Efficient Numerical Analysis of Stability of High-Order Systems With a Time Delay

TL;DR

This paper introduces an efficient numerical method for analyzing the stability of high-order systems with time delays, reducing conservativeness and computational costs compared to existing approaches.

Contribution

It presents a novel methodology derived from exact methods that is computationally efficient for large, high-order systems with time delays.

Findings

Method reduces conservativeness in stability analysis.

Demonstrated efficiency on a system with over 400 states.

Compared favorably to existing techniques in computational cost.

Abstract

Time delays are a common perturbation in systems with many states, such as networked, distributed, or decentralized systems. Current methods analyzing the stability of large systems with time delay typically produce very conservative results. While more exact methods exist, these become inefficient for large systems. This paper provides a methodology for analyzing the stability of time-delayed systems that is derived from exact methods but is efficient for high-order systems. The computational and memory cost of this new technique is compared to the costs of existing techniques, and its efficiency is shown using a distributed system with over four hundred states.