A fundamental insight into the robustness of feedback loops was provided by the introduction of the gap metric into systems theory by Zames and El-Sakkary. This led to a systematic approach to optimise the tolerance of uncertainty in this metric and which brought out connections with H-infinity optimisation. This talk will attempt a tutorial overview of these contributions and some developments which followed from them.
Consideration of the follow-on work will include discussions on: (1) geometric approach to robust control in Hilbert space, (2) reworking of the operator theoretic approach to systems theory, (3) topological aspects of systems uncertainty and least conservative metrics (Vinnicombe metric), (4) study of feedback interconnections and the behavioural viewpoint.
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