User manual and tutorial for ISIM1s: a tiny MATLAB package for single stage invariant manifold-guided impulsive stabilization of delay equations

TL;DR

This paper introduces ISIM1s, a MATLAB package that simplifies the derivation of impulsive controllers for stabilizing delay differential equations, with detailed guidance and tuning insights.

Contribution

The paper provides a manual and tutorial for a new MATLAB package that automates the design of stabilizing impulsive controllers for delay equations.

Findings

Package effectively derives stabilizing controllers for various delay equations

Tutorial clarifies the role of tuning parameters in controller design

Demonstrates applicability to complex delay systems

Abstract

ISIM1s consists of a few MATLAB functions and a script that can be used to derive stabilizing impulsive controllers for delay differential equations. This document serves as both a manual and tutorial on the functionality of the ISIM1s package. Brief background on the theoretically guaranteed stabilization scenario are provided before the primary MATLAB script is explained. The tutorial demonstrates how the package can be used to derive stabilizing impulsive controllers for delay differential equations of various complexity scales. Emphasis is placed on the role of various tuning parameters.