The authors consider single-input, single-output, discrete time, time-varying systems of the form \[ y(k)= \sum_{i=1}^s a_i(k) y(k-i)+ \sum_{i=1}^t b_i(k) u(k-i)+ \eta(k)+ w(k), \] where \(y(k)\), \(u(k)\), \(\eta(k)\) and \(w(k)\) denote the output, input, uncertainty and disturbance error, respectively. The orders \(s,t\) are assumed to be known, the parameters \(a(i)\), \(b(i)\) belong to a bounded convex set, and at `frozen time' instants each system is stabilizable. If the model error \(\eta(k)\) is sufficiently small, the disturbance \(w(k)\) is uniformly bounded, and if the time average of the time-varying-parameter is sufficiently small, then an adaptive projected gradient algorithm which guarantees bounded input and output sequences is given.