Averaging analysis for discrete time and sampled data adaptive systems

We extend our earlier continuous time averaging theorems to the nonlinear discrete time case. We use theorems for the study of the convergence analysis of discrete time adaptive identification and control systems. We also derive instability theorems and use them for the study of robust stability and instability of adaptive control schemes applied to sampled data systems. As a by product we also study the effects of sampling on unmodeled dynamics in continuous time systems.