A new algorithm for linearization up to multi-output and multi-input injection for a class of systems with implicitly defined outputs

Given a class of nonlinear systems with implicitly defined outputs, we provide a new algorithm to find appropriate local coordinates, in which the resulting system takes a desired target form that is state-affine, up to output and input injection. Once in the target form, it is possible to construct a state-space observer with linear, possibly time-varying, error dynamics.