Balanced realization using an orthogonalization procedure and modular polynomial arithmetic (Q5959148)

Starting from the approaches suggested in [\textit{B. S. Lee} and \textit{F. W. Fairman}, SIAM J. Control Optim. 25, 1-17 (1987; Zbl 0663.93017)] or [\textit{C. P. Therapos}, IEEE Trans. Autom. Control 30, 297-299 (1985; Zbl 0576.93015)], the authors derive, in a unified way, a balanced realization of a continuous-time or discrete-time block-factorized transfer function matrix (TFM) making use of orthogonalization processes of input maps along with the so-called Routh-Aström tables introduced in [\textit{L. C. Calvez}, \textit{P. Vilbé}, \textit{A. Derrien} and \textit{P. Brehonnet}, General orthogonal sequences via a Routh-type stability array, Electron. Lett. 30, 544-545 (1992)] and modular polynomial arithmetic. In this respect, preliminary results about Input/Output maps and the use of Routh-Aström tables are presented in Sections 2 and 3 respectively so that as a direct application of the previous results, a method is proposed in Section 4 to achieve a balanced realization of MIMO systems known by their TFM both for continuous or discrete time systems.NEWLINENEWLINENEWLINEFinally, a numerical example concerning the design of analog circuits whose elementary circuits yield high-order block-factorized transfer functions is given.