Processing math: 0%
Realization from Moments: The Linear Case | IEEE Conference Publication | IEEE Xplore

Realization from Moments: The Linear Case


Abstract:

By exploiting the time-domain notion of moments we recover a time-domain counterpart of the fact that a certain number of steady-state responses is sufficient to realize ...Show More

Abstract:

By exploiting the time-domain notion of moments we recover a time-domain counterpart of the fact that a certain number of steady-state responses is sufficient to realize a linear system. This may pave the way to a realization theory for nonlinear systems based on their steady-state responses.
Date of Conference: 13-15 December 2023
Date Added to IEEE Xplore: 19 January 2024
ISBN Information:

ISSN Information:

Conference Location: Singapore, Singapore

Funding Agency:


I. Introduction

This paper is motivated by the simple observation that a certain number of steady-state responses is sufficient to realize a SISO linear system, that is (almost) any -moments [1], i.e., any pairs , with \begin{equation*} G(s)= \frac{b_{1}s^{n-1}+\cdots+b_{n}}{s^{n}+a_{1}s^{n-1}+\cdots+a_{n}},\end{equation*} can be used to “recover” the transfer function itself. In fact, the parameters and , can be obtained by solving the linear equations () \begin{equation*} G(s_{i})[s_{i}^{n}+a_{1}s_{i}^{n-1}+\cdots+a_{n}]=b_{1}s_{i}^{n-1}+\cdots+b_{n},\end{equation*} which are always solvable provided that , for , and that each is not a pole of .

Contact IEEE to Subscribe

References

References is not available for this document.