Robust Linear Quadratic Regulator for Uncertain Linear Discrete-Time Systems with Delay in the States: an augmented system approach

Abstract

In this paper we deal with the regulation problem for a class of uncertain discrete-time systems with known constant delays in the states. Uncertainties are assumed norm-bounded and affect all parametric matrices of the system. Applying the lifting method, the delayed system is transformed into an augmented delay-free system. Then, the control law is obtained from combination of penalty functions and robust regularized least-squares problem, when there exist uncertainties in the data. The solution provided is given in terms of augmented Riccati equations presented in a framework given by an array of matrices.