On the Global Uniform Asymptotic Stability of Time-Varying Systems

被引：17

作者：

Damak H. ^{[1
]}

Hammami M.A. ^{[1
]}

Kalitine B. ^{[2
]}

机构：

[1] University of Sfax Tunisia, Sfax

[2] University of Bielorussie, Minsk

来源：

Differential Equations and Dynamical Systems | 2014年 / 22卷 / 2期

关键词：

Invariance principle; Lyapunov functions; Nonlinear differential equations; Practical stability;

D O I：

10.1007/s12591-012-0157-z

中图分类号：

学科分类号：

摘要：

This work is motivated by the problem of practical stability of nonlinear time-varying system x(t) = f(t,x(t)), x(t0) = x0 where t ε ℝ, x ε ℝn, and f: ℝ × ℝn → ℝn is continuous in t and locally Lipschitz in x We give some sufficient conditions to guarantee practical uniform asymptotic stability. An invariance principle is given when the origin is not an equilibrium point. The main result of this paper is illustrated by an example in three dimensional. © 2013 Foundation for Scientific Research and Technological Innovation.

引用

页码：113 / 124

页数：11

共 18 条

[1]

Balan R., An extension of Barbashin-Krasovski-LaSalle, Nonlinear Dyn. Syst. Theory, 8, 3, pp. 255-268, (2008)

[2]

Ben Abdallah A., Ellouze I., Hammami M.A., Practical stability of nonlinear time-varying cascade systems, J. Dyn. Control Syst, 15, 1, pp. 45-62, (2009)

[3]

Bihari I., A generalization of a lemma of Bellman and its application to uniqueness problems of differential equations, Acta Math. Hung., 7, 1, pp. 81-94, (1956)

[4]

Chaillet A., Loria A., Uniform global practical asymptotique stability for time-varying cascaded systems, Eur. J. Control, 6, pp. 595-605, (2006)

[5]

Chaillet A., Loria A., Necessary and sufficient conditions for uniform semiglobal practical asymptotic stability: application to cascaded systems, Automatica, 42, pp. 1899-1906, (2006)

[6]

Guo Z., Huang L., Global exponential stability of a general class of recurrent neural networks with variable delays, Differ. Equ. Dyn. Syst., 11, pp. 133-148, (2011)

[7]

Hahn W., Stability of Motion, (1967)

[8]

Kalitine B., Sur la stabilit des ensembles compacts positivement invariants des systmes dynamiques, RAIRO: Autom. Syst. Anal. Control, 16, 3, pp. 275-286, (1982)

[9]

Kalitine B., Stability of Closed invariant sets of semidynamical systems. The method of sign definite Lyapunov functions, Differ. Equ, 38, 11, pp. 1662-1664, (2002)

[10]

Khalil H.K., Nonlinear Systems, (2002)

← 1 2 →