Input-output pseudolinearization on controlled invariant submanifolds

The original notion of input-output pseudolinearization on equilibrium submanifolds is extended to general controlled invariant submanifolds for nonlinear systems. Input-output pseudolinearizing feedback laws render the input-output behavior of linearizations about nominal trajectories in the submanifold trajectory-independent and equal to that of a fixed linear time-invariant system, thereby facilitating the subsequent construction of control laws for stabilization and tracking. Sufficient existence conditions are derived that are weaker than the familiar relative degree conditions for nonlinear input-output decoupling that have come to be associated with exact input-output linearization. As with other work on input-state pseudolinearization, the study of a class of linear parameter-varying (LPV) systems provides valuable insight into the nonlinear problem.