Realisation of linear time-varying systems

ABSTRACT

In this paper, the realisation problem of linear multi-input multi-output, time-varying systems is studied. The approach, based on the theory of non-commutative polynomial rings, yields explicit and simple formulas for computation of the state coordinates as well as for state equations in observable canonical form. The formulas are based on (left) Euclidean polynomial division.

Keywords:

• Time-varying systems
• realisation problem
• observable canonical form
• non-commutative polynomial rings

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. We write a (without argument) meaning the left polynomial and a(s) meaning the respective operator, acting on $\mathcal{E}$. The same convention holds for the vectors/matrices of polynomials.

2. Hereinafter we do not write comma between the row indices unless there is a possibility of confusion.

Additional information

Funding

The research was supported by the Estonian Research Council, personal research funding grant PUT481.