Bounds of the Chaotic System for Couette–Taylor Flow and Its Application in Finite-Time Control

Abstract

In this paper, the boundedness of solutions of the chaotic system for the incompressible flow between two concentric rotating cylinders, known as Couette–Taylor flow, has been studied. Based on Lagrange multiplier method and generalized positive definite and radially unbound Lyapunov functions with respect to the parameters of the system, we derive the ultimate bound and the globally exponentially attractive set for this system. Then, the result is applied to the finite-time stabilization. Moreover, numerical simulations are presented to show the effectiveness of the method.