Rank Criterion Method for Invertibility of Multivariable Affine Nonlinear System

The main difficult in the application of inverse system method to nonlinear control system is to determine the invertibility of the system. In order to investigate new method for analyzing invertibility of system, a rank criterion method is introduced to multivariable affine nonlinear system, by which the problem of invertibility is converted to determine the rank condition of the Jacobi matrix about output and its derivation of system. The rank criterion theorem such that affine nonlinear system be invertible is proved and an algorithm is obtained to determine invertibility of the system. Finally, the algorithm mentioned is verified by using an example. The effectiveness of rank criterion method is validated by comparison with differential geometry method and inverse system method.