Quasi feedback forms for differential-algebraic systems

TL;DR

This paper introduces a quasi proportional feedback form for differential-algebraic systems, offering geometric insight and computational simplicity while preserving key structural properties.

Contribution

It develops a novel quasi proportional feedback form for linear differential-algebraic systems, enhancing interpretability and ease of computation compared to existing forms.

Findings

The quasi proportional feedback form is easy to compute.

It provides geometric insight into the system structure.

It retains essential control system properties.

Abstract

We investigate feedback forms for linear time-invariant systems described by differential-algebraic equations. Feedback forms are representatives of certain equivalence classes. For example state space transformations, invertible transformations from the left, and proportional state feedback constitute an equivalence relation. The representative of such an equivalence class, which we call proportional feedback form for the above example, allows to read off relevant system theoretic properties. Our main contribution is to derive a quasi proportional feedback form. This form is advantageous since it provides some geometric insight and is simple to compute, but still allows to read off the relevant structural properties of the control system. We also derive a quasi proportional and derivative feedback form. Similar advantages hold.