A rank constrained LMI algorithm for the robust H∞ control of an uncertain system via a stable output feedback controller

The paper presents a numerical algorithm for constructing a stable output feedback controller for the robust HH
^∞
control of an uncertain system. The uncertain systems under consideration contain structured uncertainty described by integral quadratic constraints. The controller is designed to achieve absolute stabilization with a specified level of disturbance attenuation. The main result gives an algorithm for constructing the desired controller in terms of LMIs subject to rank constraints.