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Titlebook: Metric Constrained Interpolation, Commutant Lifting and Systems; C. Foias,A. E. Frazho,M. A. Kaashoek Book 1998 Springer Basel AG 1998 Ope

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Parameterization of Intertwining Liftings and its Applicationsset of contractive analytic operator-valued functions. A Redheffer scattering interpolation of this parameterization is given. In the final three sections, state space formulas are given for the Redheffer scattering matrix parameterizing the set of all solutions for the standard left Nevanlinna-Pick
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Applications to Control Systems and scalar output systems, which already gives a flavor of the subject. In the first section a basic feedback control problem is presented. Then for this problem the Youla parameterization of all stabilizing controllers is given (in Section 2). The third section employs some of the interpolation re
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Nonstationary Systems and Point Evaluationvation for the interpolation problems considered in the previous chapter. Special attention is paid to the interpretation of the nonstationary version of point evaluation. It will also be shown how one may convert a time-varying system into an infinite dimensional time-invariant system, which gives
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Reduction Techniques: From Nonstationary to Stationary and Vice Versais based on a transformation (and its inverse) which maps a doubly infinite operator matrix . into a doubly infinite block Laurent matrix . where [F]. is the matrix which one obtains from F if all (operator) entries in F are set to zero except those on the n-th diagonal which are left unchanged.
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Applications to Control Systemssults of the previous chapters to solve a H. and H. error tracking problem. Section four presents a special two block problem as a natural problem in control. The final section presents a brief introduction to multivariable case and introduces the model matching problem. Finally, some numerical examples are also given.
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