Mathematical Problems of Control Theory : An Introduction

by Leonov, Gennady A.

• ISBN13: 9789810246945
• ISBN10: 9810246943
• Format: Hardcover
• Copyright: 2001-09-01
• Publisher: WORLD SCIENTIFIC PUB CO INC

Summary

Shows clearly how the study of concrete control systems has motivated the development of the mathematical tools needed for solving such problems. The Aizerman and Brockett problems are discussed and an introduction to the theory of discrete control systems is given.

Table of Contents

Preface	v
The Watt governor and the mathematical theory of stability of motion	1	(32)
The Watt flyball governor and its modifications	1	(6)
The Hermite---Mikhailov criterion	7	(6)
Theorem on stability by the liner approximation	13	(12)
The Watt governor transient processes	25	(8)
Linear electric circuits. Transfer functions and frequency responses of linear blocks	33	(20)
Description of linear blocks	33	(7)
Transfer functions and frequency responses of linear blocks	40	(13)
Controllability, observability, stabilization	53	(40)
Controllability	53	(9)
Observability	62	(4)
A special form of the systems with controllable pair (A, b)	66	(1)
Stabilization. The Nyquist criterion	67	(5)
The time-varying stabilization. The Brockett problem	72	(21)
Two-dimensional control systems. Phase portraits	93	(40)
An autopilot and spacecraft orientation systems	93	(13)
A synchronous electric machine control and phase locked loops	106	(20)
The mathematical theory of populations	126	(7)
Discrete systems	133	(22)
Motivation	133	(7)
Linear discrete systems	140	(8)
The discrete phase locked loops for array processors	148	(7)
The Aizerman conjecture. The Popov method	155	(12)
Bibliography	167	(4)
Index	171