Robust servo synthesis by minimization of induced l/2 and l/i∞ norms

The problem of designing induced l
₂
(i.e.
H

_∞
) and l (i.e. lscr
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.