Constructive criterion algorithm of the global controllability for a class of planar polynomial systems

In this study, a constructive criterion algorithm of the global controllability for a class of planar polynomial systems is obtained. This algorithm is imposed on the coefficients of polynomials only and can be realised easily by computer. The analysis is based on a classical result in real algebraic geometry - Sturm theorem and its modern progress. According to this algorithm, the global controllability of the system can be determined in finite steps arithmetic operations. Finally, the authors give some examples to show the application of the author´s results.