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A Small-Gain Analysis for an All-Pairs Shortest-Path Algorithm: Global Exponential Input-to-State Stability

Abstract

In this article, we propose a distributed all-pairs shortest-path algorithm that finds the shortest path between every pair of nodes in an undirected graph and analyzes its robust stability from a control perspective. The proposed algorithm and the derived stability results outperform the previous related works in two aspects. First, while previous works consider the additive noise on the measured edge weight as the perturbation, in this article, we consider a general perturbation such that the edge weight is bounded and time-varying. Moreover, we consider quantization effects on the communication channels. Second, by using a Lyapunov-based small-gain theorem, we prove the global exponential input-to-state stability of the proposed algorithm under perturbations, implying its global exponential stability without perturbations and quantization effects while previous works only give global asymptotic stability or regional exponential stability results of theirs. Simulations are provided to verify the validity of our results.

article Article

date_range 2024

language English

link Link of the paper

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Mo Yuanqiu

Yu Lanlin

Du Haibo

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Featured Keywords

Global exponential input-to-state stability

shortest-path problem

small-gain theorem

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Assessment of reinforced concrete building damages following the Kahramanmaraş earthquakes in Malatya, Turkey (February 6, 2023)

Abstract

Earthquakes of magnitude Mw = 7.7 and Mw = 7.6 hit the city of Kahramanmaraş (Turkey) on 6 February 2023. These earthquakes caused serious damage in 11 provinces in Turkey resulting in over 50,000 deaths and huge economic losses with the collapse of thousands of buildings. Two consecutive devastating earthquakes have severely damaged the reinforced concrete building stock located in Malatya. There are many reasons reinforced concrete structures suffer damage under the influence of seismic loads. These reasons can be listed as material and section properties that do not comply with earthquake codes, workmanship defects, ground parameters that are not considered and design errors, as seen in field investigations after earthquakes in Turkey in the past. In this research, a field study was conducted on reinforced concrete buildings damaged after the earthquakes in Malatya province. The causes of structural damages in reinforced concrete buildings between 6–26 years of age were assessed in terms of design and material defects. The structural damages were mainly caused due to insufficient stirrups in structural members, short column, strong beam–weak column, failures of infill walls, soft story type collapse, poor concrete quality, and reinforcement corrosion. In addition to the field investigation, the spectrum relationships created using raw acceleration data obtained from DEMP (Disaster and Emergency Management Presidency) stations in Malatya province were compared with the design response spectra.

article Article

date_range 2024

language English

link Link of the paper

Collapsed buildings

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