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

ABSTRACT

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.