Design of state observer for genetic regulatory networks with interval time-varying delays

The aim of this paper is to propose a new design approach to a state observer for genetic regulatory networks with interval time-varying delays. By constructing an appropriate Lyapunov-Krasovskii functional containing triple-integral terms and introducing a new inequality to estimate the derivatives of triple-integral terms, a delay-range-dependent and delay-rate-dependent sufficient condition of Linear matrix inequality (LMI) form is established so that the resultant error system is asymptotically stable. Thereby, a state observer can be easily obtained based on the solution to the LMIs. A numerical example is offered to illustrate the effectiveness of the proposed approach.