The work proves that in an impulsive bioprocess the stable oscillation period exists for any microorganisms - i.e. microorganisms of any characteristics of biomass yield and specific growth rate - pointing out the practical and scientific importance of the presented solution. Moreover, universal stability conditions of the impulsive bioprocess are presented. In order to obtain the universality of the solution, a sigmoid function is introduced for description of the biomass yield changes. Further, the universal mathematical model of the impulsive bioprocess is established, tested and discussed. This work shows among others that the impulsive bioprocess extends functionality of a simple continuous bioprocess providing in an easy way to control biomass concentration. The article also introduces a new objective function and then presents and discusses aspects of the impulsive bioprocess multi-criteria optimization. The analytical results presented in the work are validated by numerical simulations.