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

2013 ◽  
Vol 136 (2) ◽  
Author(s):  
K. Mathiyalagan ◽  
R. Sakthivel ◽  
S. Marshal Anthoni
Keyword(s):  
Asymptotic Stability ◽  
Fuzzy Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Analysis Theory ◽  
The Matrix ◽  
Stability Issue ◽  
Delay Dependent ◽  
Takagi Sugeno

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.

scholarly journals Passivity Analysis and Passive Control for T-S Fuzzy Systems with Leakage Delay and Mixed Time-Varying Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Ting Lei ◽  
Zengshun Chen ◽  
Qiankun Song ◽  
Zhenjiang Zhao
Keyword(s):  
Fuzzy Systems ◽  
Passive Control ◽  
Functional Method ◽  
Leakage Delay ◽  
Linear Matrix ◽  
Time Varying ◽  
The Matrix ◽  
Delay Dependent ◽  
Takagi Sugeno ◽  
Passivity And Passification

The passivity and passification for Takagi-Sugeno (T-S) fuzzy systems with leakage delay and both discrete and distributed time-varying delays are investigated. By employing the Lyapunov functional method and using 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.

Improved Delay-Dependent Stability of Nonlinear Quadratic TS Fuzzy Systems

2019 ◽  
Vol 29 (09) ◽  
pp. 2050134 ◽  
Author(s):  
Khadija Naamane ◽  
El Houssaine Tissir
Keyword(s):  
Fuzzy Systems ◽  
Model Transformation ◽  
Linear Matrix ◽  
Time Varying Delay ◽  
Small Gain ◽  
The Stability ◽  
Delay Dependent ◽  
Takagi Sugeno ◽  
Delay Dependent Stability ◽  
Varying Delay

This paper focuses on the problem of delay-dependent stability for nonlinear quadratic Takagi–Sugeno (TS) fuzzy systems with time-varying delay using the input–output approach. The results are based on the model transformation by employing a three-terms approximation of delayed state vector. By applying the scaled small-gain theorem and Lyapunov–Krasovskii functional, the stability criteria is obtained in terms of linear matrix inequalities. Furthermore, the Wirtinger-based integral inequality approach has been employed to derive less conservative results. Finally, the numerical examples are provided to demonstrate the effectiveness of the obtained results and for comparison with previous work.

Fault-Distribution Dependent Reliable H∞ Control for Takagi-Sugeno Fuzzy Systems

2014 ◽  
Vol 136 (2) ◽  
Author(s):  
R. Sakthivel ◽  
P. Vadivel ◽  
K. Mathiyalagan ◽  
A. Arunkumar
Keyword(s):  
Fuzzy Systems ◽  
State Feedback ◽  
Linear Matrix ◽  
Closed Loop System ◽  
Actuator Failure ◽  
Time Varying Delay ◽  
Actuator Failures ◽  
Delay Dependent ◽  
Takagi Sugeno ◽  
Varying Delay

This paper is concerned with the problem of robust reliable H∞ control for a class of uncertain Takagi-Sugeno (TS) fuzzy systems with actuator failures and time-varying delay. The main objective is to design a state feedback reliable H∞ controller such that, for all admissible uncertainties as well as actuator failure cases, the resulting closed-loop system is robustly asymptotically stable with a prescribed H∞ performance level. Based on the Lyapunov-Krasovskii functional (LKF) method together with linear matrix inequality (LMI) technique, a delay dependent sufficient condition is established in terms of LMIs for the existence of robust reliable H∞ controller. When these LMIs are feasible, a robust reliable H∞ controller can be obtained. Finally, two numerical examples with simulation result are utilized to illustrate the applicability and effectiveness of our obtained result.

scholarly journals Robust Fault Estimation for a Class of T-S Fuzzy Singular Systems with Time-Varying Delay via Improved Delay Partitioning Approach

2016 ◽  
Vol 2016 ◽  
pp. 1-15 ◽  
Author(s):  
Chao Sun ◽  
FuLi Wang ◽  
XiQin He
Keyword(s):  
Singular Systems ◽  
Singular System ◽  
Fault Estimation ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
System A ◽  
Delay Dependent ◽  
Takagi Sugeno ◽  
Varying Delay

The problem of delay-dependent robust fault estimation for a class of Takagi-Sugeno (T-S) fuzzy singular systems is investigated. By decomposing the delay interval into two unequal subintervals and with a new and tighter integral inequality transformation, an improved delay-dependent stability criterion is given in terms of linear matrix inequalities (LMIs) to guarantee that the fuzzy singular system with time-varying delay is regular, impulse-free, and stable firstly. Then, based on this criterion, by considering the system fault as an auxiliary disturbance vector and constructing an appropriate fuzzy augmented system, a fault estimation observer is designed to ensure that the error dynamic system is regular, impulse-free, and robustly stable with a prescribedH∞performance satisfied for all actuator and sensor faults simultaneously, and the obtained fault estimates can practically better depict the size and shape of the faults. Finally, numerical examples are given to show the effectiveness of the proposed approach.

scholarly journals Delay-Range-Dependent Stability Criteria for Takagi-Sugeno Fuzzy Systems with Fast Time-Varying Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Pin-Lin Liu
Keyword(s):  
Linear Matrix ◽  
Fast Time ◽  
Time Varying ◽  
Stability Criteria ◽  
Decomposition Approach ◽  
Time Varying Delay ◽  
Delay Decomposition Approach ◽  
Delay Dependent ◽  
Takagi Sugeno ◽  
Varying Delay

The problem of delay-range-dependent stability for T-S fuzzy system with interval time-varying delay is investigated. The constraint on the derivative of the time-varying delay is not required, which allows the time delay to be a fast time-varying function. By developing delay decomposition approach, integral inequalities approach (IIA), and Leibniz-Newton formula, the information of the delayed plant states can be taken into full consideration, and new delay-dependent sufficient stability criteria are obtained in terms of linear matrix inequalities (LMIs) which can be easily solved by various optimization algorithms. Simulation examples show resulting criteria outperform all existing ones in the literature. It is worth pointing out that our criteria are carried out more efficiently for computation and less conservatism of the proposed criteria.

New Approach to Delay-Dependent Stability Analysis and Stabilization for Fuzzy Systems with Time-Varying Delay

2013 ◽  
Vol 389 ◽  
pp. 471-476 ◽  
Author(s):  
Gang Guo ◽  
Su Ping Zhao
Keyword(s):  
Fuzzy Systems ◽  
Stability Control ◽  
Linear Matrix ◽  
Time Varying ◽  
New Approach ◽  
Time Varying Delay ◽  
Stabilization Condition ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Varying Delay

A new method is proposed for the delay-dependent stability control of fuzzy systems with time-varying delay. A new fuzzy Lyapunov-Krasovskii functional (LKF) is introduced to establish a delay-dependent stability criterion. Based on parallel distributed compensation (PDC) scheme, a stabilization condition is derived and the corresponding controller can be obtained by solving a set of linear matrix inequalities (LMIs).

scholarly journals State Estimation for Discrete-Time Takagi-Sugeno Fuzzy Systems with Time-Varying Delays

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Ting Lei ◽  
Qiankun Song ◽  
Yurong Liu
Keyword(s):  
State Estimation ◽  
Discrete Time ◽  
Fuzzy Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Globally Asymptotically Stable ◽  
Inequality Technique ◽  
Delay Dependent ◽  
Takagi Sugeno ◽  
Error State

The state estimation problem is investigated for discrete-time Takagi-Sugeno fuzzy systems with time-varying delays. By constructing appropriate Lyapunov-Krasovskii functionals and employing matrix inequality technique, a delay-dependent linear matrix inequalities (LMIs) criterion is developed to estimate the systems state with some observed output measurements such that the error-state system is globally asymptotically stable. An example with simulations is given to show the effectiveness of the proposed criterion.

scholarly journals Robust ℋ∞ filtering design for Takagi–Sugeno fuzzy systems with time-varying delay via delta operator approach

2018 ◽  
Vol 10 (1) ◽  
pp. 168781401774539 ◽  
Author(s):  
Min Xu
Keyword(s):  
Fuzzy Systems ◽  
Design Procedure ◽  
Linear Matrix ◽  
Delta Operator ◽  
Time Varying ◽  
Parameter Uncertainties ◽  
Operator Approach ◽  
Time Varying Delay ◽  
Takagi Sugeno ◽  
Varying Delay

The problem of robust ℋ∞ filtering design for Takagi–Sugeno fuzzy systems with time-varying delay via delta operator approach is investigated. The time-varying delay and parameter uncertainties are assumed to be of an internal-like type and a structured linear fractional form, respectively. Based on a Lyapunov–Krasovskii functional in delta domain, robust ℋ∞ filter scheme is proposed. Then, a sufficient condition is established for the existence of the desired filter in terms of linear-matrix inequalities. A numerical example is provided to illustrate the design procedure of the present method.

scholarly journals Novel Delay-Dependent Stabilization for Fuzzy Stochastic Systems with Multiplicative Noise Subject to Passivity Constraint

Processes ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 1445
Author(s):  
Cheung-Chieh Ku ◽  
Wen-Jer Chang ◽  
Kuan-Wei Huang
Keyword(s):  
Fuzzy Systems ◽  
Multiplicative Noise ◽  
Stochastic Systems ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Time Varying Delay ◽  
Delay Dependent ◽  
Varying Delay

A novel delay-dependent stability criterion for Takagi-Sugeno (T-S) fuzzy systems with multiplicative noise is addressed in this paper subject to passivity performance. The general case of interval time-varying delay is considered for the practical control issue. For the criterion, an integral Lyapunov-Krasovskii function is proposed to derive some sufficient relaxed conditions and to avoid the derivative of the membership function. Moreover, a free-matrix inequality is adopted to deal with the delay terms such that the available derivative of time-varying delay is bigger than one. In order to employ a convex optimization algorithm to find the control gain, a projection lemma is applied to acquire the Linear Matrix Inequality (LMI) form of the sufficient conditions. With the obtained gains, a fuzzy controller is designed by the concept of Parallel Distributed Compensation (PDC) such that the delayed T-S fuzzy systems with multiplicative noise are asymptotically stable and passive in the mean square. Finally, a stabilization problem of the ship’s autopilot dynamic system and some comparisons are discussed during the simulation results.

Sign in / Sign up

Export Citation Format

Share Document