About finite nonlinear zeros for decouplable systems

Abstract We establish that the eigenvalues of the gradient at an equilibrium point of the ‘zero-dynamics’ defined by Byrnes and Isidori [1], are nothing but the finite linear zeros of the linearized system at the equilibrium, if the nonlinear system can be input-output decoupled by feedback and its linearization is controllable. This property allows us to describe (and to give an algorithm to find) the output functions leading to stability while using a linear model following controller. We study on an example the problem of both stability and maximal linearization.