Stability Analysis of Nonlinear Systems Controlled by SDRE Using Colored Map

摘要

In this paper, we present an analysis method on stability of a nonlinear system controlled by the State Dependent Riccati Equation, SDRE, using a colored map. It is shown in the literature that the SDRE-based control system design for nonlinear systems is useful and powerful. However, the stability can be only proven locally, and the global stability is definitely difficult to be shown analytically. Therefore, the degree of stability is analyzed by making a colored map like to the Julia set, in which the color corresponds to the settling time. Two examples using pendulums are presented to illustrate the effectiveness of the presented analysis method.