Robust stabilizability for linear systems with both parameter variation and unstructured uncertainty

The authors consider the problem of finding a single compensator which stabilizes a plant having both parameter variation and high-frequency unstructured uncertainty. An uncertain system model is proposed to characterize plants containing those two different uncertainties. Closed-loop stability criteria are then proposed for the model. Robust stabilizability for single-input single-output (SISO) systems is studied. A number of assumptions describing the set of admissable SISO plants are imposed. The satisfaction of these assumptions guarantees the existence of a proper stable compensator C(s) achieving robust stabilization. The algorithm used for controller design is recursive in nature and allows the designer to select one compensator coefficient at a time. Also, the minimum order of the desired stabilizer C(s) depends only on the largest relative degree of the nominal plants, which often leads to a lower-order compensator.>