A systematic approach towards robust stability analysis of integral delay systems with general interval kernels

TL;DR

This paper presents a fully algebraic, computationally efficient method for robust stability analysis of integral delay systems with general interval kernels, outperforming traditional Lyapunov-Krasovskii approaches.

Contribution

It introduces a novel algebraic algorithm that handles a wider class of uncertain kernel functions beyond exponential types, reducing conservatism and computational cost.

Findings

Algorithm outperforms Lyapunov-Krasovskii methods in examples

Applicable to general real-valued kernel functions within bounds

Easier to implement and less conservative

Abstract

Robust stability problem of integral delay systems with uncertain kernel matrix functions is addressed in this paper. On the basis of characteristic equation and the argument principle, an algorithm is generated which is shown to outperform the Lyapunov-Krasovskii (LK) approaches with respect to conservatism in the presented examples. Despite the conventional manual use of Nyquist criterion, the proposed algorithm is fully algebraic, cheaper and easily implemented in computer programs. In addition, the proposed method is applicable to a wider range of uncertain systems compared to the existing literature. Namely, despite the previously published results on this problem, the kernel matrix function here is not limited to exponential type and can include any real function within known bounds as its elements.