控制论的数学问题
2001-12
World Scientific Pub Co Inc
Leonov, Gennady A.
172
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This book 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.
PrefaceChapter 1 The Watt governor and the mathematical theory of stability of motion 1.1 The Watt flyball governor and its modifications 1.2 The Hermite--Mikhailov criterion 1.3 Theorem on stability by the linear approximation 1.4 The Watt governor transient processesChapter 2 Linear electric circuits. Transfer functions and frequency responses of linear blocks 2.1 Description of linear blocks 2.2 Transfer functions and frequency responses of linear blocks Chapter 3 Controllability, observability, stabilization 3.1 Controllability 3.2 Observability 3.3 A special form of the systems with controllable pair (A, b) 3.4 Stabilization. The Nyquist criterion . 3.5 The time-varying stabilization. The Brockett problemChapter 4 Two-dimensional control systems. Phase portraits 4.1 An autopilot and spacecraft orientation system 4.2 A synchronous electric machine control and phase locked loops 4.3 The mathematical theory of populationsChapter 5 Discrete systemsChapter 6 The Aizerman conjecture.The Popov method Bibliography Index
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