Razumikhin-type Theorems on Practical Stability of Dynamic Equations on Time Scales | Zendy

Bacem Ben Nasser | Zendy; Michaël Defoort | Zendy; Mohamed Djemaï | Zendy; TaousMeriem LalegKirati | Zendy

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Razumikhin-type Theorems on Practical Stability of Dynamic Equations on Time Scales

Author(s) -

Bacem Ben Nasser,

Michaël Defoort,

Mohamed Djemaï,

TaousMeriem LalegKirati

Publication year - 2018

Publication title -

ifac-papersonline

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.308

H-Index - 72

eISSN - 2405-8971

pISSN - 2405-8963

DOI - 10.1016/j.ifacol.2018.08.021

Subject(s) - type (biology) , mathematics , dynamic equation , exponential stability , stability (learning theory) , lyapunov function , stability theory , work (physics) , inequality , mathematical analysis , computer science , nonlinear system , physics , ecology , quantum mechanics , machine learning , biology , thermodynamics

In this work, we investigate some Razumikhin-type criteria for the uniform global practical asymptotic stability on arbitrary time domains, for time-varying dynamic equations. Using Lyapunov-type functions on time scales, we develop appropriate inequalities ensuring that trajectories decay to the neighborhood of the trivial solution asymptotically. Some numerical examples are discussed to illustrate our results.

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