A new error model for adaptive systems

A simple error model is described for both discrete and continuous time adaptive systems. The stability of the model for both bounded and unbounded inputs is analyzed for the discrete case and extended to continuous time models. It is shown that
\Delta\phi(k)\in I^{2}
in the former case and
\phi(t)\in L^{2}
in the latter case due to the presence of a feedback signal and these in turn play an important role in the stability analysis of discrete and continuous time adaptive systems.