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.

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 Stability Properties of a Discretized Neutral Delay Differential Equation

2013 ◽  
Vol 54 (1) ◽  
pp. 83-92 ◽  
Author(s):  
Jana Hrabalová
Keyword(s):  
Differential Equation ◽  
Asymptotic Stability ◽  
Delay Differential Equation ◽  
Stability Region ◽  
Sufficient Conditions ◽  
Neutral Delay ◽  
Neutral Delay Differential Equation ◽  
Asymptotic Stability Region ◽  
Delay Differential ◽  
Necessary And Sufficient

Abstract The paper discusses the asymptotic stability region of a discretization of a linear neutral delay differential equation x′(t) = ax(t - τ) + bx'(t - τ). We present necessary and sufficient conditions specifying this region and describe some of its properties.

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.

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