Strong stability of an optimal control hybrid system in fed-batch fermentation

In this paper, we consider a nonlinear hybrid dynamic (NHD) system to describe fed-batch culture where there is no analytical solutions and no equilibrium points. Our goal is to prove the strong stability with respect to initial state for the NHD system. To this end, we construct corresponding linear variational system (LVS) for the solution of the NHD system, also prove the boundedness of fundamental matrix solutions for the LVS. On this basis, the strong stability is proved by such boundedness.