Following the recent developments in the field of absolute stability, Prof. Xiaoxin Liao, in conjunction with Prof. Pei Yu, has created a second edition of his seminal work on the subject. Liao begins with an introduction to the Lurie problem and Lurie control system, before moving on to the simple algebraic sufficient conditions for the absolute stability of autonomous and non-autonomous ODE systems, as well as several special classes of Lurie-type systems. The focus of the book then shifts toward the new results and research that have appeared in the decade since the first edition was published. This book is aimed to be used by undergraduates in the areas of applied mathematics, nonlinear control systems, and chaos control and synchronisation, but may also be useful as a reference for researchers and engineers. The book is self-contained, though a basic knowledge of calculus, linear system and matrix theory, and ordinary differential equations is a prerequisite.
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. 1. 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 well-known frequency criterion and consequently ma de a decisive breakthrough in the study of absolute stability.
The main purpose of developing stability theory is to examine dynamic responses of a system to disturbances as the time approaches infinity. It has been and still is the object of intense investigations due to its intrinsic interest and its relevance to all practical systems in engineering, finance, natural science and social science. This monograph provides some state-of-the-art expositions of major advances in fundamental stability theories and methods for dynamic systems of ODE and DDE types and in limit cycle, normal form and Hopf bifurcation control of nonlinear dynamic systems. Presents comprehensive theory and methodology of stability analysis Can be used as textbook for graduate students in applied mathematics, mechanics, control theory, theoretical physics, mathematical biology, information theory, scientific computation Serves as a comprehensive handbook of stability theory for practicing aerospace, control, mechanical, structural, naval and civil engineers
This volume presents an overview of some recent developments on the absolute stability of nonlinear control systems. Chapter 1 introduces the main tools and the principal results used in this book, such as Lyapunov 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 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. For applied mathematicians, and engineers whose work involves control systems.
Following the recent developments in the field of absolute stability, Prof. Xiaoxin Liao, in conjunction with Prof. Pei Yu, has created a second edition of his seminal work on the subject. Liao begins with an introduction to the Lurie problem and Lurie control system, before moving on to the simple algebraic sufficient conditions for the absolute stability of autonomous and non-autonomous ODE systems, as well as several special classes of Lurie-type systems. The focus of the book then shifts toward the new results and research that have appeared in the decade since the first edition was published. This book is aimed to be used by undergraduates in the areas of applied mathematics, nonlinear control systems, and chaos control and synchronisation, but may also be useful as a reference for researchers and engineers. The book is self-contained, though a basic knowledge of calculus, linear system and matrix theory, and ordinary differential equations is a prerequisite.
The main purpose of developing stability theory is to examine dynamic responses of a system to disturbances as the time approaches infinity. It has been and still is the object of intense investigations due to its intrinsic interest and its relevance to all practical systems in engineering, finance, natural science and social science. This monograph provides some state-of-the-art expositions of major advances in fundamental stability theories and methods for dynamic systems of ODE and DDE types and in limit cycle, normal form and Hopf bifurcation control of nonlinear dynamic systems. Presents comprehensive theory and methodology of stability analysis Can be used as textbook for graduate students in applied mathematics, mechanics, control theory, theoretical physics, mathematical biology, information theory, scientific computation Serves as a comprehensive handbook of stability theory for practicing aerospace, control, mechanical, structural, naval and civil engineers
This book discusses key issues in the planning and operation of large-scale integrated energy systems (LSIES). It establishes individual-based models for LSIES and develops multi-objective optimization algorithms and multi-attribute decision making support systems, which are applied to the planning and optimal operation of LSIES. It is a valuable reference work for researchers, students and engineers who are interested in energy systems, operation research and decision theory.
Now revised and updated to incorporate numerous new materials, this is the major source for researching American Christian activity in China, especially that of missions and missionaries. It provides a thorough introduction and guide to primary and secondary sources on Christian enterprises and individuals in China that are preserved in hundreds of libraries, archives, historical societies, headquarters of religious orders, and other repositories in the United States. It includes data from the beginnings of Christianity in China in the early eighth century through 1952, when American missionary activity in China virtually ceased. For this new edition, the institutional base has shifted from the Princeton Theological Seminary (Protestant) to the Ricci Institute for Chinese-Western Cultural Relations at the University of San Francisco (Jesuit), reflecting the ecumenical nature of this monumental undertaking.
This collection offers fresh perspectives on Sino-Western cultural relations, with particular regard to the experience of Christianity in China. The contributors include authorities from China (including Hong Kong and Taiwan), Europe (including Russia and Eastern Europe), and North America.
This volume represents an overview of some recent developments on the absolute stability of nonlinear systems. The contents are divided into six chapters - chapter 1 introduces the main tools and the principal results used in this text, such as Liapunov functions, K-class functions, Dini-derivatives, M-matrices and the principal theorems on global stability.
School Choice in China explores the major characteristics of schooling options in China, highlighting how largely middle-class parents exploit their cultural, economic and social capital for their children's admission into choice schools. It highlights how payments such as choice fees, donations, prize-winning certificates and awards, as well as the use of guanxi, result in Chinese school choice as a parent-driven, bottom-up movement. The author also explores how schools and local governments cash in on the school choice fever in order to obtain significant economic returns, leading to policies that accommodate the needs of mostly middle-class families. He argues that although this system seems to create winners among the parties involved, it exacerbates the educational inequality that already exists in Chinese society. Chapters include: Positional competition for cultural capital Exploitation of social capital Economics of school choice Class reproduction through parental choice This book is not simply a detailed analysis of Chinese school choice practices, but also a study of the competitive middle class search for advantage for their children. As such it will be beneficial to undergraduates, postgraduates, education professionals, policy makers, and anyone with an interest in education, sociology, social policy, and the rise and future of China.
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