Stability Analysis of Nonlinear Hybrid System in Microbial Fed-batch Culture∗

In this paper, we study the stability of the nonlinear hybrid system describing the concentrations of extracellular and intracellular substances in the process of bio-dissimilation of glycerol to 1,3-propanediol. We prove an asymptotical stability lemma in nonlinear impulsive hybrid systems and obtain the strict stability and uniformly asymptotical stability for the nonlinear hybrid system. These results provide less conservative stability conditions for hybrid system as compared to classical results in the literature and allow us to characterize the invariance of a class of nonlinear hybrid dynamical systems.