An operator theoretic approach to robust control analysis for
linear time-varying systems, with the emphasis on the conceptual
similarity with the H control theory for time-invariant systems. It
clarifies the major difficulties confronted in the time varying
case and all the necessary operator theory is developed from first
principles, making the book as self-contained as possible. After
presenting the necessary results from the theories of Toeplitz
operators and nest algebras, linear systems are defined as
input-output operators and the relationship between stabilisation
and the existence of co-prime factorisations is described. Uniform
optimal control problems are formulated as model-matching problems
and are reduced to four block problems, while robustness is
considered both from the point of view of fractional
representations and the "time varying gap" metric, as is the
relationship between these types of uncertainties. The book closes
with the solution of the orthogonal embedding problem for
time-varying contractive systems. As such, this book is useful to
both mathematicians and to control engineers.
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