scholarly journals Input-to-state stability of multi-group stochastic coupled systems with time-varying delay

Filomat ◽  
2017 ◽  
Vol 31 (7) ◽  
pp. 2109-2121
Author(s):  
Xiaoling Zou ◽  
Jiacheng Xu
Keyword(s):  
Graph Theory ◽  
Coupled Oscillators ◽  
Coupled Systems ◽  
Theoretic Approach ◽  
Time Varying ◽  
Systematic Method ◽  
Graph Theoretic ◽  
Time Varying Delay ◽  
Graph Theoretic Approach ◽  
Varying Delay

We investigate the issue of p-th moment exponentially input-to-state stability (pMEISS) of multi-group stochastic coupled systems with time-varying delay (MSCSTD) in this paper. By means of results from graph theory, we develop a systematic method that allows one to construct a proper Lyapunov function for MSCSTD. More specifically, two kinds of sufficient criteria, which are called Lyapunov-type and coefficient-type respectively, are derived to ensure pMEISS for MSCSTD by using the graph-theoretic approach. To make results more understandable, we apply them to a typical stochastic coupled oscillators with control inputs.

scholarly journals Modeling, Analysis, and Comparison of Nanotechnology System: A Graph-Theoretic Approach

2020 ◽  
Author(s):  
Tanvir Singh ◽  
V.P. Agrawal
Keyword(s):  
Graph Theory ◽  
Complete Analysis ◽  
Theoretic Model ◽  
Theoretic Approach ◽  
Graph Theoretic ◽  
Systems Model ◽  
System A ◽  
Modeling Analysis ◽  
Graph Theoretic Approach ◽  
Permanent Function

Nanotechnology can create many new nanomaterials and nanodevices with a vast range of applications, such as in medicine, electronics, biomaterials, and energy production, etc. An attempt is made to develop an integrated systems model for the structure of the nanotechnology system in terms of its constituents and interactions between the constituents and processes, etc. using graph theory and matrix algebra. The nanotechnology system is first modeled with the help of graph theory, secondly by variable adjacency matrix and thirdly by multinomial (which is known as a permanent function). The permanent function provides an opportunity to carry out a structural analysis of nanotechnology system in terms of its strength, weakness, improvement, and optimization, by correlating the different systems with its structure. The physical meaning has been associated with each term of the permanent function. Different structural attributes of the nanotechnology system are identified concurrently to reduce cost, time for design and development, and also to develop a graph-theoretic model, matrix model, and multinomial permanent model of nanotechnology system. The top-down approach for a complete analysis of any nanotechnology systems is given. The general methodology is presented for the characterization and comparison of two nanotechnology systems.

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