Journal of Systems Science and Complexity

, Volume 28, Issue 5, pp 1049–1057 | Cite as

Application of Sturm Theorem in the global controllability of a class of high dimensional polynomial systems

  • Xueli Xu
  • Qianqian Li
  • Yimin SunEmail author


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.


Global controllability high dimensional systems number of sign variations polynomial Sturm theorem 


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Copyright information

© Institute of Systems Science, Academy of Mathematics and Systems Science, CAS and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Guangdong Province Key Laboratory of Computational Science, School of Mathematics and Computational ScienceSun Yat-Sen UniversityGuangzhouChina

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