# Linear Multivariable Systems

## Wolovich, William A.

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This text was developed over a three year period of time (1971- 1973) from a variety of notes and references used in the presentation of a senior/first year graduate level course in the Division of En- gineering at Brown University titled Linear System Theory. The in- tent of the course was not only to introduce students to the more modern, state-space approach to multivariable control system analysis and design, as opposed to the classical, frequency domain approach, but also to draw analogies between the two approaches whenever and wherever possible. It is therefore felt that the material presented will have broader appeal to practicing engineers than a text devoted exclusively to the state-space approach. It was assumed that students taking the course had also taken, as a prerequisite, an undergraduate course in classical control theory and also were familiar with certain standard linear algebraic notions as well as the theory of ordinary differential equations, although a substantial effort was expended to make the material as self-contained as possible. In particular, Chapter 2 is employed to familiarize the reader with a good deal of the mathematical material employed through- out the remainder of the text. Chapters 3 through 5 were drawn, in part, from a number of contemporary state-space and matrix algebraic references, as well as some recent research of the author, especially those portions which deal with polynomial matrices and the differential operator approach.

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Contenuti:

1 — Introduction.- 2 — Mathematical Preliminaries.- 2.1 Introduction.- 2.2 Linear Vector Spaces.- 2.3 Linear Operators.- 2.4 Scalar Matrices.- 2.5 Polynomial Matrices.- 2.6 Concluding Remarks and References.- Problems — Chapter 2.- 3 — The State Space.- 3.1 Introduction.- 3.2 State Representations.- 3.3 The Determination of eAt.- 3.4 Equivalent Systems.- 3.5 Controllability and Observability.- 3.6 Controllable and Observable Companion Forms.- 3.7 Concluding Remarks and References.- Problems — Chapter 3.- 4 — Frequency Domain Representations.- 4.1 Introduction.- 4.2 The Transfer Matrix.- 4.3 The Structure Theorem.- 4.4 Realization Theory (Time Domain Reduction).- 4.5 Concluding Remarks and References.- Problems — Chapter 4.- 5 — Differential Operator Representations.- 5.1 Introduction.- 5.2 Transfer and Equivalence Relations.- 5.3 Differential Operator Controllability and Observability.- 5.4 Realization Theory (Frequency Domain Reduction).- 5.5 System Invertibility and Functional Reproducibility.- 5.6 Concluding Remarks and References.- Problems — Chapter 5.- 6 — Linear State Variable Feedback.- 6.1 Introduction.- 6.2 Quadratic Optimization.- 6.3 Pole Assignment via the Controllable Companion Form.- 6.4 Asymptotic State Estimation.- 6.5 Concluding Remarks and References.- Problems — Chapter 6.- 7 — Frequency Domain Compensation.- 7.1 Introduction.- 7.2 Frequency Domain Implications of State Feedback.- 7.3 Frequency Domain State Estimation and Feedback.- 7.4 A General Compensation Technique.- 7.5 Concluding Remarks and References.- Problems — Chapter 7.- 8 — Design Objectives.- 8.1 Introduction.- 8.2 Arbitrary Pole Placement.- 8.3 Decoupling.- 8.4 Static Decoupling.- 8.5 Exact Model Matching.- 8.6 Concluding Remarks and References.- Problems — Chapter 8.- References.

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## 1.Linear Multivariable Systems (Paperback)

Editore: Springer-Verlag New York Inc., United States (1974)
ISBN 10: 0387901019 ISBN 13: 9780387901015
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Descrizione libro Springer-Verlag New York Inc., United States, 1974. Paperback. Condizione libro: New. 240 x 170 mm. Language: English . Brand New Book ***** Print on Demand *****.This text was developed over a three year period of time (1971- 1973) from a variety of notes and references used in the presentation of a senior/first year graduate level course in the Division of En- gineering at Brown University titled Linear System Theory. The in- tent of the course was not only to introduce students to the more modern, state-space approach to multivariable control system analysis and design, as opposed to the classical, frequency domain approach, but also to draw analogies between the two approaches whenever and wherever possible. It is therefore felt that the material presented will have broader appeal to practicing engineers than a text devoted exclusively to the state-space approach. It was assumed that students taking the course had also taken, as a prerequisite, an undergraduate course in classical control theory and also were familiar with certain standard linear algebraic notions as well as the theory of ordinary differential equations, although a substantial effort was expended to make the material as self-contained as possible. In particular, Chapter 2 is employed to familiarize the reader with a good deal of the mathematical material employed through- out the remainder of the text. Chapters 3 through 5 were drawn, in part, from a number of contemporary state-space and matrix algebraic references, as well as some recent research of the author, especially those portions which deal with polynomial matrices and the differential operator approach. Softcover reprint of the original 1st ed. 1974. Codice libro della libreria AAV9780387901015

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## 2.Linear Multivariable Systems (Paperback)

Editore: Springer-Verlag New York Inc., United States (1974)
ISBN 10: 0387901019 ISBN 13: 9780387901015
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Descrizione libro Springer-Verlag New York Inc., United States, 1974. Paperback. Condizione libro: New. 240 x 170 mm. Language: English . Brand New Book ***** Print on Demand *****. This text was developed over a three year period of time (1971- 1973) from a variety of notes and references used in the presentation of a senior/first year graduate level course in the Division of En- gineering at Brown University titled Linear System Theory. The in- tent of the course was not only to introduce students to the more modern, state-space approach to multivariable control system analysis and design, as opposed to the classical, frequency domain approach, but also to draw analogies between the two approaches whenever and wherever possible. It is therefore felt that the material presented will have broader appeal to practicing engineers than a text devoted exclusively to the state-space approach. It was assumed that students taking the course had also taken, as a prerequisite, an undergraduate course in classical control theory and also were familiar with certain standard linear algebraic notions as well as the theory of ordinary differential equations, although a substantial effort was expended to make the material as self-contained as possible. In particular, Chapter 2 is employed to familiarize the reader with a good deal of the mathematical material employed through- out the remainder of the text. Chapters 3 through 5 were drawn, in part, from a number of contemporary state-space and matrix algebraic references, as well as some recent research of the author, especially those portions which deal with polynomial matrices and the differential operator approach. Softcover reprint of the original 1st ed. 1974. Codice libro della libreria AAV9780387901015

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## 3.Linear Multivariable Systems (Applied Mathematical Sciences)

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Descrizione libro Springer, 1974. Paperback. Condizione libro: New. book. Codice libro della libreria 0387901019

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## 4.Linear Multivariable Systems.

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Descrizione libro Springer, 2016. Paperback. Condizione libro: New. PRINT ON DEMAND Book; New; Publication Year 2016; Not Signed; Fast Shipping from the UK. No. book. Codice libro della libreria ria9780387901015_lsuk

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## 5.Linear Multivariable Systems

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Descrizione libro Springer-Verlag New York Inc., 1974. PAP. Condizione libro: New. New Book. Shipped from US within 10 to 14 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Codice libro della libreria I2-9780387901015

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## 6.Linear Multivariable Systems

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Descrizione libro Springer, 1974. Paperback. Condizione libro: NEW. 9780387901015 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. Codice libro della libreria HTANDREE0411082

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## 7.Linear Multivariable Systems

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Descrizione libro Springer-Verlag New York Inc., 1974. PAP. Condizione libro: New. New Book. Delivered from our UK warehouse in 3 to 5 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Codice libro della libreria LQ-9780387901015

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## 8.Linear Multivariable Systems (Applied Mathematical Sciences)

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Descrizione libro Springer, 1974. Paperback. Condizione libro: New. Softcover reprint of the origina. This item is printed on demand. Codice libro della libreria DADAX0387901019

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## 9.Linear Multivariable Systems Applied Mathematical Sciences

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Descrizione libro Springer. Paperback. Condizione libro: New. Paperback. 358 pages. Dimensions: 9.4in. x 6.7in. x 0.9in.This text was developed over a three year period of time (1971- 1973) from a variety of notes and references used in the presentation of a seniorfirst year graduate level course in the Division of En- gineering at Brown University titled Linear System Theory. The in- tent of the course was not only to introduce students to the more modern, state-space approach to multivariable control system analysis and design, as opposed to the classical, frequency domain approach, but also to draw analogies between the two approaches whenever and wherever possible. It is therefore felt that the material presented will have broader appeal to practicing engineers than a text devoted exclusively to the state-space approach. It was assumed that students taking the course had also taken, as a prerequisite, an undergraduate course in classical control theory and also were familiar with certain standard linear algebraic notions as well as the theory of ordinary differential equations, although a substantial effort was expended to make the material as self-contained as possible. In particular, Chapter 2 is employed to familiarize the reader with a good deal of the mathematical material employed through- out the remainder of the text. Chapters 3 through 5 were drawn, in part, from a number of contemporary state-space and matrix algebraic references, as well as some recent research of the author, especially those portions which deal with polynomial matrices and the differential operator approach. This item ships from multiple locations. Your book may arrive from Roseburg,OR, La Vergne,TN. Paperback. Codice libro della libreria 9780387901015

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## 10.Linear Multivariable Systems. (Applied Mathematical Sciences)

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Descrizione libro Springer, 1974. Condizione libro: New. This item is printed on demand for shipment within 3 working days. Codice libro della libreria LP9780387901015

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