scholarly journals Nonfragile H∞ Filter Design for Nonlinear Continuous-Time System with Interval Time-Varying Delay

2018 ◽  
Vol 2018 ◽  
pp. 1-17
Author(s):  
Zhongda Lu ◽  
Guoliang Zhang ◽  
Yi Sun ◽  
Jie Sun ◽  
Fangming Jin ◽  
...  
Keyword(s):  
Continuous Time ◽  
Filter Design ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Decoupling Method ◽  
Interval Time ◽  
Time Varying Delay ◽  
Error System ◽  
Delay Dependent

This paper investigates nonfragile H∞ filter design for a class of continuous-time delayed Takagi-Sugeno (T-S) fuzzy systems with interval time-varying delays. Filter parameters occur multiplicative gain variations according to the filter’s implementation, to handle this variations, a nonfragile H∞ filter is presented and a novel filtering error system is established. The nonfragile H∞ filter guarantees the filtering error system to be asymptotically stable and satisfies given H∞ performance index. By constructing a novel Lyapunov-Krasovskii function and using the linear matrix inequality (LMI), delay-dependent conditions are exploited to derive sufficient conditions for nonfragile designing H∞ filter. Using new matrix decoupling method to reduce the computational complexity, the filter parameters can be obtained by solving a set of linear matrix inequalities (LMIs). Finally, numerical examples are given to show the effectiveness of the proposed method.

scholarly journals Event-Based Nonfragile H∞ Filter Design for Networked Control Systems with Interval Time-Varying Delay

2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Zhongda Lu ◽  
Guangtao Ran ◽  
Guoliang Zhang ◽  
Fengxia Xu
Keyword(s):  
Networked Control Systems ◽  
Filter Design ◽  
Linear Matrix ◽  
Time Varying ◽  
Sampled Data ◽  
Interval Time ◽  
Time Varying Delay ◽  
Error System ◽  
Varying Delay ◽  
Event Triggered

This paper first investigates the event-triggered nonfragile H∞ filter design for a class of nonlinear NCSs with interval time-varying delay. An event-triggered scheme is addressed to determine sampled data to be transmitted so that network communication resource can be saved significantly. The nonfragile filter design is assumed to include multiplicative gain variations according to the filter’s implement. Under the event-triggered scheme, the filtering error system is modeled as a system with interval time-varying delay. By constructing a new Lyapunov-Krasovskii functional and employing Wirtinger inequality, a sufficient condition is derived, which guarantees that the filtering error system is asymptotically stable with the prescribed H∞ performance. The nonfragile filter parameters are obtained by solving a set of linear matrix inequalities. Two numerical examples are given to show the usefulness and the effectiveness of the proposed method.

A DELAY-DEPENDENT APPROACH TO ROBUST TAKAGI–SUGENO FUZZY CONTROL OF UNCERTAIN RECURRENT NEURAL NETWORKS WITH MIXED INTERVAL TIME-VARYING DELAYS

2011 ◽  
Vol 20 (08) ◽  
pp. 1571-1589 ◽  
Author(s):  
K. H. TSENG ◽  
J. S. H. TSAI ◽  
C. Y. LU
Keyword(s):  
Fuzzy Control ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Upper And Lower Bounds ◽  
Linear Matrix ◽  
Uncertain Parameters ◽  
Time Varying ◽  
Interval Time ◽  
Delay Dependent ◽  
Takagi Sugeno

This paper deals with the problem of globally delay-dependent robust stabilization for Takagi–Sugeno (T–S) fuzzy neural network with time delays and uncertain parameters. The time delays comprise discrete and distributed interval time-varying delays and the uncertain parameters are norm-bounded. Based on Lyapunov–Krasovskii functional approach and linear matrix inequality technique, delay-dependent sufficient conditions are derived for ensuring the exponential stability for the closed-loop fuzzy control system. An important feature of the result is that all the stability conditions are dependent on the upper and lower bounds of the delays, which is made possible by using the proposed techniques for achieving delay dependence. Another feature of the results lies in that involves fewer matrix variables. Two illustrative examples are exploited in order to illustrate the effectiveness of the proposed design methods.

On Improved Delay-Range-Dependent Stability Criteria for Linear Systems with Interval Time-Varying Delay

2013 ◽  
Vol 427-429 ◽  
pp. 1306-1310
Author(s):  
Jun Jun Hui ◽  
He Xin Zhang ◽  
Fei Meng ◽  
Xin Zhou
Keyword(s):  
Functional Method ◽  
Linear Matrix ◽  
Time Varying ◽  
Stability Criteria ◽  
Interval Time ◽  
Time Varying Delay ◽  
Weighting Matrix ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Varying Delay

In this paper, we consider the problem of robust delay-dependent stability for a class of linear uncertain systems with interval time-varying delay. By using the directly Lyapunov-Krasovskii (L-K) functional method, integral inequality approach and the free weighting matrix technique, new less conservative stability criteria for the system is formulated in terms of linear matrix inequalities .Numerical examples are given to show the effectiveness of the proposed approach.

scholarly journals Stability Analysis and Robust H∞ Filtering for Discrete-time Nonlinear Systems with Time-varying Delays

2021 ◽  
Vol 20 ◽  
pp. 281-288
Author(s):  
Mengying Ding ◽  
Yali Dong
Keyword(s):  
Nonlinear Systems ◽  
Discrete Time ◽  
Filter Design ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Asymptotically Stable ◽  
Matrix Inequalities ◽  
Error System ◽  
Error Dynamics

In this paper, we investigate the problem of robust H∞ filter design for a class of discrete-time nonlinear systems. The systems under consider involves time-varying delays and parameters uncertainties. The main objective is to design a linear full-order filter to ensure that the resulting filtering error system is asymptotically stable with a prescribed H∞ performance level. By constructing an appropriate Lyapunov-Krasovskii functional, some novel sufficient conditions are established to guarantee the filter error dynamics system is robust asymptotically stable with H∞ performance γ , and the H∞ filter is designed in term of linear matrix inequalities. Finally, a numerical example is provided to illustrate the efficiency of proposed method.

scholarly journals Improved Delay-Dependent Stability Analysis for Neural Networks with Interval Time-Varying Delays

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Jun-kang Tian ◽  
Yan-min Liu
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Upper And Lower Bounds ◽  
Linear Matrix ◽  
Time Varying ◽  
Interval Time ◽  
Time Varying Delay ◽  
Improved Stability ◽  
Delay Dependent ◽  
Delay Partitioning

The problem of delay-dependent asymptotic stability analysis for neural networks with interval time-varying delays is considered based on the delay-partitioning method. Some less conservative stability criteria are established in terms of linear matrix inequalities (LMIs) by constructing a new Lyapunov-Krasovskii functional (LKF) in each subinterval and combining with reciprocally convex approach. Moreover, our criteria depend on both the upper and lower bounds on time-varying delay and its derivative, which is different from some existing ones. Finally, a numerical example is given to show the improved stability region of the proposed results.

scholarly journals Delay-Dependent Robust Exponential Stability for Uncertain Neutral Stochastic Systems with Interval Time-Varying Delay

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
Weihua Mao ◽  
Feiqi Deng ◽  
Anhua Wan
Keyword(s):  
Exponential Stability ◽  
Stochastic Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Mean Square ◽  
Robust Exponential Stability ◽  
Interval Time ◽  
Time Varying Delay ◽  
Mean Square Exponential Stability ◽  
Delay Dependent

This paper discusses the mean-square exponential stability of uncertain neutral linear stochastic systems with interval time-varying delays. A new augmented Lyapunov-Krasovskii functional (LKF) has been constructed to derive improved delay-dependent robust mean-square exponential stability criteria, which are forms of linear matrix inequalities (LMIs). By free-weight matrices method, the usual restriction that the stability conditions only bear slow-varying derivative of the delay is removed. Finally, numerical examples are provided to illustrate the effectiveness of the proposed method.

scholarly journals Improved Results on FuzzyH∞Filter Design for T-S Fuzzy Systems

2010 ◽  
Vol 2010 ◽  
pp. 1-21 ◽  
Author(s):  
Jiyao An ◽  
Guilin Wen ◽  
Wei Xu
Keyword(s):  
Upper Bound ◽  
Fuzzy Systems ◽  
Filter Design ◽  
Linear Matrix ◽  
Time Varying ◽  
Bounded Interval ◽  
Time Varying Delay ◽  
Error System ◽  
Varying Delay ◽  
Uniformly Bounded

The fuzzyH∞filter design problem for T-S fuzzy systems with interval time-varying delay is investigated. The delay is considered as the time-varying delay being either differentiable uniformly bounded with delay derivative in bounded interval or fast varying (with no restrictions on the delay derivative). A novel Lyapunov-Krasovskii functional is employed and a tighter upper bound of its derivative is obtained. The resulting criterion thus has advantages over the existing ones since we estimate the upper bound of the derivative of Lyapunov-Krasovskii functional without ignoring some useful terms. A fuzzyH∞filter is designed to ensure that the filter error system is asymptotically stable and has a prescribedH∞performance level. An improved delay-derivative-dependent condition for the existence of such a filter is derived in the form of linear matrix inequalities (LMIs). Finally, numerical examples are given to show the effectiveness of the proposed method.

scholarly journals Robust Stability and Stabilization of a Class of Uncertain Nonlinear Discrete-Time Stochastic Systems with Interval Time-Varying Delays

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
Shuang Liang ◽  
Yali Dong
Keyword(s):  
Discrete Time ◽  
Stochastic Stability ◽  
Stochastic Systems ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Interval Time ◽  
Stochastic Stabilization ◽  
Stability And Stabilization ◽  
Delay Dependent

This paper deals with the problems of the robust stochastic stability and stabilization for a class of uncertain discrete-time stochastic systems with interval time-varying delays and nonlinear disturbances. By utilizing a new Lyapunov-Krasovskii functional and some well-known inequalities, some new delay-dependent criteria are developed to guarantee the robust stochastic stability of a class of uncertain discrete-time stochastic systems in terms of the linear matrix inequality (LMI). Then based on the state feedback controller, the delay-dependent sufficient conditions of robust stochastic stabilization for a class of uncertain discrete-time stochastic systems with interval time-varying delays are established. The controller gain is designed to ensure the robust stochastic stability of the closed-loop system. Finally, illustrative examples are given to demonstrate the effectiveness of the proposed method.

New Delay-Dependent Stability Criteria for Systems with Interval Time-Varying Delay

2011 ◽  
Vol 48-49 ◽  
pp. 734-739 ◽  
Author(s):  
Dong Sheng Xu ◽  
Jun Kang Tian
Keyword(s):  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Stability Criteria ◽  
Integral Term ◽  
Interval Time ◽  
Time Varying Delay ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Varying Delay

This paper is concerned with delay-dependent stability for systems with interval time varying delay. By defining a new Lyapunov functional which contains a triple-integral term with the idea of decomposing the delay interval of time-varying delay, an improved criterion of asymptotic stability is derived in term of linear matrix inequalities. The criterion proves to be less conservative with fewer matrix variables than some previous ones. Finally, a numerical example is given to show the effectiveness of the proposed method.

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