# Abstract:

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.

# Keywords:

feedback control, perturbed bilinear system, limit cycle

70K05, 37G15

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