Solution Method For Higher Order System

TL;DR

This paper presents a method to linearize higher order state space systems while preserving key system characteristics, enabling analysis through eigenvector recovery without complex computations.

Contribution

It introduces a novel approach to recover zero directions of higher order systems directly from linearizations using Fiedler pencils, avoiding arithmetic operations.

Findings

Zero directions can be recovered from eigenvectors of Fiedler pencils

System characteristics are preserved during linearization

Method simplifies analysis of higher order systems

Abstract

Consider a higher order state space system and the aim of this paper is to linearize the system preserving system characteristics. That is, linearization preserving system characteristics(e.g, controllability, observability, various zeros and transfer function) for analysis of higher order systems gives the solution for higher order system. We study recovery of zero directions of higher order state space system from those of the linearizations. That is, the zero directions of the transfer functions associated to higher order state space system are recovered from the eigenvectors of the Fiedler pencils without performing any arithmetic operations