Robust stability analysis for discrete-time genetic regulatory networks with probabilistic time delays

A Recursive Approach to Quantized H∞ State Estimation for Genetic Regulatory Networks Under Stochastic Communication Protocols

This paper deals with the finite-horizon quantized H_∞ state estimation problem for a class of discrete time-varying genetic regulatory networks with quantization effects under stochastic communication protocols (SCPs). To better reflect the data-driven flavor of today's biological research, the network measurements (typically gigabytes in size by high-throughput sequencing technologies) are transmitted to a remote state estimator via two independent communication networks of limited bandwidths. To lighten the communication loads and avoid undesired data collisions, the measurement outputs are quantized and then transmitted under two SCPs introduced to schedule the large-scale data transmissions. The purpose of this paper is to design a time-varying state estimator such that the error dynamics of the state estimation satisfies a prescribed H_∞ performance requirement over a finite horizon in the presence of nonlinearities, quantization effects, and SCPs. By utilizing the completing-the-square technique, sufficient conditions are derived to ensure the H_∞ estimation performance and the parameters of the state estimator are designed by solving coupled backward recursive Riccati difference equations. A numerical example is given to illustrate the effectiveness of the design scheme of the proposed state estimator.

Robust Stability of Discrete-Time Randomly Switched Delayed Genetic Regulatory Networks with Known Sojourn Probabilities

This study investigates stability problems related to discrete-time randomly switched genetic regulatory networks (GRNs) with time-varying delays. A new discrete-time randomly switched GRN model with known sojourn probabilities is proposed. By utilizing the discrete Wirtinger-based inequality and a newly proposed constraint condition on the feedback regulatory function, which have not been fully used in stability analysis of discrete-time GRNs, we establish delay-dependent stability and robust stability criteria. These criteria possess the sojourn probabilities of randomly switched GRNs. Two numerical examples are provided to demonstrate the effectiveness of the established results.