Robust adaptive stabilization for time-varying systems with unmodelled dynamics and disturbances

In this paper, robust adaptive stabilization is discussed for time-varying discrete time systems with disturbances and unmodelled dynamics. Both bounded and unbounded stochastic disturbances are considered. 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 constructed on the basis of the solution to a finite time Riccati equation and a projected gradient estimator. It is shown that the closed-loop system is stable if both the time average of the parameter variations and the model error are sufficiently small.