State estimation for delayed genetic regulatory networks based on passivity theory

•This paper is concerned with the state estimation problem for delayed genetic regulatory networks based on passivity theory.•The main purpose is to design the state estimator to approximate the true concentrations of the mRNA and protein through measurement outputs.•Time-varying delays are explicitly assumed to be non-differentiable and the constraint on the delay is removed.•A novel delay-dependent passivity criterion is established for GRNs. This paper is concerned with the state estimation problem for delayed genetic regulatory networks (GRNs) based on passivity analysis approach. The main purpose of the problem is to design the estimator to approximate the true concentrations of the mRNA and protein through available measurement outputs. Time-varying delays are explicitly assumed to be non-differentiable and constraint on the derivative of the time-varying delay is less than one can be removed. Based on the Lyapunov–Krasovskii functionals involving triple integral terms, using some integral inequalities and convex combination technique, a delay-dependent passivity criterion is established for GRNs in terms of linear matrix inequalities (LMIs) that can efficiently be solved by any available LMI solvers. Finally, numerical examples and simulation are presented to demonstrate the efficiency of the proposed estimation schemes.