Ebook: Linear Algebra for Control Theory

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.

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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.

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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.
Content:
Front Matter....Pages i-xvi
Recursive Modeling of Discrete-Time Time Series....Pages 1-20
Pole Placement, Internal Stabilization and Interpolation Conditions for Rational Matrix Functions: A Grassmannian Formulation....Pages 21-29
Feedback Stabilizibility over Commutative Rings....Pages 31-42
Output Feedback in Descriptor Systems....Pages 43-53
On Realization Theory for Generalized State-Space Systems over a Commutative Ring....Pages 55-60
Problems and Results in a Geometric Approach to the Theory of Systems over Rings....Pages 61-74
Completion of a Matrix so that the Inverse has Minimum Norm. Application to the Regularization of Descriptor Control Problems....Pages 75-86
On the Rutishauser’s Approach to Eigenvalue Problems....Pages 87-102
The Block form of Linear Systems over Commutative Rings with Applications to Control....Pages 103-116
Diffeomorphisms between Sets of Linear Systems....Pages 117-157
Transfer Function Approach to Disturbance Decoupling Problem....Pages 159-176
Some Numerical Challenges in Control Theory....Pages 177-189
Erratum....Pages 191-191

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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.
Content:
Front Matter....Pages i-xvi
Recursive Modeling of Discrete-Time Time Series....Pages 1-20
Pole Placement, Internal Stabilization and Interpolation Conditions for Rational Matrix Functions: A Grassmannian Formulation....Pages 21-29
Feedback Stabilizibility over Commutative Rings....Pages 31-42
Output Feedback in Descriptor Systems....Pages 43-53
On Realization Theory for Generalized State-Space Systems over a Commutative Ring....Pages 55-60
Problems and Results in a Geometric Approach to the Theory of Systems over Rings....Pages 61-74
Completion of a Matrix so that the Inverse has Minimum Norm. Application to the Regularization of Descriptor Control Problems....Pages 75-86
On the Rutishauser’s Approach to Eigenvalue Problems....Pages 87-102
The Block form of Linear Systems over Commutative Rings with Applications to Control....Pages 103-116
Diffeomorphisms between Sets of Linear Systems....Pages 117-157
Transfer Function Approach to Disturbance Decoupling Problem....Pages 159-176
Some Numerical Challenges in Control Theory....Pages 177-189
Erratum....Pages 191-191
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