Journal of Systems Science and Complexity

, Volume 28, Issue 5, pp 1049–1057

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

Article

## Abstract

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.

## Keywords

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

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