ASYMPTOTIC STABILITY OF NONLINEAR DELAY-DIFFERENCE SYSTEM VIA MATRIX INEQUALITIES AND APPLICATION

2009 ◽  
Vol 06 (03) ◽  
pp. 389-397 ◽  
Author(s):  
K. RATCHAGIT
Keyword(s):  
Asymptotic Stability ◽  
Zero Solution ◽  
Discrete Version ◽  
Multiple Delays ◽  
Difference System ◽  
Matrix Inequalities ◽  
Delay Difference ◽  
Lyapunov Second Method ◽  
Nonlinear Delay ◽  
Delay Difference System

In this paper, we derive a sufficient condition for asymptotic stability of the zero solution of delay-difference system of nonlinear delay-difference system in terms of certain matrix inequalities by using a discrete version of the Lyapunov second method. The result is applied to obtain new stability condition in terms of certain matrix inequalities for some class of nonlinear delay-difference system such as delay-difference system of nonlinear delay-difference system with multiple delays in terms of certain matrix inequalities. Our results can be well suited for computational purposes.

ASYMPTOTIC STABILITY OF DELAY-DIFFERENCE SYSTEM OF HOPFIELD NEURAL NETWORKS VIA MATRIX INEQUALITIES AND APPLICATION

2007 ◽  
Vol 17 (05) ◽  
pp. 425-430 ◽  
Author(s):  
KREANGKRI RATCHAGIT
Keyword(s):  
Neural Networks ◽  
Asymptotic Stability ◽  
Zero Solution ◽  
Hopfield Neural Networks ◽  
Discrete Version ◽  
Multiple Delays ◽  
Difference System ◽  
Matrix Inequalities ◽  
Delay Difference ◽  
Delay Difference System

In this paper, we derive a sufficient condition for asymptotic stability of the zero solution of delay-difference system of Hopfield neural networks in terms of certain matrix inequalities by using a discrete version of the Lyapunov second method. The result is applied to obtain new asymptotic stability condition for some class of delay-difference system such as delay-difference system of Hopfield neural networks with multiple delays in terms of certain matrix inequalities. Our results can be well suited for computational purposes.

ASYMPTOTIC STABILITY OF DELAY-DIFFERENCE CONTROL SYSTEM VIA MATRIX INEQUALITIES AND APPLICATION

2010 ◽  
Vol 03 (02) ◽  
pp. 347-355 ◽  
Author(s):  
K. Ratchagit
Keyword(s):  
Control System ◽  
Asymptotic Stability ◽  
Zero Solution ◽  
Discrete Version ◽  
Stability Conditions ◽  
Multiple Delays ◽  
Matrix Inequalities ◽  
Delay Difference ◽  
Lyapunov Second Method

In this paper, we obtain some criteria for determining the asymptotic stability of the zero solution of delay-difference control system in terms of certain matrix inequalities by using a discrete version of the Lyapunov second method. The result has been applied to obtain new stability conditions for some classes of delay-difference control system such as delay-difference control system with multiple delays in terms of certain matrix inequalities. Our results can be well suited for computational purposes.

scholarly journals OSCILLATION OF THREE DIMENSIONAL NEUTRAL DELAYDIFFERENCE SYSTEMS

2016 ◽  
Vol 12 (10) ◽  
pp. 6751-6757
Author(s):  
K THANGAVELU ◽  
G SARASWATHI
Keyword(s):  
Three Dimensional ◽  
Difference System ◽  
Neutral Delay ◽  
Oscillation Criteria ◽  
Delay Difference ◽  
Delay Difference System

This paper deals with the some oscillation criteria for the three dimensional neutral delay difference system of the form Δ xn+pnxn-k =bnynα Δ yn =cn znβ Δ(zn)=-anxn-l+1γ , n=1,2,…, Examples illustrating the results are inserted.

scholarly journals Dynamics of a Family of Nonlinear Delay Difference Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Qiuli He ◽  
Taixiang Sun ◽  
Hongjian Xi
Keyword(s):  
Asymptotic Stability ◽  
Difference Equation ◽  
Difference Equations ◽  
Sufficient Conditions ◽  
Positive Equilibrium ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Delay Difference Equations ◽  
Delay Difference ◽  
Nonlinear Delay

We study the global asymptotic stability of the following difference equation:xn+1=f(xn-k1,xn-k2,…,xn-ks;xn-m1,xn-m2,…,xn-mt),n=0,1,…,where0≤k1<k2<⋯<ksand0≤m1<m2<⋯<mtwith{k1,k2,…,ks}⋂‍{m1,m2,…,mt}=∅,the initial values are positive, andf∈C(Es+t,(0,+∞))withE∈{(0,+∞),[0,+∞)}. We give sufficient conditions under which the unique positive equilibriumx-of that equation is globally asymptotically stable.

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