Preprint
Razumikhin-type ISS Lyapunov function and small gain theorem for discrete time time-delay systems with application to a biased min-consensus protocol
ArXiv.org
Cornell University
10/05/2023
DOI: 10.48550/arxiv.2310.03347
Abstract
This paper considers small gain theorems for the global asymptotic and
exponential input-to-state stability for discrete time time-delay systems using
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 Razumikhin-type Lyapunov
function and the small gain theorem. Previous necessary ad 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.
Details
- Title: Subtitle
- Razumikhin-type ISS Lyapunov function and small gain theorem for discrete time time-delay systems with application to a biased min-consensus protocol
- Creators
- Yuanqiu MoWenwu YuHuazhou HouSoura Dasgupta
- Resource Type
- Preprint
- Publication Details
- ArXiv.org
- DOI
- 10.48550/arxiv.2310.03347
- ISSN
- 2331-8422
- Publisher
- Cornell University; Ithaca, New York
- Language
- English
- Date posted
- 10/05/2023
- Academic Unit
- Electrical and Computer Engineering
- Record Identifier
- 9984473764002771
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