State estimator design for genetic regulatory networks with leakage and discrete heterogeneous delays: A nonlinear model transformation approach

Abstract

We address the state estimation problem for a class of genetic regulatory networks (GRNs) with leakage and discrete heterogeneous delays in this paper. In order to simplify the complexity of designing the state estimator for nonlinear delayed model of GRNs, a state estimate algorithm based on a model transformation method is presented, which goal is to get the entire system state. First, in light of the Lagrange’s mean-value theorem, the nonlinear model transformation method is applied to describe the nonlinear error system as a linear time-varying model. Second, by constructing the Lyapunov–Krasovskii functional dependent on the composite function variables of state estimate errors, a new technique lemma is provided and applied to the stability analysis. Third, the sufficient condition of state estimator design is obtained in term linear matrix inequalities, under which, the certification of the uniform asymptotic stability for state estimate error system is derived. Finally, a simulation example illustrates the rationality and effectiveness of the proposed theoretical results.