On the inversion of a class of nonlinear systems

This paper deals with the inversion problem of affine square multi-input multi-output (MIMO) nonlinear systems. It presents a new algorithm unifying the construction of the inverse of a dynamical system with a regular or a singular characteristic matrix. This algorithm is based on the determination of a projector on the fibre bundle of the state space and incorporates a regularization of the singular case. It has the advantage of avoiding the input derivatives. Numerical examples are given to illustrate the proposed approach.