Robust servo synthesis by minimization of induced l2 and l∞ norms

The problem of designing induced l(2) (i.e. H-infinity) and l(infinity) (i.e. l(1)) output-feedback controllers for linear discrete-time systems with polytopic type uncertainties is considered. The design process involves a state augmentation procedure which results in a nonminimal system the states of which are obtained by delayed inputs and outputs of the plant. Applying state-feedback control to this plant, using an LMI technique, output-feedback controllers are readily obtained which are of order comparable to the one of the plant. These controllers ensure quadratic stability and disturbance attenuation with a prescribed level within the uncertainty polytope. The resulting method is simple and most powerful. It is illustrated via a solution of an ECC'95 benchmark problem that deals with the control of a flexible transmission system with varying loads.