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Mathematical Problems in Engineering
Volume 2016 (2016), Article ID 8325054, 8 pages
Research Article

Mathematical Modeling of Smart Space for Context-Aware System: Linear Algebraic Representation of State-Space Method Based Approach

Department of Electronic Engineering, Kwangwoon University, Seoul 139-701, Republic of Korea

Received 28 August 2015; Revised 16 February 2016; Accepted 14 March 2016

Academic Editor: Mustafa Tutar

Copyright © 2016 Sung-Hyun Yang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A smart space is embedded with several components such as sensors, actuators, and computing devices that enable the sensing and control of the environment, and the inhabitants interact with the devices in the smart space whenever they need to. To model a smart space, a dynamic relationship needs to be established among the elements of the space whereby the interactions with devices are considered a dynamic-process state. In this paper, a linear model of a smart space is presented using a state equation, where the two coefficient matrices and need to be defined to model the smart space, and the coefficient matrix is used to determine the states of the devices; similarly, the situation of the smart space is determined using coefficient . An algorithm is presented to make a linear model from the logical functions that are used to describe the system. This model is flexible in terms of the control of the smart-space environment because the environmental factors are represented by a matrix element. This linear smart-space model is helpful for the control of a context-aware system, and we use an example to illustrate the effectiveness of the proposed model.