Journal article
Razumikhin-type ISS Lyapunov function and small gain theorem for discrete time time-delay systems with application to a biased min-consensus protocol
Automatica (Oxford), Vol.174, 112111
04/2025
DOI: 10.1016/j.automatica.2025.112111
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.
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 Mo - Southeast UniversityWenwu Yu - Southeast UniversityHuazhou Hou - Purple Mountain LaboratoriesSoura Dasgupta - Department of Electrical and Computer Engineering, University of Iowa, Iowa City (IA) 52242, USA
- Resource Type
- Journal article
- Publication Details
- Automatica (Oxford), Vol.174, 112111
- DOI
- 10.1016/j.automatica.2025.112111
- ISSN
- 0005-1098
- eISSN
- 1873-2836
- Publisher
- Elsevier Ltd
- Grant note
- BK20230826; BK20220812 / Natural Science Foundation of Jiangsu Province, China (http://dx.doi.org/10.13039/501100004608) 62303112; 62203109 / National Natural Science Foundation of China (http://dx.doi.org/10.13039/501100001809)
- Language
- English
- Date published
- 04/2025
- Academic Unit
- Electrical and Computer Engineering
- Record Identifier
- 9984781276102771
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