scholarly journals On the Estimation of Asymptotic Stability Region of Nonlinear Polynomial Systems: Geometrical Approaches

10.5772/5388 ◽  
2008 ◽  
Author(s):  
Anis Bacha ◽  
Houssem Jerbi ◽  
Naceur Benhadj
Keyword(s):  
Asymptotic Stability ◽  
Stability Region ◽  
Polynomial Systems ◽  
Asymptotic Stability Region

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 Chaotic Particle Swarm Optimisation for Enlarging the Domain of Attraction of Polynomial Nonlinear Systems

Electronics ◽  
2020 ◽  
Vol 9 (10) ◽  
pp. 1704
Author(s):  
Faiçal Hamidi ◽  
Messaoud Aloui ◽  
Houssem Jerbi ◽  
Mourad Kchaou ◽  
Rabeh Abbassi ◽  
...  
Keyword(s):  
Iterative Procedure ◽  
Stability Region ◽  
Linear Inequality ◽  
Time Derivative ◽  
Domain Of Attraction ◽  
Polynomial Systems ◽  
Software Environment ◽  
Novel Technique ◽  
Asymptotic Stability Region ◽  
Achievable Region

A novel technique for estimating the asymptotic stability region of nonlinear autonomous polynomial systems is established. The key idea consists of examining the optimal Lyapunov function (LF) level set that is fully included in a region satisfying the negative definiteness of its time derivative. The minor bound of the biggest achievable region, denoted as Largest Estimation Domain of Attraction (LEDA), can be calculated through a Generalised Eigenvalue Problem (GEVP) as a quasi-convex Linear Inequality Matrix (LMI) optimising approach. An iterative procedure is developed to attain the optimal volume or attraction region. Furthermore, a Chaotic Particular Swarm Optimisation (CPSO) efficient technique is suggested to compute the LF coefficients. The implementation of the established scheme was performed using the Matlab software environment. The synthesised methodology is evaluated throughout several benchmark examples and assessed with other results of peer technique in the literature.

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.

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