Strong Stability of Optimal Design for a Time-varying Dynamic System in Batch Culture

In this study, we prove strong stability for a typical time-varying nonlinear dynamic system in batch culture, which is hard to obtain analytical solutions and equilibrium points. To this end, firstly, we construct a linear variational system to the nonlinear dynamic system. Secondly, we give a proof that the fundamental matrix solution to this dynamic system is bounded. Combined with the above two points, the strong stability for the nonlinear dynamic system is proved.