H∞$$ {H}_{\infty } $$ Controller Design for Delayed Genetic Regulatory Networks With Hub Structure and Bidirectional Coupling

ABSTRACT This paper is devoted to investigate controller design problem for genetic regulatory networks (GRNs) with hub structure, bidirectional couplings, and multiple delays. Multiple time‐varying transmission delays and unbounded distributed delays are involved. First, a bounded real lemma (BRL) is established by proposing a direct method that is on the basis of the solutions of the considered GRN. Second, based on the obtained BRL, state feedback controllers are designed to ensure that the obtained closed‐loop GRN is globally exponentially stable (GES) with an performance index. Finally, the validity of the theoretical results is verified by two numerical examples.