On constrained dynamics and a pseudo-normal form for nonlinear systems

A nonlinear system in pseudo-normal form has the property that its family of linearizations about constant operating points specifies a family of linear systems in normal form. The purpose of this paper is to show that under certain assumptions a pseudo-normal form can be defined that has the following properties in common with the exact normal form: a family of locally maximal controlled invariant submanifolds corresponding to a family of constant output constraints exists and is rendered invariant by a single static state feedback, and the associated family of internal system dynamics is clearly displayed