Geodesic
The existence of limit cycle for perturbed bilinear systems
Kybernetika, Tome 48 (2012) no. 2, pp. 177-189

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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.
Classification : 37G15, 70K05
Keywords: perturbed bilinear system; feedback control; limit cycle 
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     author = {Damak, Hanen and Hammami, Mohamed Ali and Sun, Yeong-Jeu},
     title = {The existence of limit cycle for perturbed bilinear systems},
     journal = {Kybernetika},
     pages = {177--189},
     publisher = {mathdoc},
     volume = {48},
     number = {2},
     year = {2012},
     mrnumber = {2954318},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2012__48_2_a0/}
}
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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/