A global Implicit Function Theorem without initial point and its applications to control of non-affine systems of high dimensions

Control system design for non-affine systems is a difficult problem because of the lack of mathematical tools. The key to the problem is solving for an implicit function but the known results for implicit functions are not applicable for higher dimensional systems except for single-input and single-output systems. In this paper, a new version of a global implicit function theorem in higher dimension is presented and proved. This result can be applied to show the controllability of a class of non-affine multi-input and multi-output (MIMO) system so that approximation based control system design can be applied with ease.