Sampled-data non-fragile state estimation for delayed genetic regulatory networks under stochastically switching sampling periods

Abstract

This paper is concerned with the non-fragile state estimation (NFSE) problem for a class of delayed genetic regulatory networks (GRNs) under stochastic sampling mechanisms. The measurement output is sampled before being transmitted to the estimator where the sampling period switches between two different values in a random way. By transforming the sampling periods into bounded time-delays, the issue of designing a non-fragile state estimator based on stochastically sampled measurements is converted into the NFSE problem for GRNs with multiple probabilistic interval delays. Then, by constructing a Lyapunov–Krasovskii functional and employing the Gronwall’s inequality together with Jensen’s inequality, a sufficient criterion is obtained to ensure the exponential mean-square stability of the corresponding estimation error dynamics. Furthermore, the desired non-fragile estimator gain is obtained via solving a convex optimization problem. Finally, the validity of the developed stochastic sampled-data NFSE scheme is verified via a numerical example.