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Delay-Dependent Stability and Performance Analysis for Time Delay Systems Interconnected over an Undirected Graph

Xiaojuan Xue 1,2, Huiling Xu 1, and Li Xu 2
1. School of Science, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu, P.R. China
2. Department of Electronics and Information Systems, Akita Prefectural University, Akita, Japan

Abstract—Time delay is usually inevitable in a system consisting of spatially and/or wirelessly interconnected units or subsystems. This paper deals with the fundamental problem of stability and contractive performance for systems interconnected over an undirected graph with time delay in the states of subsystems. A sufficient condition for the well-posedness, delay-dependent stability and contractiveness of such systems is derived by means of finite-dimensional linear matrix inequalities (LMIs), which provides a useful tool for further exploration of the controller design problem. A numerical example is also presented to show the validity of the obtained results. 
 
Index Terms—delay-dependent stability, contractiveness, time delay systems, undirected graph, LMIs

Cite: Xiaojuan Xue, Huiling Xu, and Li Xu, "Delay-Dependent Stability and Performance Analysis for Time Delay Systems Interconnected over an Undirected Graph," International Journal of Electrical and Electronic Engineering & Telecommunications, Vol. 7, No. 4, pp. 141-145, October 2018. Doi: 10.18178/ijeetc.7.4.141-145

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