Robust adaptive stabilization of time-varying discrete time systems

In this paper, a robust adaptive regulator is constructed for time-varying discrete time systems with bounded disturbances and unmodelled dynamics. It is assumed that the parameters of the nominal model belong to a bounded convex set and that the 'frozen time' nominal model is stabilizable for all possible parameter values. Requiring neither external excitation nor stable invertibility of the nominal model, an adaptive regulator is consturcted from the. solution to a finite time Riccati equation. No upper bound of the disturbances is assumed to be available. It is shown that the input and output sequences of the closed-loop system ate bounded if both the time average of the parameter variations and the model error are sufficiently small.