Robust Control Theory in Hilbert Space

This book presents an operator theoretic approach to robust control analysisfor linear timevarying systems. It emphasizes the conceptual similarity withthe H co... » 

This book presents an operator theoretic approach to robust control analysisfor linear timevarying systems. It emphasizes the conceptual similarity withthe H control theory for timeinvariant systems and at the same time clarifiesthe major difficulties confronted in the time varying case. The necessaryoperator theory is developed from first principles and the book is as selfcontained as possible. After presenting the necessary results from the theoriesof Toeplitz operators and nest algebras linear systems are defined as inputoutput operators and the relationship between stabilization and the existanceof coprime factorizations is described. Uniform optimal control problems areformulated as modelmatching problems and are reduced to four block problems.Robustness is considered both from the point of view of fractionalrepresentations and the time varying gap metric and the relationship betweenthese types of uncertainties is clarified. The book closes with the solution ofthe orthogonal embedding problem for time varying contractive systems. Thisbook will be useful to both mathematicians interested in the potentialapplications of operator theory in control and control engineers who wish todeal with some of the more mathematically sophisticated extension of theirwork. TOCBasic Hilbert Space Theory. Geometry of Hilbert Space. BasicOperator Theory. Banach Algebras. Exercises. Operator TheoreticPreliminaries. Functional Calculus for Selfadjoint Operators. PolarDecompositions. Weak Convergence in H. Operator Topologies. The Minimum Modulusof an Operator. Exercises. A Distance Formula and Some Consequences. OperatorMatrices. Multiplication Operators and Neharis Theorem. Nest Algebras.Exercises. «