Nonlinear measures and its application to the chaos control

In this paper, we introduce the nonlinear measure of time-continuous system into the control of chaos, and verify that nonlinear measure can characterize the exponential stability and the size of stable basin. We also, based on it and the polar coordinates transformation, derive a general and precise algorithm for determining the radius of stable basin in controlling time-continuous chaotic dynamical system and for estimating the exponential decay of the controlled system converge to the desired goal dynamics. Furthermore, we take the well-known Lorenz, Rösslor system and Chua system as examples to illustrate the implementation of our theory.