Application of Sturm Theorem in the global controllability of a class of high dimensional polynomial systems
- 103 Downloads
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.
KeywordsGlobal controllability high dimensional systems number of sign variations polynomial Sturm theorem
Unable to display preview. Download preview PDF.
- Wu W T, Mathematics Mechanization: Mechanical Geometry Theorem-Proving, Mechanical Geometry Problem-Solving and Polynomial Equations-Solving, Kluwer Academic Publishers, Boston, 2000.Google Scholar
- Kostrikin A I, Introduction to Algebra I, Translated by Zhang Y B, Second Edition, Higher Education Press, Beijing, 2006 (in Chinese).Google Scholar
- Yang L and Xia C B, Automated Proving and Discovering for Inequalities, Science Press, Beijing, 2008 (in Chinese).Google Scholar
- Collins G E and Akritas A G, Polynomial real root isolation using descarte’s rule of signs, Proceedings of the 1976 ACM Symposium on Symbolic and Algebraic Computation, 1976, 272–275.Google Scholar
- Wang D M, Mou C Q, Li X L, Yang J, Jin Y, and Huang Y L, Polynomial Algebra, Higher Education Press, Beijing, 2011 (in Chinese).Google Scholar