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The existence of limit cycle for perturbed bilinear systems

Hanen Damak;  Mohamed Ali Hammami;  Yeong-Jeu Sun — 2012

Kybernetika

In this paper, the feedback control for a class of bilinear control systems with a small parameter is proposed to guarantee the existence of limit cycle. We use the perturbation method of seeking in approximate solution as a finite Taylor expansion of the exact solution. This perturbation method is to exploit the “smallness” of the perturbation parameter ε to construct an approximate periodic solution. Furthermore, some simulation results are given to illustrate the existence of a limit cycle for...

Practical h -stability behavior of time-varying nonlinear systems

Abir Kicha;  Hanen Damak;  Mohamed Ali Hammami — 2023

Commentationes Mathematicae Universitatis Carolinae

We deal with the problem of practical uniform h -stability for nonlinear time-varying perturbed differential equations. The main aim is to give sufficient conditions on the linear and perturbed terms to guarantee the global existence and the practical uniform h -stability of the solutions based on Gronwall’s type integral inequalities. Several numerical examples and an application to control systems with simulations are presented to illustrate the applicability of the obtained results.

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