On discrete dynamic output feedback min-max controllers

The paper considers output feedback min-max controllers for uncertain linear systems. A constructive design procedure is presented that solves the problem of realizing stabilizing discrete time min-max controllers via measured outputs for non-square systems with matched uncertainties. The conditions for the existence of a static output feedback controller are given and a parameterization of the available design freedom is proposed. An explicit procedure shows how a Lyapunov matrix, which satisfies both the discrete Riccati inequality and a structural constraint, is obtained. The introduction of a compensator is considered in cases where static output feedback min-max controllers cannot be synthesized. A dynamic output feedback min-max scheme is proposed which is applicable for a class of uncertain systems with matched uncertainty under mild conditions. Again, an explicit parameterization of the design freedom is given.