Mechanical Normal Form of First Order State-Space Systems

TL;DR

This paper introduces a state transformation that converts certain first-order state-space systems into a mechanical normal form, enabling the use of specialized algorithms for second-order differential equations.

Contribution

It presents a novel state transformation method that achieves a mechanical normal form for specific first-order systems, facilitating advanced analysis and control.

Findings

Transformation exists under certain system conditions

Enables application of mechanical system algorithms

Simplifies analysis of eligible state-space systems

Abstract

In this work a state transformation is presented that transforms a given state-space system to a normal form related to mechanical systems. The underlying state-space system must meet certain requirements such that a transformation exist. If the requirements are satisfied one obtains second order differential equations which allow the application of customized and specialized algorithms.