A New Measure of Dynamic Similarity for Nonlinear Systems based on Gap Metric and Deterministic Learning Theory

For nonlinear dynamical systems, structural stability is a fundamental concept. It provides a qualitative tool for analyzing the equivalent relation between a nonlinear dynamical system and its perturbed system. Currently, most researches about structural stability, including some applications in practical systems, are mainly limited to qualitative analysis. In this paper, our focus is on the quantitative property of structural stability. A new measure will be proposed from the perspective of structural stability and gap metric under the Deterministic Learning theory, which provides more incentives for further applications in pattern recognition, classification as well as fault detection. Simulation studies are included to further demonstrate the effectiveness of this measure.