Pseudolinearization on controlled invariant submanifolds

We extend the original notion of pseudolinearization on equilibrium submanifolds to general controlled invariant submanifolds for nonlinear systems. This extension is motivated by nonlinear tracking and regulation problems in which the control objective is to stabilize any nominal trajectory in the submanifold. A pseudolinearizing transformation renders linearizations about nominal trajectories in the submanifold trajectory-independent so that local stabilization to the submanifold can be achieved using linear time-invariant control laws. Necessary and sufficient conditions for pseudolinearization via static state feedback and coordinate change are derived which are weaker than those for exact feedback linearization. The study of a class of linear parameter-varying (LPV) systems provides valuable insight into the nonlinear problem