Dissipative Control of Markovian Jumping Genetic Regulatory Networks with Time-Varying Delays and Reaction–Diffusion Driven by Fractional Brownian Motion

This paper conducts a dissipative analysis for comprehensive genetic regulatory network models with fractional Brownian motion (fBm), diffusion-reaction processes, Markovian jump and time-varying delay. By constructing an appropriate Lyapunov–Krasovskii functional, utilizing linear matrix inequality (LMI) technique and stochastic theory, several sufficient conditions of global dissipativity and strictly \(({{\mathscr {Q}}},{{\mathscr {S}}},{{\mathscr {R}}})\)-\(\gamma \)-dissipativity of the solution are established. Moreover, the global attractive sets which are positive invariant are obtained. Finally, two numerical examples are given to illustrate the effectiveness of the theoretical results.