Linear Algebra for Control Theory

1. Front Matter

   Pages i-xvi

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2. Recursive Modeling of Discrete-Time Time Series

   • A. C. Antoulas

   Pages 1-20

3. Pole Placement, Internal Stabilization and Interpolation Conditions for Rational Matrix Functions: A Grassmannian Formulation

   • Joseph A. Ball, Joachim Rosenthal

   Pages 21-29

4. Feedback Stabilizibility over Commutative Rings

   • J. W. Brewer, L. C. Klingler, Wiland Schmale

   Pages 31-42

5. Output Feedback in Descriptor Systems

   • Angelika Bunse-Gerstner, Volker Mehrmann, Nancy K. Nichols

   Pages 43-53

6. On Realization Theory for Generalized State-Space Systems over a Commutative Ring

   • J. Daniel Cobb

   Pages 55-60

7. Problems and Results in a Geometric Approach to the Theory of Systems over Rings

   • G. Conte, A. M. Perdon

   Pages 61-74

8. Completion of a Matrix so that the Inverse has Minimum Norm. Application to the Regularization of Descriptor Control Problems

   • L. Elsner, C. He, V. Mehrmann

   Pages 75-86

9. On the Rutishauser’s Approach to Eigenvalue Problems

   • L. Faybusovich

   Pages 87-102

10. The Block form of Linear Systems over Commutative Rings with Applications to Control

    • Edward W. Kamen

    Pages 103-116

11. Diffeomorphisms between Sets of Linear Systems

    • R. Ober, P. A. Fuhrmann

    Pages 117-157

12. Transfer Function Approach to Disturbance Decoupling Problem

    • Marek Rakowski

    Pages 159-176

13. Some Numerical Challenges in Control Theory

    • Paul Van Dooren

    Pages 177-189

14. Erratum

    • Joseph A. Ball, Joachim Rosenthal

    Pages 191-191

During the past decade the interaction between control theory and linear algebra has been ever increasing, giving rise to new results in both areas. As a natural outflow of this research, this book presents information on this interdisciplinary area. The cross-fertilization between control and linear algebra can be found in subfields such as Numerical Linear Algebra, Canonical Forms, Ring-theoretic Methods, Matrix Theory, and Robust Control. This book's editors were challenged to present the latest results in these areas and to find points of common interest. This volume reflects very nicely the interaction: the range of topics seems very wide indeed, but the basic problems and techniques are always closely connected. And the common denominator in all of this is, of course, linear algebra.
This book is suitable for both mathematicians and students.

• Control Theory
• Eigenvalue
• Interpolation
• Matrix
• Matrix Theory
• algebra
• linear algebra

• Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, Urbana, USA

  Paul Dooren

• Department of Mathematics, Ohio State University, Columbus, USA

  Bostwick Wyman

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