On the robustness of LQ regulators for discrete time systems

The authors present a sufficient condition for quadratic stabilizability of uncertain linear discrete time systems using LQ (linear quadratic) regulators. The true system is represented by a nominal model plus additive terms representing the uncertainties in the state and input matrices. With a proper choice of these terms, one may represent the most common types of uncertainties encountered in the literature. The main result of the present work is a robustification procedure for discrete time LQ regulators, which is based on a sufficient condition for quadratic stabilizability. The conservativeness of the proposed condition is discussed and some examples are given