Delay decomposition approach to \(\mathcal {H}_{\infty }\) filtering analysis of genetic oscillator networks with time-varying delays

In this paper, the \(\mathcal {H}_{\infty }\) filtering problem is treated for N coupled genetic oscillator networks with time-varying delays and extrinsic molecular noises. Each individual genetic oscillator is a complex dynamical network that represents the genetic oscillations in terms of complicated biological functions with inner or outer couplings denote the biochemical interactions of mRNAs, proteins and other small molecules. Throughout the paper, first, by constructing appropriate delay decomposition dependent Lyapunov–Krasovskii functional combined with reciprocal convex approach, improved delay-dependent sufficient conditions are obtained to ensure the asymptotic stability of the filtering error system with a prescribed \(\mathcal {H}_{\infty }\) performance. Second, based on the above analysis, the existence of the designed \(\mathcal {H}_{\infty }\) filters are established in terms of linear matrix inequalities with Kronecker product. Finally, numerical examples including a coupled Goodwin oscillator model are inferred to illustrate the effectiveness and less conservatism of the proposed techniques.