Bellman-Gronwall Inequality Approach to Oscillator Design for the Specific Bilinear Systems

In this paper, the existence of limit cycles for the specific bilinear systems is explored. Based on the Bellman- Gronwall inequality approach, not only the exponentially stable limit cycles phenomenon of such systems can be certified but also the oscillation behaviors of such systems can be correctly predicted. Finally, a numerical example is provided to illustrate the feasibility and effectiveness of the obtained result.