Stability of an windup prevention scheme in recursive parameter estimation

Stability properties of a recently suggested anti-windup algorithm for recursive parameter estimation are analyzed. Convergence of the resulting from recursion dynamic system is equivalent to that of a linear time-varying difference matrix equation. The linear mapping associated with the system is shown to be a paracontraction with respect to a certain norm but not a contraction. A special case of the studied matrix difference equation arises in the normalized LMS-algorithm.