A Recursive Approach to Quantized ${H_{\infty}}$ State Estimation for Genetic Regulatory Networks Under Stochastic Communication Protocols

This paper deals with the finite-horizon quantized H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> state estimation problem for a class of discrete timevarying 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 highthroughput 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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> 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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> 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.