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Time Invariant Systems

  • C. Foias
  • A. E. Frazho
  • I. Gohberg
  • M. A. Kaashoek
Part of the Operator Theory Advances and Applications book series (OT, volume 100)

Abstract

Throughout this book the interconnection between interpolation and input-output systems in state space form plays a fundamental role. This chapter introduces discrete time-invariant input-output systems, and various notions connected with them. The chapter also serves as a further motivation for the interpolation problems considered earlier. An introduction to the state space theory is given. Moreover, it is shown that point and operator evaluation naturally occur in linear systems. State space techniques are used to compute the norm of certain Hankel operators, which is precisely the error in the corresponding Nehari interpolation problem. State space techniques are also used to give explicit state space formulas to connect the Nevanlinna-Pick problem to the Sarason problem, and the Nudelman problem to the two-sided Sarason problem. The last section presents some aspects of unitary systems that will be used later.

Keywords

Toeplitz Operator Interpolation Problem Hankel Operator Lyapunov Equation Time Invariant System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Basel AG 1998

Authors and Affiliations

  • C. Foias
    • 1
  • A. E. Frazho
    • 2
  • I. Gohberg
    • 3
  • M. A. Kaashoek
    • 4
  1. 1.Department of MathematicsIndiana UniversityBloomingtonUSA
  2. 2.Department of AeronauticsPurdue UniversityWest LafayetteUSA
  3. 3.School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact SciencesTel Aviv UniversityRamat AvivIsrael
  4. 4.Dept. of Mathematics and Computer ScienceVrije Universiteit AmsterdamAmsterdamThe Netherlands

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