Right coprime factorizations and stabilization for nonlinear systems

Abstract

The problem of constructing right coprime factorizations (which are based on the graph of an input-output map instead of the Bezout identity) of nonlinear input-output maps is considered. The map is assumed to arise from a state variable realization with a fixed initial state. The main result is that the existence of a stabilizing state feedback implies the existence of a right coprime factorization for the map. The technique is illustrated by application to nonlinear systems which are affine in the control and have a controllable linear past and nonlinear systems which are feedback linearizable. A notion of input-output stability that requires a bound on the magnitude of the input signals is introduced. Methods of constructing such bounds are developed. For a locally feedback linearizable system, the problem of input bounds is transferred to the equivalent linear system. This leads to a technique that allows state and input constraints for a feedback linearizable system to be mapped to the equivalent linear system.