ROBUST DISTURBANCE REJECTION IN L1 OPTIMAL-CONTROL SYSTEMS

Given a class of plants formed by perturbing a nominal discrete-time linear shift-invariant plant with norm bounded unstructured perturbation, the problem of finding a single compensator that will stabilize all plants in this class and at the same time minimize the worst case norm of a certain performance measure is addressed. Assuming the performance measure of interest is the sensitivity function, first an expression for the supremum, over all plants in this class, of such a measure is derived for a system with a robustly stabilizing compensator. This is achieved by first showing that the proposed expression is an upper bound for the worst case sensitivity norm, and then by constructing a plant in the allowable class that will achieve this upper bound. Combined with already known necessary and sufficient conditions for robust stability, the derived expression provides an effective way of combining both robust stability and performance in one, easy to compute, measure. Secondly, a scheme for finding a controller that minimizes the worst case norm of the sensitivity function while achieving robust stability, is provided. This makes possible the incorporation of stability and performance robustness requirements in one design procedure. © 1990.