Gain and phase margins of the discrete-time guaranteed cost regulator

As well known, the guaranteed cost regulator of linear, discrete-time uncertain systems ensures closed-loop asymptotic stability in presence of parametric uncertainties of a given class. In this paper it is shown that this controller provides also interesting robustness properties in the presence of both the above parametric uncertainties and unstructured uncertainties located at the system input. Furthermore, it is shown that these properties are similar to those provided for systems without parametric uncertainties, by the discrete-time LQ regulator