Reduced-order state observers for genetic regulatory networks with time-varying delays

This paper involves the reduced-order state observer design for genetic regulatory networks with time-varying delays. The aim is to design reduced-order state observer based on available network outputs. A Lyapunov-Krasovskii functional including quadruplicate integrals is introduced, and its derivative is estimated by using the appropriate inequalities, reciprocal convex technique and convex technique. Delay-dependent sufficient conditions expressed by linear matrix inequalities are obtained to ensure that the resultant error system is asymptotically stable. Moreover, the concrete expression of the desired reduced-order state observer is given. Finally, a numerical example is presented to explain the obtained theoretical results.