A novel $H_{\mathrm{\infty }}$ state observer design method for genetic regulatory networks with time-varying delays

In this article, a novel method is proposed to investigate the $H_{\mathrm{\infty }}$ state observer design problem for genetic regulatory networks with time-varying delays and disturbances. First, the structure of the desired state observer is constructed, and the parameterized bounds of the error system solutions are given. Then, a bounded real lemma is established to provide the existence of the state observer and ensure that the error system is globally exponentially stable at an $H_{\mathrm{\infty }}$ performance level. Third, based on the obtained bounded real lemma, the explicit expressions of the $H_{\mathrm{\infty }}$ state observer can be obtained by solving several matrix inequalities. The effectiveness of the proposed novel observer design method is illustrated via a numerical example.