A Unifying Method to Construct Rational Basis Functions for Linear and Nonlinear Systems

Abstract

This paper proposes a general and unifying method for constructing rational basis functions (RBFs). The proposal is specifically designed for finding characterizing matrices of linear RBF state equations. Analytic expressions for the realization of such state-space matrices are also developed. As will be shown, the construction method here proposed can be easily applied (but is not limited) to several RBF sets which have been successfully adopted in both linear and nonlinear system identification areas.