scholarly journals Delay-Dependent Stability Analysis of Uncertain Fuzzy Systems with State and Input Delays under Imperfect Premise Matching

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Zejian Zhang ◽  
Xiao-Zhi Gao ◽  
Kai Zenger ◽  
Xianlin Huang
Keyword(s):  
Fuzzy Systems ◽  
Design Method ◽  
Integral Term ◽  
Flexibility Design ◽  
State And Input Delays ◽  
The Stability ◽  
Input Delays ◽  
Delay Dependent ◽  
Imperfect Premise Matching ◽  
Delay Dependent Stability

This paper discusses the stability and stabilization problem for uncertain T-S fuzzy systems with time-varying state and input delays. A new augmented Lyapunov function with an additional triple-integral term and different membership functions of the fuzzy models and fuzzy controllers are introduced to derive the stability criterion, which is less conservative than the existing results. Moreover, a new flexibility design method is also provided. Some numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed method.

New Approach to Non-Fragile Control of Uncertain Fuzzy Systems with Time-Delay

2013 ◽  
Vol 433-435 ◽  
pp. 1131-1135
Author(s):  
Li Li
Keyword(s):  
Fuzzy System ◽  
Fuzzy Systems ◽  
Time Delays ◽  
Upper Bounds ◽  
Stability Conditions ◽  
New Approach ◽  
State And Input Delays ◽  
Input Delays ◽  
Delay Dependent ◽  
Delay Dependent Stability

This paper focuses on the delay-dependent stability analysis and stabilization for T-S fuzzy system systems with state and input delays. Some new and less conservative delay-dependent small stability conditions are explicitly obtained. The upper bounds of time-delays are obtained by using small convex optimization.Finally, a numerical example is included to show the effectiveness.

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 New Stability Analysis for Linear Systems with Time-Varying Delay Based on Combined Convex Technique

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Bin Yang ◽  
Chen-xin Fan
Keyword(s):  
Linear Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Integral Term ◽  
Time Varying Delay ◽  
Wirtinger Inequality ◽  
The Stability ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Varying Delay

A novel combined convex method is developed for the stability of linear systems with a time-varying delay. A new delay-dependent stability condition expressed in terms of linear matrix inequalities (LMIs) is derived by employing a dedicated constructed Lyapunov-Krasovskii functional (LKF), utilizing the Wirtinger inequality and the reciprocally convex approach to handle the integral term of quadratic quantities. Different from the previous convex techniques which only tackle the time-varying delay, our method adopts the idea of combined convex technique which can tackle not only the delay but also the delay variation. Four well-known examples are illustrated to show the effectiveness of the proposed results.

LMI-Based Robust Control of Norm-Bounded Uncertain Perturbed Discrete Systems with both State and Input Delays

2012 ◽  
Vol 591-593 ◽  
pp. 1208-1211
Author(s):  
Yang Li
Keyword(s):  
Controller Design ◽  
Design Method ◽  
Discrete Systems ◽  
Optimization Techniques ◽  
Linear Matrix ◽  
Parameter Uncertainties ◽  
Operating Region ◽  
State And Input Delays ◽  
Input Delays ◽  
Delay Dependent

This paper is concerned with the problem of norm-bounded uncertain perturbed discrete systems(NUPDS) with both state and input delays.Based on constructing a quadratic Lyapunov function, a delay-dependent criteria, which is expressed in terms of linear matrix inequalities(LMIs), has been proposed to guarantee the asymptotic stability of the system.Compared with existed open literature, this paper suggests a novel controller design method , which deals with more aspects including time-varying parameter uncertainties, perturbation, state and input time-delays.In addition, we also consider the condition of operating region is outer approximated by extended ellipsoids, which can be ultilized for dealing with the perburbed term of the system. The solution of the LMIs can be obtained easily by using existed efficient convex optimization techniques. In the end, a numerical example is given to illustrate the effectiveness of the proposed theoretical result.

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