Lipschitz stability analysis of fractional-order gene regulatory networks with impulsive perturbations and distributed delays

A model of fractional-order discontinuous impulsive delayed gene regulatory networks (GRNs) was investigated in this paper. The impulsive perturbations were at fixed moments of time and measured the impulsive control effects which can be controlled appropriately. A fractional-order modeling approach was applied and distributed delays were taken into account for greater model flexibility. In this paper, rather than studying the classical Lyapunov-type stability of an equilibrium point, we addressed the extended Lipschitz stability behavior of the considered GRNs. By applying the impulsive fractional Lyapunov functions technique, new criteria were derived to ensure the global uniform Lipschitz stability for the fractional impulsive delayed GRNs. Furthermore, the effects of considering uncertain parameters were also analyzed. Finally, an illustrating example was given to support the obtained theoretical results.