Robust filtering for gene expression time series data with variance constraints

Abstract

In this paper, an uncertain discrete-time stochastic system is employed to represent a model for gene regulatory networks from time series data. A robust variance-constrained filtering problem is investigated for a gene expression model with stochastic disturbances and norm-bounded parameter uncertainties, where the stochastic perturbation is in the form of a scalar Gaussian white noise with constant variance and the parameter uncertainties enter both the system matrix and the output matrix. The purpose of the addressed robust filtering problem is to design a linear filter such that, for the admissible bounded uncertainties, the filtering error system is Schur stable and the individual error variance is less than a prespecified upper bound. By using the linear matrix inequality (LMI) technique, sufficient conditions are first derived for ensuring the desired filtering performance for the gene expression model. Then the filter gain is characterized in terms of the solution to a set of LMIs, which can easily be solved by using available software packages. A simulation example is exploited for a gene expression model in order to demonstrate the effectiveness of the proposed design procedures.

Keywords:

• Microarray data
• Gene expression model
• Robust filtering
• Stochastic disturbances
• Error variance constraints

Acknowledgements

This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grants GR/S27658/01 and EP/C524586/1, the Biotechnology and Biological Sciences Research Council (BBSRC) of the UK under Grants BB/C506264/1 and 100/EGM17735, the Nuffield Foundation of the UK under Grant NAL/00630/G, and the Alexander von Humboldt Foundation of Germany.