The concept of the exponentially stable limit cycle (ESLC) is introduced, and the ESLC phenomenon for a class of nonlinear systems is explored. Based on time-domain approach with differential inequality, the existence and uniqueness of the ESLC for such nonlinear systems can be guaranteed. Besides, the period of oscillation, the amplitude of oscillation, and guaranteed convergence rate can be accurately estimated. Finally, two numerical simulations are provided to illustrate the feasibility and effectiveness of the obtained result.
"Existence and Uniqueness of the Exponentially Stable Limit Cycle for a Class of Nonlinear Systems via Time-Domain Approach with Differential Inequality." J. Appl. Math. 2013 1 - 7, 2013. https://doi.org/10.1155/2013/712932