A Realization Procedure for Systems of Nonlinear Higher-order Differential Equations

Abstract

Abstract Nonlinear realization theory has ooncentrated so far on the realization of non-linear input-output naps, despite the fact that many (physical) nonlinear systems are more naturally described by a set of algebraic and (higher-order) differential equations involving the external variables (inputs and outputs) of the system. In this paper we deal with the realization problem for this last case. We show that under general conditions the existence of minimal realizations involving a set of auxiliary variables, called driving variables, is guaranteed. In general these extra variables cannot be omitted. Sufficient conditions are given for the existence of realizations involving only the state and the external variables. We give a constructive procedure to obtain realizations with or without driving variables. This realization procedure is also applied to systems given by the interconnection of nonlinear state space systems.