposed method.

Fuzzy fault-detection filtering for uncertain stochastic time-delay systems with randomly missing data

This paper is concerned with the robust H∞ fault-detection problem for a class of uncertain discrete stochastic Takagi–Sugeno fuzzy systems with time-varying delays, parameter uncertainties and randomly missing data in a network environment. We deal with the fault detection by designing fuzzy-rule-independent and fuzzy-rule-dependent fault detection filters, which guarantee the fault detection system is not only robustly stochastically stable, but also satisfies a prescribed H∞ performance level for all admissible uncertainties. Lyapunov stability theory and the linear matrix inequality technique are utilized to derive novel conditions for the desired fault detection filters. The residual evaluation function and detection threshold are also discussed in order to detect the occurrence of faults. A numerical example and a nonlinear mass-spring-damper mechanical system are provided to demonstrate that our fault-detection system is sensitive to faults and simultaneously robust to disturbances.

New Stability Criteria for Stochastic Takagi–Sugeno Fuzzy Systems With Time-Varying Delays

This paper is concerned with the asymptotic stability issue for a class of stochastic Takagi–Sugeno (TS) fuzzy systems with time-varying delays. Then, by utilizing a delay-fractioning method, the stochastic analysis theory combined with the matrix inequality technique, a new set of sufficient condition in terms of linear matrix inequalities is presented which ensures the asymptotic stability of the stochastic TS fuzzy systems with time-delays. The results obtained in this paper are delay-dependent in the sense that they depend on not only the lower bound but also the upper bound of the time-varying delay. Numerical examples are given to illustrate the effectiveness and less conservativeness of the obtained results.

Passivity and passification for stochastic Takagi–Sugeno fuzzy systems with mixed time-varying delays

In this paper, the passivity and passification for stochastic Takagi–Sugeno (T–S) fuzzy systems with both discrete and distributed time-varying delays are investigated without assuming the differentiability of the time-varying delays. By utilizing the Lyapunov functional method, the Itô differential rule and the matrix inequality techniques, several delay-dependent criteria to ensure the passivity and passification of the considered T–S fuzzy systems are established in terms of linear matrix inequalities (LMIs) that can be easily checked by using the standard numerical software. The obtained results generalize some previous results. Two examples are given to show the effectiveness of the proposed criteria.

${\cal H}_{\infty}$ Model Reduction of Takagi–Sugeno Fuzzy Stochastic Systems

This paper is concerned with the problem of H(∞) model reduction for Takagi-Sugeno (T-S) fuzzy stochastic systems. For a given mean-square stable T-S fuzzy stochastic system, our attention is focused on the construction of a reduced-order model, which not only approximates the original system well with an H(∞) performance but also translates it into a linear lower dimensional system. Then, the model reduction is converted into a convex optimization problem by using a linearization procedure, and a projection approach is also presented, which casts the model reduction into a sequential minimization problem subject to linear matrix inequality constraints by employing the cone complementary linearization algorithm. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed methods.

Delay-dependent robust H ∞ control for uncertain stochastic T–S fuzzy systems with time-varying state and input delays

In this article, the problem of delay-dependent robust H ∞ control for uncertain stochastic Takagi–Sugeno fuzzy systems with time-varying state and input delays is investigated. The parameter uncertainties are assumed to be time-varying and norm bounded. Through construction of a new Lyapunov–Krasovskii functional, the delay-dependent robust H ∞ control scheme is presented in terms of linear matrix inequalities (LMIs). By solving these LMIs, a desired fuzzy controller can be obtained. Finally, a numerical example is given to illustrate the effectiveness of the developed method.

Passive fuzzy controller design for stochastic Takagi—Sugeno fuzzy systems with time-varying delay

This paper discusses the issue of stability and stabilization for the non-linear stochastic systems with time-varying delay subject to passivity performance. Based on the fuzzy modelling approach, the non-linear systems can be represented by a stochastic T—S fuzzy model whose consequent part is described by linear differential equations with a multiplicative noise term. For analysing the stability of the stochastic T—S fuzzy model, the less conservative stability criterion derived by Itô's formula and the Lyapunov—Krasovskii function is proposed as a linear matrix inequality (LMI) problem. Furthermore, the passivity theory is employed to discuss the external disturbance effect on the considered system. Through applying the above techniques, the sufficiency conditions are derived to design fuzzy controllers such that the stochastic T—S fuzzy model with time delay is asymptotically stable and passive in the mean square. Finally, two numerical examples are proposed to show the application and effectiveness of the proposed fuzzy controller design method.