scholarly journals A Symbolic Computation Approach Towards the Asymptotic Stability Analysis of Differential Systems with Commensurate Delays

2019 ◽  
pp. 169-185
Author(s):  
Yacine Bouzidi ◽  
Adrien Poteaux ◽  
Alban Quadrat
Keyword(s):  
Stability Analysis ◽  
Asymptotic Stability ◽  
Symbolic Computation ◽  
Differential Systems ◽  
Commensurate Delays

scholarly journals On the Stability Analysis of Linear Unperturbed Non-integer Differential Systems

2021 ◽  
pp. 85-89
Author(s):  
Ubong D. Akpan
Keyword(s):  
Stability Analysis ◽  
Asymptotic Stability ◽  
Differential System ◽  
Differential Systems ◽  
Caputo Derivatives ◽  
Fractional Differential System ◽  
Fractional Differential ◽  
The Stability

In this paper, the stability of non-integer differential system is studied using Riemann-Liouville and Caputo derivatives. The stability notion for determining the stability/asymptotic stability or otherwise fractional differential system is given. Example is provided to demonstrate the effectiveness of the result.

scholarly journals Stability Analysis of Perturbed Linear Non-integer Differential Systems

2021 ◽  
pp. 24-29
Author(s):  
Ubong D. Akpan
Keyword(s):  
Stability Analysis ◽  
Asymptotic Stability ◽  
Differential System ◽  
Caputo Derivative ◽  
Differential Systems ◽  
Fractional Differential System ◽  
Liouville Derivative ◽  
Fractional Differential ◽  
The Stability

In this work, the effect of perturbation on linear fractional differential system is studied. The analysis is done using Riemann-Liouville derivative and the conclusion extended to using Caputo derivative since the result is similar. Conditions for determining the stability and asymptotic stability of perturbed linear fractional differential system are given.

scholarly journals Asymptotic Stability of Caputo Type Fractional Neutral Dynamical Systems with Multiple Discrete Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Hai Zhang ◽  
Daiyong Wu ◽  
Jinde Cao
Keyword(s):  
Asymptotic Stability ◽  
Matrix Theory ◽  
Sufficient Conditions ◽  
Algebraic Approach ◽  
Stability Criteria ◽  
Differential Systems ◽  
Discrete Delays ◽  
Transcendental Equations ◽  
The Stability ◽  
Theoretical Results

We discuss the delay-independent asymptotic stability of Caputo type fractional-order neutral differential systems with multiple discrete delays. Based on the algebraic approach and matrix theory, the sufficient conditions are derived to ensure the asymptotic stability for all time-delay parameters. By applying the stability criteria, one can avoid solving the roots of transcendental equations. The results obtained are computationally flexible and convenient. Moreover, an example is provided to illustrate the effectiveness and applicability of the proposed theoretical results.

scholarly journals Almost sure asymptotic stability analysis of the θ-Maruyama method applied to a test system with stabilising and destabilising stochastic perturbations

2012 ◽  
Vol 15 ◽  
pp. 71-83 ◽  
Author(s):  
Gregory Berkolaiko ◽  
Evelyn Buckwar ◽  
Cónall Kelly ◽  
Alexandra Rodkina
Keyword(s):  
Stability Analysis ◽  
Asymptotic Stability ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Equilibrium Solution ◽  
Test System ◽  
Dimensional System ◽  
Step Size ◽  
Stochastic Perturbations ◽  
Stability And Instability

AbstractWe perform an almost sure linear stability analysis of the θ-Maruyama method, selecting as our test equation a two-dimensional system of Itô differential equations with diagonal drift coefficient and two independent stochastic perturbations which capture the stabilising and destabilising roles of feedback geometry in the almost sure asymptotic stability of the equilibrium solution. For small values of the constant step-size parameter, we derive close-to-sharp conditions for the almost sure asymptotic stability and instability of the equilibrium solution of the discretisation that match those of the original test system. Our investigation demonstrates the use of a discrete form of the Itô formula in the context of an almost sure linear stability analysis.

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