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.

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.

scholarly journals Stability conditions for linear delay difference equations: a survey and perspectives

2015 ◽  
Vol 63 (1) ◽  
pp. 1-29 ◽  
Author(s):  
Jan Čermák
Keyword(s):  
Asymptotic Stability ◽  
Difference Equations ◽  
Sufficient Conditions ◽  
Zero Solution ◽  
Stability Conditions ◽  
Linear Delay ◽  
Necessary And Sufficient ◽  
Delay Difference Equations ◽  
Delay Difference ◽  
Theoretical Results

Abstract The paper presents an overview of the basic results and methods for stability investigations of higher-order linear autonomous difference equations. The presented criteria formulate several types of necessary and sufficient conditions for the asymptotic stability of the zero solution of studied equations, with a special emphasize put on delay difference equations. Various comments, comparisons, examples and illustrations are given to support theoretical results.

scholarly journals Stability investigation of quadratic systems with delay

2000 ◽  
Vol 13 (1) ◽  
pp. 85-92 ◽  
Author(s):  
Vladimir Davydov ◽  
Denis Khusainov
Keyword(s):  
Asymptotic Stability ◽  
Quadratic Form ◽  
Stability Region ◽  
Zero Solution ◽  
Stability Conditions ◽  
Quadratic Systems ◽  
Systems Of Differential Equations ◽  
Asymptotic Stability Region ◽  
Lyapunov’S Second Method ◽  
Form Stability

Systems of differential equations with quadratic right-hand sides with delay are considered in the paper. Compact matrix notation form is proposed for the systems of such type. Stability investigations are performed by Lyapunov's second method with functions of quadratic form. Stability conditions of quadratic systems with delay, uniformly by argument deviation, and with delay depending on the system's parameters are derived. A guaranteed radius of the ball of asymptotic stability region for zero solution is obtained.

scholarly journals Further results on the asymptotic stability of Riemann–Liouville fractional neutral systems with variable delays

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Yener Altun
Keyword(s):  
Asymptotic Stability ◽  
Zero Solution ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Stability Criteria ◽  
Neutral Systems ◽  
Variable Delays ◽  
The Stability ◽  
Derivatives Of ◽  
Fractional Neutral Systems

Abstract In this paper, the investigation of the asymptotic stability of Riemann–Liouville fractional neutral systems with variable delays has been presented. The advantage of the Lyapunov functional was used to achieve the desired results. The stability criteria obtained for zero solution of the system were formulated as linear matrix inequalities (LMIs) which can be easily solved. The advantage of the considered method is that the integer-order derivatives of the Lyapunov functionals can be directly calculated. Finally, three numerical examples have been evaluated to illustrate that the proposed method is flexible and efficient in terms of computation and to demonstrate the feasibility of established assumptions by MATLAB-Simulink.

scholarly journals A note on asymptotic stability conditions for delay difference equations

2005 ◽  
Vol 2005 (7) ◽  
pp. 1007-1013 ◽  
Author(s):  
T. Kaewong ◽  
Y. Lenbury ◽  
P. Niamsup
Keyword(s):  
Asymptotic Stability ◽  
Sufficient Conditions ◽  
Stability Conditions ◽  
Delay Difference Equation ◽  
Linear Delay ◽  
Necessary And Sufficient ◽  
Positive Integers ◽  
Delay Difference Equations ◽  
Delay Difference ◽  
Asymptotic Stability Conditions

We obtain necessary and sufficient conditions for the asymptotic stability of the linear delay difference equationxn+1+p∑j=1Nxn−k+(j−1)l=0, wheren=0,1,2,…,is a real number, andk,l, andNare positive integers such thatk>(N−1)l.

Two types of stability conditions for linear delay difference equations

2015 ◽  
Vol 9 (1) ◽  
pp. 120-138 ◽  
Author(s):  
Jan Cermák ◽  
Jiří Jánský ◽  
Petr Tomásek
Keyword(s):  
Differential Equation ◽  
Asymptotic Stability ◽  
Linear Difference Equation ◽  
Stability Conditions ◽  
Linear Delay ◽  
Delay Differential ◽  
Necessary And Sufficient ◽  
Delay Difference Equations ◽  
Delay Difference ◽  
Asymptotic Stability Conditions

The paper discusses asymptotic stability conditions for a four-parameter linear difference equation appearing in the process of discretization of a delay differential equation. We present two types of conditions, which are necessary and sufficient for asymptotic stability of the studied equation. A relationship between both the types of conditions is established and some of their consequences are discussed.

Asymptotic stability of fractional difference equations with bounded time delays

2020 ◽  
Vol 23 (2) ◽  
pp. 571-590
Author(s):  
Mei Wang ◽  
Baoguo Jia ◽  
Feifei Du ◽  
Xiang Liu
Keyword(s):  
Asymptotic Stability ◽  
Difference Equation ◽  
Difference Equations ◽  
Integral Inequality ◽  
Time Delays ◽  
Asymptotical Stability ◽  
Stability Conditions ◽  
Fractional Difference ◽  
Fractional Difference Equations ◽  
Fractional Difference Equation

AbstractIn this paper, an integral inequality and the fractional Halanay inequalities with bounded time delays in fractional difference are investigated. By these inequalities, the asymptotical stability conditions of Caputo and Riemann-Liouville fractional difference equation with bounded time delays are obtained. Several examples are presented to illustrate the results.

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