| Description |
1 online resource (viii, 172 pages) : illustrations. |
| Physical Medium |
polychrome |
| Description |
text file |
| Series |
Series on stability, vibration, and control of systems. Series A ; v. 6
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Series on stability, vibration, and control of systems. Series A ; v. 6.
|
| Bibliography |
Includes bibliographical references (pages 167-169) and index. |
| Contents |
Machine generated contents note: Chapter 1 The Watt governor and the mathematical theory of stability of motion 1 -- 1.1 The Watt flyball governor and its modifications 1 -- 1.2 The Hermite-Mikhailov criterion 7 -- 1.3 Theorem on stability by the linear approximation 13 -- 1.4 The Watt governor transient processes 25 -- Chapter 2 Linear electric circuits. Transfer functions and -- frequency responses of linear blocks 33 -- 2.1 Description of linear blocks 33 -- 2.2 Transfer functions and frequency responses of linear blocks .40 -- Chapter 3 Controllability, observability, stabilization 53 -- 3.1 Controllability53 -- 3.2 Observability62 -- 3.3 A special form of the systems with controllable pair (A, b) 66 -- 3.4 Stabilization. The Nyquist criterion 67 -- 3.5 The time-varying stabilization. The Brockett problem 72 -- Chapter 4 Two-dimensional control systems. Phase portraits 93 -- 4.1 An autopilot and spacecraft orientation system 93 -- 4.2 A synchronous electric machine control and phase locked loops 106 -- 4.3 The mathematical theory of populations 126 -- Chapter 5 Discrete systems 133 -- 5.1 Motivation 133 -- 5.2 Linear discrete systems 140 -- 5.3 The discrete phase locked loops for array processors 148 -- Chapter 6 The Aizerman conjecture. The Popov method 155. |
| Summary |
This work shows clearly how the study of concrete control systems has motivated the development of the mathematical tools needed for solving such problems. In many cases, by using this apparatus, far-reaching generalizations have been made, and its further development will have an important effect on many fields of mathematics. In the book, a way is demonstrated in which the study of the Watt flyball governor has given rise to the theory of stability of motion. The criteria of controllability, observability, and stabilization are stated. Analysis is made of dynamical systems, which describe an autopilot, spacecraft orientation system, controllers of a synchronous electric machine, and phase-locked loops. The Aizerman and Brockett problems are discussed and an introduction to the theory of discrete control systems is given. |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Subject |
Control theory -- Mathematical models.
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Control theory -- Mathematical models. |
| Genre/Form |
Electronic books.
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Electronic books.
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| Other Form: |
Print version: Leonov, Gennadiĭ Alekseevich. Mathematical problems of control theory. Singapore ; River Edge, NJ : World Scientific, ©2001 9810246943 9789810246945 (DLC) 2002278973 (OCoLC)48821685 |
| ISBN |
9789812799852 (electronic book) |
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9812799850 (electronic book) |
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1281951404 |
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9781281951403 |
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