This paper deals with the recursive robust control problem for linear discrete-time systems subject to uncertainties and delayed state. Uncertainties are modeled norm-bounded and are present in parametric matrices and in weighting matrices. Applying the lifting method, the delayed system is transformed into an augmented delay-free system. Then, the regulator is deduced from a combination of penalty functions and the optimal solution of regularized least-squares problems with uncertainties. The main feature of this approach is the recursiveness established by Riccati equations, which are presented in a symmetric matrix framework. The numerical example illustrates the performance of the proposed regulator when compared to another approach in the literature.
