Application of Sturm Theorem in the Global Controllability of a Class of High Dimensional Polynomial Systems  

作　　者：XU Xueli LI Qianqian SUN Yimin 

机构地区：[1]Guangdong Province Key Laboratory of Computational Science, School of Mathematics and Computational Science, Sun Yat-Sen University

出　　处：《Journal of Systems Engineering and Electronics》2015年第5期1049-1057,共9页系统工程与电子技术（英文版）

基　　金：supported by the Natural Science Foundation of China under Grant Nos.60804008,61174048and 11071263;the Fundamental Research Funds for the Central Universities and Guangdong Province Key Laboratory of Computational Science at Sun Yat-Sen University

摘　　要：In this paper, the global controllability for a class of high dimensional polynomial systems has been investigated and a constructive algebraic criterion algorithm for their global controllability has been obtained. By the criterion algorithm, the global controllability can be determined in finite steps of arithmetic operations. The algorithm is imposed on the coefficients of the polynomials only and the analysis technique is based on Sturm Theorem in real algebraic geometry and its modern progress. Finally, the authors will give some examples to show the application of our results.In this paper, the global controllability for a class of high dimensional polynomial systems has been investigated and a constructive algebraic criterion algorithm for their global controllability has been obtained. By the criterion algorithm, the global controllability can be determined in finite steps of arithmetic operations. The algorithm is imposed on the coefficients of the polynomials only and the analysis technique is based on Sturm Theorem in real algebraic geometry and its modern progress. Finally, the authors will give some examples to show the application of our results.

关 键 词：Global controllability high dimensional systems number of sign variations polynomial Sturm theorem. 

分 类 号：O175.12[理学—数学] TP242[理学—基础数学]