Stability Analysis And Controller Synthesis For A Class Of Polynomial Systems

Polynomial nonlinear systems appear widely in the real world. Many control problems in the field of biochemical, chemical process, electric circuits and so on can be modeled as, transformed into, or approximated by polynomial nonlinear systems. Researching polynomial nonlinear systems has significance for the investigation of nonlinear systems, because polynomial nonlinear systems have universality in the nonlinear systems family. Therefore, how to analyze and synthesize polynomial nonlinear systems is a promising work for nonlinear control theory development and engineering applications. In recent years, considerable attention has been devoted to the study of polynomial nonlinear systems in numerical approach. Significant progress has been made in the stability analysis of polynomial nonlinear systems by those numerical approaches.This thesis explores of a class of special time-invariant polynomial nonlinear systems. And it researches their stability analysis and controller synthesis.The main research content are showed as follows:1. The Lyapunov stability is introduced. In the field of stability analysis, the Lyapunov stability criterions are a major cornerstone of the Control Theory. It was put forward at the end of the 19th century by Lyapunov. And then it was developed by Malkin, Chetaev, Zubov, Krasovskii, Razumikhin and so on. After that it became a sophisticated system.2. The related concepts of Sum-of-Squares (SOS) optimization algorithm and canonical quadratic distance problems(CQDP) optimization algorithm are introduced, and algorithm 3.1 bases on SOS to estimates the domain of attraction. And then the improved algorithm 3.2 is given at the basis of algorithm 3.1. Finally, it is illustrated with an example. The example shows that good results can be got by using algorithm 3.2 for some two-dimensional systems.3. The disturbance analysis based on Sum-of-Squares (SOS) optimization algorithm is introduced. And then the state feedback controller in algorithm 4.1 based on Sum-of-Squares (SOS) is introduced. Furthermore, the improved algorithm 4.2 is given at the basis of algorit-hm 4.1 to design the state feedback controller. At last, it is illustrated with an case. The case denominates the better results can be obtained by using algorithm 4.2 for some two-dimensio-nal systems.