Limit cycles design for a class of bilinear control systems

In this paper, the feedback control for a class of bilinear control systems is investigated. Using the Bellman-Gronwall inequality, a feedback control is proposed to guarantee the existence of limit cycles for such bilinear control systems. Moreover, the exponentially stable limit cycles, the guaranteed convergence rate, and frequency of oscillation can be correctly estimated. Finally, a numerical example is provided to illustrate the use of the main result.