An LPV based robust peak-to-peak state estimation for genetic regulatory networks with time varying delay

This paper addresses the nonlinear observer design problem for gene regulatory networks with time-varying delay, focusing on the case of unstable GRNs with oscillatory behavior. Currently available approaches are conservative due to presence of nonlinear terms, which should be dealt with. In addition, nonlinear terms are only known approximately in practice and therefore previous works may lead to undesirable performance. To address conservativeness issue, we have provided an LPV approach. Besides, to diminish effects of uncertain nonlinear terms on observer performance, a peak-to-peak state estimation problem is considered. By defining appropriate Lyapunov–Krasovskii functional, sufficient conditions are derived that guarantee the desirable performance. The superiority of the proposed method to existing approaches is illustrated by means of a numerical example. Moreover, good performance of state estimation in presence of uncertainty is demonstrated by simulations.