Geodesic
The existence of limit cycle for perturbed bilinear systems
Kybernetika, Tome 48 (2012) no. 2, pp. 177-189 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 37G15, 70K05
Keywords: perturbed bilinear system; feedback control; limit cycle 
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Damak, Hanen; Hammami, Mohamed Ali; Sun, Yeong-Jeu. The existence of limit cycle for perturbed bilinear systems. Kybernetika, Tome 48 (2012) no. 2, pp. 177-189. http://geodesic.mathdoc.fr/item/KYB_2012_48_2_a0/

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