SSD -- Software for Systems with Delays: Reproducible Examples and Benchmarks on Model Reduction and H2 Norm Computation

TL;DR

SSD is a MATLAB toolbox that enables analysis, model reduction, and H2 norm computation for retarded time delay systems, incorporating new algorithms and benchmarks for delay systems.

Contribution

The paper introduces SSD, a MATLAB package with novel algorithms for delay system reduction and H2 norm calculation, including the first extension of frequency-limited balanced reduction to delay systems.

Findings

Implemented a MATLAB package for delay systems analysis

Extended frequency-limited balanced reduction to delay systems

Provided benchmark problems for H2 norm and model reduction

Abstract

We present SSD, Software for Systems with Delays, a de novo MATLAB package for the analysis and model reduction of retarded time delay systems (RTDS). Underneath, our delay system object bridges RTDS representation and Linear Fractional Transformation (LFT) representation of MATLAB. This allows seamless use of many available visualizations of MATLAB. In addition, we implemented a set of key functionalities such as H2 norm and system gramian computations, balanced realization and reduction by direct integral definitions and utilizing sparse computation. As a theoretical contribution, we extend the frequency-limited balanced reduction to delay systems first time, propose a computational algorithm and give its implementation. We collected two sets of benchmark problems on H2 norm computation and model reduction. SSD is publicly available in GitHub at https://github.com/gumussoysuat/ssd. Our reproducible paper and two benchmark collections are shared as executable notebooks.