Existence and uniqueness of limit cycle for a class of nonlinear discrete-time systems

In this paper, the definition of the exponentially stable limit cycle for nonlinear discrete-time systems is firstly introduced. The limit cycle phenomenon for a class of nonlinear discrete-time systems is investigated. Using analytic method, the existence and uniqueness of limit cycle for such systems can be guaranteed. Besides, the exponentially stable limit cycles, the period of oscillation, and guaranteed convergence rate can be correctly estimated. Finally, a numerical example is provided to illustrate the use of the main result.