Feedback And Optimal Sensitivity: Model Reference Transformations, Multiplicative Seminorms, And Approximate Inverses

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Authors: George Zames
Published in: IEEE Transactions On Automatic Control
Year: 1981   
DOI: 10.1109/TAC.1981.1102603
Citations: 319
EI: NO
Abstract:
in this paper , the problem of sensitivity , reduction by feedback is formulated as an optimization problem and separated from the problem of stabilization stable feedback schemes obtainable from a given plant are parameterized salient properties of sensitivity reducing schemes are derived , and it is shown that plant uncertainty reduces the ability , of feedback to reduce sensitivity the theory is developed for input output systems in a general setting of banach algebras , and then specialized to a class of multivariable , time invariant systems characterized by matrices of frequency response functions , either with or without zeros in the right half plane the approach is based on the use of a weighted seminorm on the algebra of operators to measure sensitivity , and on the concept of an approximate inverse approximate invertibility , of the plant is shown to be a necessary and sufficient condition for sensitivity reduction an indicator of approximate invertibility , called a measure of singularity , is introduced the measure of singularity of a linear time invariant plant is shown to be determined by the location of its right half plane zeros in the absence of plant uncertainty , the sensitivity , to output disturbances can be reduced to an optimal value approaching the singularity , measure in particular , if there are no right half plane zeros , sensitivity can be made arbitrarily small the feedback schemes used in the optimization of sensitivity resemble the lead lag networks of classical control design some of their properties , and methods of constructing them in special cases are presented
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