Design of robust [formula omitted] state estimator for delayed polytopic uncertain genetic regulatory networks: Dealing with finite-time boundedness

Abstract

In this paper, a robust H∞ design approach is proposed to accomplish the state estimation task for a class of continuous-time gene regulatory networks (GRNs) in the finite-time framework. For the GRNs under investigation, the distributed inter-node time delays and intra-node time delays are, respectively, taken into account in the feedback regulation function and the translation process. Moreover, the parameter uncertainty with convex polytopic constraint is introduced to characterize the unavoidable modeling errors induced by parameter sensitivity, calibration accuracy, abrupt structural changes and failures, etc. The primary objective of this paper is to design a robust state estimator for the considered GRNs based on the measured concentrations of messenger ribonucleic acid and protein such that the finite-time boundedness and the H∞ performance are guaranteed. By resorting to the Lyapunov stability theory, the Jensen’s inequality and the Gronwall inequality, some sufficient conditions are established in terms of linear matrix inequalities. Subsequently, a set of parameter matrices with special structures is designed by means of the convex optimization techniques. Finally, a numerical example is provided to demonstrate the finite-time boundedness and the robust performance of the developed state estimation approach.