The Stability Analysis of Nonlinear Systems Based on Data
|School||Wuhan University of Science and Technology|
|Course||Pattern Recognition and Intelligent Systems|
|Keywords||nonlinear systems stability analysis approximation element|
The stability analysis methods for nonlinear systems include the phase plane method, the describing function method, the absolute stability theory, and the input/output stability theory. These methods on the stability of nonlinear systems have their own applied fields and limitations because of the complexities of nonlinear systems. In recent years, the approaching element model of nonlinear systems has provided a new research way for the stability analysis of nonlinear systems.This dissertation first introduces the theory about the approaching element model, and gives a new kind of multi-output support regression algorithms, which is applied on identification of approaching element model. By establishing a transferring matrix in the element space, an algorithm for stability analysis of nonlinear systems is proposed. For quantitative describing the stability of receptive field of approaching element, the concepts of the stability level of approaching element and the stability of level-cut have been defined.At the end of this dissertation, advantages and disadvantages of the stability analysis method based on constructing element model are discussed by analyzing linear systems, nonlinear systems with single equilibrium or multiple equilibriums.