Abstract and Applied Analysis
Volume 2013 (2013), Article ID 631639, 9 pages
http://dx.doi.org/10.1155/2013/631639
Research Article

A Note on the Observability of Temporal Boolean Control Network

Wenping Shi,1 Bo Wu,1,2 and Jing Han3

1College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua 321004, China
2Academic Affairs Division, Zhejiang Normal University, Jinhua 321004, China
3Department of Mathematics, Tongji University, Shanghai 200092, China

Received 2 December 2012; Accepted 24 February 2013

Academic Editor: Qi Luo

Copyright © 2013 Wenping Shi 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.

Abstract

Temporal Boolean network is a generalization of the Boolean network model that takes into account the time series nature of the data and tries to incorporate into the model the possible existence of delayed regulatory interactions among genes. This paper investigates the observability problem of temporal Boolean control networks. Using the semi tensor product of matrices, the temporal Boolean networks can be converted into discrete time linear dynamic systems with time delays. Then, necessary and sufficient conditions on the observability via two kinds of inputs are obtained. An example is given to illustrate the effectiveness of the obtained results.