This volume is a collection of chapters covering recent advances in stochastic optimal control theory and algebraic systems theory. The book will be a useful reference for researchers and graduate students in systems and control, algebraic systems theory, and applied mathematics. Requiring only knowledge of undergraduate-level control and systems theory, the work may be used as a supplementary textbook in a graduate course on optimal control or algebraic systems theory.

Based on a streamlined presentation of the authors' successful work Linear Systems, this textbook provides an introduction to systems theory with an emphasis on control. Initial chapters present necessary mathematical background material for a fundamental understanding of the dynamical behavior of systems. Each chapter includes helpful chapter descriptions and guidelines for the reader, as well as summaries, notes, references, and exercises at the end. The emphasis throughout is on time-invariant systems, both continuous- and discrete-time.

"This is an intermediate level text, with exercises, whose avowed purpose is to provide the science and engineering graduate student with an appropriate modern mathematical (analysis and algebra) background in a succinct, but nontrivial, manner.... [T]he book is quite thorough and can serve as a text, for self-study, or as a reference." a "Mathematical Reviews

Written for graduate and advanced undergraduate students in engineering and science, this classic book focuses primarily on set theory, algebra, and analysis. Useful as a course textbook, for self-study, or as a reference, the work is intended to:

* provide readers with appropriate mathematical background for graduate study in engineering or science;

* allow students in engineering or science to become familiar with a great deal of pertinent mathematics in a rapid and efficient manner without sacrificing rigor;

* give readers a unified overview of applicable mathematics, enabling them to choose additional, advanced topical courses in mathematics more intelligently.

Whereas these objectives for writing this book were certainly pertinent over twenty years ago when the work was first published, they are even more compelling now. Todaya (TM)s graduate students in engineering or science are expected to be more knowledgeable and sophisticated in mathematics than students in the past. Moreover, todaya (TM)s graduate students in engineering or science are expected to be familiar with a great deal of ancillary material (primarily in the computer science area), acquired in courses that did not even exist a couple of decades ago.

The book is divided into three parts: set theory (Chapter 1), algebra (Chapters 2a "4), andanalysis (Chapters 5a "7). The first two chapters deal with the fundamental concepts of sets, functions, relations and equivalence relations, and algebraic structures. Chapters 3 and 4 cover vector spaces and linear transformations, and finite-dimensional vector spaces and matrices. The last three chapters investigate metric spaces, normed and inner product spaces, and linear operators. Because of its flexible structure, Algebra and Analysis for Engineers and Scientists may be used either in a one- or two-semester course by deleting appropriate sections, taking into account the studentsa (TM) backgrounds and interests.

A generous number of exercises have been integrated into the text, and a section of references and notes is provided at the end of each chapter. Applications of algebra and analysis having a broad appeal are also featured, including topics dealing with ordinary differential equations, integral equations, applications of the contraction mapping principle, minimization of functionals, an example from optimal control, and estimation of random variables.

Supplementary material for students and instructors is available at http: //Michel.Herget.net.

"There are three words that characterize this work: thoroughness, completeness and clarity. The authors are congratulated for taking the time to write an excellent linear systems textbook! a ]The authors have used their mastery of the subject to produce a textbook that very effectively presents the theory of linear systems as it has evolved over the last thirty years. The result is a comprehensive, complete and clear exposition that serves as an excellent foundation for more advanced topics in system theory and control." a "IEEE Transactions on Automatic Control

"In assessing the present book as a potential textbook for our first graduate linear systems course, I find...[that] Antsaklis and Michel have contributed an expertly written and high quality textbook to the field and are to be congratulateda ]. Because of its mathematical sophistication and completeness the present book is highly recommended for use, both as a textbook as well as a reference." a "Automatica

Linear systems theory plays a broad and fundamental role in electrical, mechanical, chemical and aerospace engineering, communications, and signal processing. A thorough introduction to systems theory with emphasis on control is presented in this self-contained textbook.

The book examines the fundamental properties that govern the behavior of systems by developing their mathematical descriptions. Linear time-invariant, time-varying, continuous-time, and discrete-time systems are covered. Rigorous development of classic and contemporary topics in linear systems, as well as extensive coverage of stability and polynomial matrix/fractional representation, provide the necessary foundation for further study of systemsand control.

Linear Systems is written as a textbook for a challenging one-semester graduate course; a solutions manual is available to instructors upon adoption of the text. The booka (TM)s flexible coverage and self-contained presentation also make it an excellent reference guide or self-study manual.

*******

For a treatment of linear systems that focuses primarily on the time-invariant case using streamlined presentation of the material with less formal and more intuitive proofs, see the authorsa (TM) companion book entitled A Linear Systems Primer.

This three-part monograph addresses topics in the areas of control systems, signal processing and neural networks. Procedures and results are determined which constitute the first successful synthesis procedure for associative memories by means of artificial neural networks with arbitrarily pre-specified full or partial interconnecting structure and with or without symmetry constraints for the connection matrix.