Identification and Realization of Polynomial Systems

Abstract

For stationary, homogeneous, continuous-time systems, we consider the discrete-time realization in the form of polynomial difference equations with a special internal structure of vectors and matrices. The system is described by a finite Volterra series. The different amplitude dependencies of the homogeneous subsystems are used to separate the response contributions of each subsystem. The identification and realization properties of degree 2 and 3 homogeneous subsystems are presented in terms of triangular kernels, and in terms of vectors and matrices. A procedure is given for constructing a minimal dimension, degree 2 and 3 homogeneous realization, with forms of observability and reachability, well known from the linear case.