Averaging analysis for discrete time and sampled data adaptive systems

Earlier continuous-time averaging theorems are extended to the nonlinear discrete-time case. These theorems are applied to the study of the convergence analysis of discrete-time adaptive identification and control systems. Instability theorems are also derived for the study of robust stability and instability of adaptive control schemes applied to sampled data systems. As a byproduct, the effects of sampling are also studied on unmodeled dynamics in continuous-time systems.>