scholarly journals Exponential Stability and Guaranteed Cost of Switched Linear Systems with Mixed Time-Varying Delays

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
El Houssaine Tissir
Keyword(s):  
Exponential Stability ◽  
Linear Systems ◽  
Time Delays ◽  
Functional Method ◽  
Linear Matrix ◽  
Switched Linear Systems ◽  
Mixed Time Delays ◽  
Guaranteed Cost ◽  
Lyapunov Functional Method ◽  
Delay Dependent

This paper deals with the problems of exponential stability and guaranteed cost of switched linear systems with mixed time delays. Based on Lyapunov functional method, we present new delay-dependent conditions that guarantee both the exponential stability and an upper bound for some performance index. The criteria are delay-dependent conditions and are given in terms of linear matrix inequalities. Numerical examples are provided to illustrate the effectiveness of the results.

scholarly journals Delay-Dependent Stability Criterion of Arbitrary Switched Linear Systems with Time-Varying Delay

2010 ◽  
Vol 2010 ◽  
pp. 1-16 ◽  
Author(s):  
Jun Li ◽  
Weigen Wu ◽  
Jimin Yuan ◽  
Qianrong Tan ◽  
Xing Yin
Keyword(s):  
Linear Systems ◽  
Stability Criterion ◽  
Linear Matrix ◽  
Time Varying ◽  
Switched Linear Systems ◽  
Time Varying Delay ◽  
Liner System ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Varying Delay

This paper deals with the problem of delay-dependent stability criterion of arbitrary switched linear systems with time-varying delay. Based on switched quadratic Lyapunov functional approach and free-weighting matrix approach, some linear matrix inequality criterions are found to guarantee delay-dependent asymptotically stability of these systems. Simultaneously, arbitrary switched linear system can be expressed as a problem of uncertain liner system, so some delay-dependent stability criterions are obtained with the result of uncertain liner system. Two examples illustrate the exactness of the proposed criterions.

Synchronization of Uncertain Neural Networks with H8 Performance and Mixed Time-Delays

2011 ◽  
pp. 1208-1232
Author(s):  
Hamid Reza Karimi
Keyword(s):  
Neural Networks ◽  
Time Delays ◽  
Sufficient Conditions ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Mixed Delays ◽  
Mixed Time Delays ◽  
Initial States ◽  
Delayed State Feedback ◽  
Delay Dependent

An exponential H8 synchronization method is addressed for a class of uncertain master and slave neural networks with mixed time-delays, where the mixed delays comprise different neutral, discrete and distributed time-delays. An appropriate discretized Lyapunov-Krasovskii functional and some free weighting matrices are utilized to establish some delay-dependent sufficient conditions for designing a delayed state-feedback control as a synchronization law in terms of linear matrix inequalities under less restrictive conditions. The controller guarantees the exponential H8 synchronization of the two coupled master and slave neural networks regardless of their initial states. Numerical simulations are provided to demonstrate the effectiveness of the established synchronization laws.

scholarly journals Delay-Dependent Dynamics of Switched Cohen-Grossberg Neural Networks with Mixed Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Peng Wang ◽  
Haijun Hu ◽  
Zheng Jun ◽  
Yanxiang Tan ◽  
Li Liu
Keyword(s):  
Neural Networks ◽  
Average Dwell Time ◽  
Functional Method ◽  
Linear Matrix ◽  
Mixed Delays ◽  
Ultimate Boundedness ◽  
Globally Exponential Stability ◽  
Lyapunov Functional Method ◽  
Uniformly Ultimate Boundedness ◽  
Delay Dependent

This paper aims at studying the problem of the dynamics of switched Cohen-Grossberg neural networks with mixed delays by using Lyapunov functional method, average dwell time (ADT) method, and linear matrix inequalities (LMIs) technique. Some conditions on the uniformly ultimate boundedness, the existence of an attractors, the globally exponential stability of the switched Cohen-Grossberg neural networks are developed. Our results extend and complement some earlier publications.

Exponential Convergence Rate Estimation for a Class of BAM Neural Networks with Time-Delays

2010 ◽  
Vol 143-144 ◽  
pp. 707-711
Author(s):  
Jian Dong Yu
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Decay Rate ◽  
Time Delays ◽  
Linear Matrix ◽  
Bam Neural Networks ◽  
Parameter Uncertainties ◽  
Mixed Time Delays ◽  
Weighting Matrix ◽  
Rate Dependent

This paper is concerned with the exponential stability analysis problem for a class of neutral bidirectional associative memory (BAM) neural networks with parameter uncertainties and mixed time-delays where the parameter uncertainties are norm-bounded and the mixed time-delays involve discrete, distributed and neutral time-delays. By utilizing free-weighting matrix method and an appropriately constructed Lyapunov-Krasovskii Functional, some nove delay-dependent and decay-rate dependent exponential stability criteria are derived in the terms of linear matrix inequalities (LMIs). Meanwhile, the maximum allowable decay rate can be estimated based on the obtained results. Two numerical examples are presented to demonstrate the effectiveness of the proposed method.

Stability Analysis of Static Neural Network with Time-Varying Delays

2014 ◽  
Vol 644-650 ◽  
pp. 2442-2445
Author(s):  
Rui Zhang ◽  
Meng Xin Li ◽  
Mei Ju Liu
Keyword(s):  
Exponential Stability ◽  
Lyapunov Functional ◽  
Global Exponential Stability ◽  
Functional Method ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Main Condition ◽  
Change Rate ◽  
Lyapunov Functional Method

In this paper, the global exponential stability is discussed for static neural networks with time varying delays. On the basis of the linear matrix inequalities (LMIs) technique, and Lyapunov functional method, we have obtained the main condition to ensure the global exponential stability of the equilibrium point for this system, which is dependent on the change rate of time varying delays. The proposed result is less restrictive than those given in the earlier literatures, easier to check in practice. Remarks are made with other previous works to show the superiority of the obtained results, and the simulation examples are used to demonstrate the effectiveness of our results.

scholarly journals Stability in Switched Cohen-Grossberg Neural Networks with Mixed Time Delays and Non-Lipschitz Activation Functions

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Huaiqin Wu ◽  
Guohua Xu ◽  
Chongyang Wu ◽  
Ning Li ◽  
Kewang Wang ◽  
...  
Keyword(s):  
Neural Networks ◽  
Time Delays ◽  
Average Dwell Time ◽  
Linear Matrix ◽  
Activation Functions ◽  
Mixed Time Delays ◽  
Switched Neural Networks ◽  
Exponentially Stable ◽  
The Stability ◽  
Delay Dependent

The stability for the switched Cohen-Grossberg neural networks with mixed time delays andα-inverse Hölder activation functions is investigated under the switching rule with the average dwell time property. By applying multiple Lyapunov-Krasovskii functional approach and linear matrix inequality (LMI) technique, a delay-dependent sufficient criterion is achieved to ensure such switched neural networks to be globally exponentially stable in terms of LMIs, and the exponential decay estimation is explicitly developed for the states too. Two illustrative examples are given to demonstrate the validity of the theoretical results.

scholarly journals Delay-dependent passivity analysis of nondeterministic genetic regulatory networks with leakage and distributed delays against impulsive perturbations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
S. Senthilraj ◽  
T. Saravanakumar ◽  
R. Raja ◽  
J. Alzabut
Keyword(s):  
Time Delays ◽  
Regulatory Networks ◽  
Functional Method ◽  
Genetic Regulatory Networks ◽  
Distributed Delays ◽  
Mixed Time Delays ◽  
Stochastically Stable ◽  
Impulsive Perturbations ◽  
Stochastic Genetic Regulatory Networks ◽  
Delay Dependent

AbstractThis work is concerned with the problem for stochastic genetic regulatory networks (GRNs) subject to mixed time delays via passivity control in which mixed time delays consist of leakage, discrete, and distributed delays. The main aim of this paper is constructing a passivity-based criteria under impulsive perturbations such that the proposed GRNs are stochastically stable. Based on the Lyapunov functional method and Jensen’s integral inequality, we obtain a new set of novel passivity based delay-dependent sufficient condition in the form of LMIs, which can be determined via existing numerical software. Finally, we propose numerical simulations to show the efficiency of the proposed method.

Synchronization of Uncertain Neural Networks with performance and Mixed Time-Delays

2011 ◽  
pp. 261-288
Author(s):  
Hamid Reza Karimi
Keyword(s):  
Neural Networks ◽  
Time Delays ◽  
Sufficient Conditions ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Mixed Delays ◽  
Mixed Time Delays ◽  
Initial States ◽  
Delayed State Feedback ◽  
Delay Dependent

An exponential H8 synchronization method is addressed for a class of uncertain master and slave neural networks with mixed time-delays, where the mixed delays comprise different neutral, discrete and distributed time-delays. An appropriate discretized Lyapunov-Krasovskii functional and some free weighting matrices are utilized to establish some delay-dependent sufficient conditions for designing a delayed state-feedback control as a synchronization law in terms of linear matrix inequalities under less restrictive conditions. The controller guarantees the exponential H8 synchronization of the two coupled master and slave neural networks regardless of their initial states. Numerical simulations are provided to demonstrate the effectiveness of the established synchronization laws.

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