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.

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.

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.

A New Approach to Robust and Non-Fragile Control of Uncertain T-S Fuzzy Systems with Interval Time-Delay

2013 ◽  
Vol 662 ◽  
pp. 801-806
Author(s):  
Li Li
Keyword(s):  
Fuzzy System ◽  
Fuzzy Systems ◽  
State Feedback ◽  
Time Varying ◽  
Parameter Uncertainties ◽  
Feedback Controllers ◽  
New Approach ◽  
Time Varying Delay ◽  
Delay Dependent ◽  
Varying Delay

This paper describes the synthesis of robust and non-fragile state feedback controllers for T-S fuzzy system with time-varying delay in a range and parameter uncertainties. A new method is proposed by de¯ning new Lyapunov functionals and introducing some free-weighting matrices. Impr oved delay-dependent results are presented.

New Sufficient Conditions on H∞ Filter Design for Nonlinear T-S Fuzzy Systems with Time Delays

2012 ◽  
Vol 263-266 ◽  
pp. 162-166
Author(s):  
Su Huan Yi ◽  
Sheng Juan Huang
Keyword(s):  
Fuzzy Systems ◽  
Time Delays ◽  
Filter Design ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying Delay ◽  
Weighting Matrix ◽  
Decoupling Approach ◽  
Takagi Sugeno ◽  
Varying Delay

This paper focuses on the problem of H∞ filter design for continuous Takagi-Sugeno (T-S) fuzzy systems with an interval time-varying delay in the state. Based on the free weighting matrix method combined with a matrix decoupling approach, some new sufficient results are proposed in forms of linear matrix inequalities (LMIs), which can achieve much less conservative feasibility conditions. Finally, the effectiveness of the proposed method is demonstrated ba an example.

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 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 Further Results Concerning Delay-DependentH∞Control for Uncertain Discrete-Time Systems with Time-Varying Delay

2009 ◽  
Vol 2009 ◽  
pp. 1-24 ◽  
Author(s):  
Guangdeng Zong ◽  
Linlin Hou ◽  
Hongyong Yang
Keyword(s):  
Discrete Time ◽  
Linear Matrix ◽  
Time Varying ◽  
Closed Loop System ◽  
Parameter Uncertainties ◽  
Time Varying Delay ◽  
Discrete Time Systems ◽  
Delay Dependent ◽  
Time Systems ◽  
Varying Delay

This paper addresses the problem ofH∞control for uncertain discrete-time systems with time-varying delays. The system under consideration is subject to time-varying norm-bounded parameter uncertainties in both the state and controlled output. Attention is focused on the design of a memoryless state feedback controller, which guarantees that the resulting closed-loop system is asymptotically stable and reduces the effect of the disturbance input on the controlled output to a prescribed level irrespective of all the admissible uncertainties. By introducing some slack matrix variables, new delay-dependent conditions are presented in terms of linear matrix inequalities (LMIs). Numerical examples are provided to show the reduced conservatism and lower computational burden than the previous results.

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

2012 ◽  
Vol 516-517 ◽  
pp. 1391-1395
Author(s):  
Ren Bo ◽  
Zhang Guo
Keyword(s):  
Stability Analysis ◽  
Fuzzy Systems ◽  
Linear Matrix ◽  
New Approach ◽  
Time Varying Delay ◽  
Fuzzy Lyapunov Function ◽  
Stabilization Condition ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Varying Delay

This paper is presented a new method for stability analysis and stabilization problems of continuous-time T-S fuzzy systems with time-delay. A fuzzy Lyapunov function is introduced to establish some delay-dependent stability criteria. Less conservative results are obtained by considering the additional useful terms when estimating the upper bound of the derivative of function. Then based on parallel distributed compensation, a delay-dependent stabilization condition is derived and the corresponding controller can be obtained by solving a set of linear matrix inequalities (LMIs).

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