On the practical ψ^γ-exponential asymptotic stability of nonlinear systems of differential equations

Miskolc Mathematical Notes

article

B. Ghanmi¹  T. Fajraoui¹  I. Basdouri¹ 

[1] University of Gafsa, Department of Mathematics

关键词: ψ−exponential asymptotic stability;    Practical ψ γ−exponential asymptotic stability;    Lyapunov theory;    Perturbed systems;    Cascaded systems;    Practical ψ γ−exponential stabilization;   

DOI  :  10.18514/MMN.2020.3226

学科分类：数学（综合）

来源: Miskolci Egyetem

【 摘 要 】

In this paper, a new type of stability for nonlinear systems of differential equations called practical \Psi^{\gamma}-exponential asymptotic stability, is presented. Some sufficient conditions for practical \Psi^{\gamma}-exponential asymptotic stability are provided by using Lyapunov theory. These results generalize fundamental well known results for practical exponential asymptotic and \Psi^{\gamma}-xponential asymptotic stability for nonlinear time-varying systems. In addition, these results are using to investigate the practical \Psi^{\gamma}-exponential asymptotic stability problem of nonlinear perturbed system and cascade systems. The last part is devoted to the study the problem of practical \Psi^{\gamma}-exponential asymptotic stabilization for some classes of nonlinear systems with delayed perturbation.

【 授权许可】

CC BY