Kybernetika 48 no. 2, 177-189, 2012

The existence of limit cycle for perturbed bilinear systems

Hanen Damak, Mohamed Ali Hammami and Yeong-Jeu Sun


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 $\varepsilon$ to construct an approximate periodic solution. Furthermore, some simulation results are given to illustrate the existence of a limit cycle for this class of nonlinear control systems.


feedback control, perturbed bilinear system, limit cycle


70K05, 37G15


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