The triple-exponential fluorescence delta-response function is derived for the photophysical model of successive complexation between ligand and analyte. Initially, a complex with 1:1 stoichiometry between ligand and analyte is formed. Further binding leads to a complex with two analyte molecules per ligand molecule. We show that this model is uniquely identifiable. This means that all deactivation and exchange rate constants in the excited state and all spectral parameters associated with photoexcitation and fluorescence emission can be uniquely determined. The issues of controllability and observability are discussed for this photophysical system. The conditions, under which a non-control fable or non-observable system is obtained, are described.