Prior knowledge and Markov parameters of linear time-invariant models

TL;DR

This paper explores how prior knowledge such as DC-gain and time constants can be directly linked to Markov parameters in linear time-invariant models to enhance subspace identification methods.

Contribution

It derives explicit relationships between prior system information and Markov parameters, enabling improved model identification techniques.

Findings

Derived formulas linking prior knowledge to Markov parameters

Proposed integration of prior info into Kung's algorithm

Potential for increased accuracy in system identification

Abstract

In many practical cases, the engineer has access to prior knowledge like rough values of the DC-gain or the main time constant of the system. In order to improve the accuracy of subspace-based identification techniques using the model Markov parameters, we derive in this short paper the direct links between these impulse response coefficients and this prior information. The next step will consist in introducing this prior knowledge explicitly in Kung's algorithm thank to dedicated equality and equality constraints.