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A unified criterion for stability is dealt for a class of chemostat model which includes a generic growth rate function representing substrate, biomass, and product inhibitions. The stability criterion is unified at sense that the growth kinetic rate takes a general form into the vector field and includes both the maintenance coefficient and the death rate parameters. Sufficient conditions are provided for multiplicity of the steady states. In addition, from a local analysis, an expression is proposed as a unified criterion for the local stability and for local bifurcations existence. Hence, a control design relies the unified criterion to account local stability and bifurcation with independence of the specific growth rate governing a chemostat. The criterion is based on partial derivatives which allows us to reduce the calculation needed to determine the equilibrium point stability and the bifurcation points existence. Analytical features of the …