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A simple sufficient criterion of the global controllability for a class of planar polynomial systems

Since the global controllability of planar nonlinear systems was completely solved and the necessary and sufficient condition was obtained, it has been certainly worth finding a feasible algorithm to check up on the condition. However, the condition is too complicated to be verified generally, which limits its application largely. This paper will investigate a sufficient condition with less computational complexity for the global controllability of planar polynomial systems. Based on the degree of criterion function of planar systems on control curves and mathematics mechanization method, we present a simple sufficient criterion algorithm for the global controllability of a class of planar polynomial systems. All conditions are imposed on the structure of the system only. Finally, we give some examples to show the application of our results.