On the Practical h-stability of Nonlinear Systems of Differential Equations

被引：0
作者：
B. Ghanmi
机构：
[1] University of Gafsa,Faculty of Sciences of Gafsa
[2] Department of Mathematics,undefined
来源：
Journal of Dynamical and Control Systems | 2019年 / 25卷
关键词：
-stability; Practical ; -stability; Lyapunov theory; Perturbed systems; Cascaded systems; Practical ; -stabilization; 34D10; 34D20; 93D05; 93D15;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, we present a new notion of stability for nonlinear systems of differential equations called practical h-stability. Necessary and sufficient conditions for practical h-stability are given using the Lyapunov theory. Our original results generalize well-known fundamental results: practical exponential stability, practical asymptotic stability, and practical stability for nonlinear time-varying systems. In addition, these results are used to study the practical h-stability of two important classes of nonlinear systems, namely perturbed and cascaded systems. The last part is devoted to the study of the problem of practical h-stabilization for certain classes of nonlinear systems.
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页码：691 / 713
页数：22
相关论文
共 35 条
[1]  
Benabdallah A(2009)Practical stability of nonlinear time-varying cascade systems J Dyn Control Syst 15 45-62
[2]  
Ellouze I(2006)Uniform global practical asymptotic stability for time-varying cascaded systems Eur J Control 12 595-605
[3]  
Hammami MA(2007)Robustness of PID-controlled manipulators vis-à-vis actuator dynamics and external disturbances Eur J Control 6 563-76
[4]  
Chaillet A(2004)Asymptotic equivalence between two linear Volterra difference systems Comput Math Appl 47 461-71
[5]  
Loría A(1997)Lipschitz stability exponential asymptotic stability for the nonlinear functional differential systems Dyn Syst Appl 6 397-410
[6]  
Chaillet A(1997)h −stability of differential systems via t∞−similarity Bull Korean Math Soc 34 371-83
[7]  
Loría A(2001)Variationally stable difference systems J Math Anal Appl 256 587-605
[8]  
Kelly R(2015)Variationally stable impulsive differential systems Dyn Syst 30 435-49
[9]  
Choi SK(2016)A converse theorem on h −stability via impulsive variational systems J Korean Math Soc 53 1115-31
[10]  
Koo N(2006)Properties of optimal sets of practical stability of differential inclusions. Part I. Part II J Autom Inf Sci 38 111-97
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