ABSTRACT
In the decade since the 1979 Allerton Conference, at which the H∞ approach to feedback design was introduced, there has been an explosion of research in H∞ theory and applications. However, the main problem for which H∞ methods were originally proposed, namely the design of feedback controllers in the presence of nonparametric or unstructured uncertainty, has not been solved for practical purposes. Plant (near) nonnuclearity raises many unanswered questions. This chapter addresses one class of such questions arising in the robust disturbance attenuation problem. Approximations which are valid for large uncertainty at high frequencies and which become exact in certain limiting situations are obtained. In the continuation, these approximations are used to derive frequency-domain conditions for optimal robust disturbance attenuation. The chapter presents a special case in which the weightings are scalar multiples of a common Hn×n∞ function.
