Studies On The Stabilization Problems For A Class Of Polynomial Systems

Polynomial nonlinear systems have a very wide range of applications in motion control systems, process systems and electronic circuit systems. Many of the control problems can become polynomial nonlinear systems by modeling. Therefore, the development of polynomial systems is very practical for the nonlinear systems. In recent year, using the method of numerical calculation in polynomial systems is a very hot study direction. Especially semi-definite programming and the decomposition of the square have achieved very good results and promoted the study process of nonlinear systems. In the actual investigate process, controller design is still a problem; there is a need for future study.This paper has investigated controller design of a class of3D polynomial systems and some problems of stabilization control on the basis of former. Research the problems of controller design of polynomial systems, through the semi-definite programming and the decomposition of the square. Paper main study work and related results including the following aspects:1. A method of stability verification of a class of polynomial systems has been studied. The stability of polynomial systems has been validated, through Lyapunov method and decomposition algorithm of polynomial and good results has been achieved;2. Controller design of a class of polynomial systems has been investigated. Firstly, refresh the polynomial systems and change into the general form of linear systems. Secondly, stabilization control problem is transformed into the problem of polynomial validation. Then, polynomial validation is transformed into matrix inequality by polynomial decomposition algorithm. Finally, matrix inequality is solved by semi-definite programming solver tool;3. Controller design of a class of general form polynomial systems has been studied. Controller design of polynomial systems is designed by the theorem and the general method of controller design.