State Estimator Design for Genetic Regulatory Networks with Discrete and Leakage Delays

In this article, the state estimation issue is addressed for a class of genetic regulatory networks with discrete and leakage delays. The main purpose is to calculate and complete the system state information through the significant measurement outputs. Firstly, the original nonlinear error system is translated into a linearly uncertain one by applying the Lagrange’s Mean–Value Theorem. Secondly, a sufficient condition is established to ensure the robust asymptotic stability of error system by resorting to Lyapunov–Krasovskii functional, convex combination technique, Jensen’s inequality, linear matrix inequality combined with Barbalat’s lemma. Meantime, the state observer gains are derived in term of the feasible solutions to inequalities. Finally, a group of numerical examples are given to verify the effect of leakage delay on system stability and the effectiveness of the devised state observer.