Expansion of digraph size of 1-D fractional system with delay: Solutions for full characteristic polynomial

Abstract

Previous method for determination of state matrices of fractional-order dynamic system by use of digraphs had problemswith characteristic polynomials that were of full size (i.e. had all the terms) due to the constraints onmatrix sizeminimality. This article proposes the alternative approach that allows to obtain solutions that can be easily computed even for full polynomials, but creates digraphs (and state matrices) of larger size. Proposed method is illustrated with the symbolic example of full characteristic polynomial showing the difference between the two approaches.