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Mathematical Problems in Engineering
Volume 2013, Article ID 878146, 9 pages
Research Article

A Constructive Positive Realization with Sparse Matrices for a Continuous-Time Positive Linear System

Department of Computer Engineering, Chungnam National University, 99 Daehak-ro, Yuseong-gu, Daejeon 305-764, Republic of Korea

Received 9 September 2013; Revised 22 November 2013; Accepted 10 December 2013

Academic Editor: Yong-Kui Chang

Copyright © 2013 Kyungsup Kim. 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.


This paper discusses a computational method to construct positive realizations with sparse matrices for continuous-time positive linear systems with multiple complex poles. To construct a positive realization of a continuous-time system, we use a Markov sequence similar to the impulse response sequence that is used in the discrete-time case. The existence of the proposed positive realization can be analyzed with the concept of a polyhedral convex cone. We provide a constructive algorithm to compute positive realizations with sparse matrices of some positive systems under certain conditions. A sufficient condition for the existence of a positive realization, under which the proposed constructive algorithm works well, is analyzed.