The principal reason for using feedback is to reduce the effect of uncertainties in the description of a system which is to be controlled. H loop-shaping is emerging as a powerful but straightforward method of designing robust feedback controllers for complex systems. However, in order to use this, or other modern design techniques, it is first necessary to generate an accurate model of the system (thus appearing to remove the reason for needing feedback in the first place). The -gap metric is an attempt to resolve this paradox - by indicating in what sense a model should be accurate if it is to be useful for feedback design.This book develops in detail the H loop-shaping design method, the -gap metric and the relationship between the two, showing how they can be used together for successful feedback design.
An introduction to H-infinity control; H-infinity loop-shaping; the v-gap metric; more H-infinity loop-shaping; complexity and robustness; design examples; topologies, metrics and operator theory; approximation in the graph topology; the best possible H-infinity robustness results; state-space formulae and proofs; singular value inequalities.