Absolute Stability of Nonlinear Control Systems（英文影印版）（硬皮精装）

　　this volume presents an overview of some recent developments on the absolutestability of nonlinear control systems.
　　 the contents are divided into six chapters as follows: chapter 1 introduces the main tools and the principal results used in this book, such as liapunov functions, kclass functions, dini-derivatives, m-matrices arid the principal theorems on global stability. chapter 2 presents the absolute stability theory of autonomous control systems and the well-known lurie problem. chapter 3 gives some simple algebraic necessary and sufficient conditions for the absolute stability of several special control systems.chapter 4 discusses nonautonomous and discrete control systems. chapter 5 deals with the absolute stability of control systems with m nonlinear control terms. chapter 6 devotes itself to the absolute stability of control systems described by functional differential equations. ..
　　 the book concludes with a useful bibliography.
　　 applied mathematicians, and engineers whose work involves control systems. ...

chapter 1. principal theorems on global stability.
1.1.liapunov functions and k-class functions
1.2.dini-derivatives
1.3.m-matrices
1.4.principal theorems on global stability
1.5.partial global stability
1.6.global stability of sets
1.7.nonautonomous systems
1.8.the systems with separable variables
1.9.autonomous systems with generalized separable variables
1.10.nonautonomous systems with separable variables
1.11.notes
chapter 2. autonomous control systems
2.1.the expression and classification of the problems
2.2.necessary and sufficient conditions for absolute stability
2.3.the s-method and modified s-method
2.4.direct control systems
2.5.indirect control systems
2.6.notes
chapter 3. special control systems

　　As is well-known, a control system always works under a variety of accidental or continued disturbances. Therefore, in designing and analysing the control system, stability is the first thing to be considered. Classic control theory was basically limited to a discussion of linear systems with constant coefficients. The fundamental tools for such studies were the Routh-Hurwitz algebraic criterion and the Nyquist geometric criterion. However, modern control theory mainly deals with nonlinear problems. The stability analysis of nonlinear control systems based on Liapunov stability theory can be traced back to the Russian school of stability. .
　　In 1944, the Russian mathematician Lurie, a specialist in control theory, discussed the stability of an autopilot. The well-known Lurie problem and the concept of absolute stability are presented, which is of universal significance both in theory and practice. Up until the end of the 1950's, the field of absolute stability was monopolized mainly by Russian scholars such as A. I. Lurie, M. A. Aizeman, A.M. Letov and others. At the beginning of the 1960's, some famous American mathematicians such as J.P. LaSalle,S. Lefschetz and R. E. Kalman engaged themself in this field. Meanwhile, the Romanian scholar Popov presented a we!l-known frequency criterion and consequently made a decisive breakthrough in the study of absolute stability.Since then, V.A. Yacubovich, R.E. Kalman, K.R. Meyer and others have devoted themselves to the study of equivalent relations between Lurie's method (integral term and quadratic Liapunov function method) and Popov's frequency method.
　　Although absolute stability has a history of forty years, and hundreds of related articles and quite a number of monographs have been published, these fail to match the requirement of the rapid progress of science and technology.Hitherto, there are more than enough sufficient conditions for absolute stability, but at the same time the number of known necessary and sufficient conditions is rather small and these conditions are mainly limited to the Lurie-type direct control system (i. e. , the elementary condition) and indirect Control system (i. e., the first critical case). The more complicated critical cases are rarely discussed. Among the sufficient conditions obtained, the descriptive results on existence are far more frequent than those of constructive algebraic criteria. No matter whether they are the V-function of the Lurie-type or of the Popov-type, they all contain undetermined matrices or parameters. It is quite difficult to determine these matrices or parameters. Even though the Popov frequency criterion is simple in form, it is rather difficult to put into practice -- it is very complicated to set up, to calculate the inverse matrix and to verify the definite signs of the rational fraction of the undetermined parameters on the infinite interval. One of the main causes of the above mentioned difficulties is that outdated old methods are being employed instead of trying to find some newer methods. For example, some modern tools such as M-matrices, K-class functions and Dini-derivatives, the theories and methods of stability of part of the variables, and the stability of sets, have not yet been applied to the study of absolute stability. ..
　　The main purpose of this book is to introduce the latest results of the author and some others on developments in the study of absolute stability of nonlinear control systems in recent years. The characteristics of these results are: theoretically, to give as many as possible necessary and sufficient conditions of absolute stability of various nonlinear control systems; in applications, to derive simple enough and even constructive algebraic sufficient conditions from these theoretical necessary and sufficient conditions for use in practical work and in methodology. While promoting the extensive use of modern methods and tools such as M-matrices, K-class functions, Diniderivatives, partial stability, and set stability, traditional methods and results will not be neglected.
　　The content of this monograph is the following. Chapter 1 introduces the main tools and the principal results used in this book, such as Liapunov functions, K-class functions, Dini-derivatives, M-matrices, and the principal theorems on global stability. Chapter 2 presents the absolute stability theory of autonomous control systems and the well-known Lurie problem. Chapter 3 gives some simple algebraic necessary and sufficient conditions for absolute stability of several special control systems. Chapter 4 discusses nonautonomous and discrete control systems. Chapter 5 deals with the absolute stability of control systems with m nonlinear control terms. Chapter 6 is devoted to the absolute stability of control systems described by functional differential equations.
　　The author wishes to express his most sincere thanks to Professor Xianrou Sun for reading the manuscript. Thanks are also due to Mrs LO Hong for her help and comment, and to Mr Wu Weihua and Mrs Shu Weihua and others for their careful typing of this manuscript in its final form. Finally, the author is also grateful to Kluwer Academic Publishers and Science Press of China for their help in the preparation of this publication. ...
　　Liao Xiaoxin
　　Wuhan, P. R. China