Razumikhin-type ISS Lyapunov function and small gain theorem for discrete time time-delay systems with application to a biased min-consensus protocol

IF 4.8 2区计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS

Automatica Pub Date : 2025-01-22 DOI:10.1016/j.automatica.2025.112111

Yuanqiu Mo , Wenwu Yu , Huazhou Hou , Soura Dasgupta

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引用次数: 0

Abstract

This paper considers small gain theorems for the global asymptotic and exponential input-to-state stability for discrete time time-delay systems using dissipative-form Razumikhin-type Lyapunov function. Among other things, unlike the existing literature, it provides both necessary and sufficient conditions for exponential input-to-state stability in terms of the dissipative-form Razumikhin-type Lyapunov function and the small gain theorem. Previous necessary and sufficient conditions were with the more computationally onerous, Krasovskii-type Lyapunov functions. The result finds application in the robust stability analysis of a graph-based distributed algorithm, namely, the biased min-consensus protocol, which can be used to compute the length of the shortest path from each node to its nearest source in a graph. We consider the biased min-consensus protocol under perturbations that are common in communication networks, including noise, delay and asynchronous communication. By converting such a perturbed protocol into a discrete time time-delay nonlinear system, we prove its exponential input-to-state stability under perturbations using our Razumikhin-type Lyapunov-based small gain theorem. Simulations are provided to verify the theoretical results.

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来源期刊

Automatica 工程技术-工程：电子与电气

CiteScore

10.70

自引率

7.80%

发文量

617

审稿时长

5 months

期刊介绍： Automatica is a leading archival publication in the field of systems and control. The field encompasses today a broad set of areas and topics, and is thriving not only within itself but also in terms of its impact on other fields, such as communications, computers, biology, energy and economics. Since its inception in 1963, Automatica has kept abreast with the evolution of the field over the years, and has emerged as a leading publication driving the trends in the field. After being founded in 1963, Automatica became a journal of the International Federation of Automatic Control (IFAC) in 1969. It features a characteristic blend of theoretical and applied papers of archival, lasting value, reporting cutting edge research results by authors across the globe. It features articles in distinct categories, including regular, brief and survey papers, technical communiqués, correspondence items, as well as reviews on published books of interest to the readership. It occasionally publishes special issues on emerging new topics or established mature topics of interest to a broad audience. Automatica solicits original high-quality contributions in all the categories listed above, and in all areas of systems and control interpreted in a broad sense and evolving constantly. They may be submitted directly to a subject editor or to the Editor-in-Chief if not sure about the subject area. Editorial procedures in place assure careful, fair, and prompt handling of all submitted articles. Accepted papers appear in the journal in the shortest time feasible given production time constraints.