Stability analysis of a reduced model of the lac operon under impulsive and switching control

The study of the stability is an important motif in biological systems. Stability plays a significant role in some of the basic processes of life. In this paper, we provide a theoretical method for analyzing the exponential stability of a reduced model of the lac operon under the impulsive and switching control. Under the hybrid control, the reduced model becomes a nonlinear hybrid impulsive and switching system, and we get the sufficient conditions of its exponential stability. Finally, we give examples to illustrate the effectiveness of our method.