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. The material presented is broad enough to give the reader a clear picture of the dynamical behavior of linear systems as well as their advantages and limitations. Fundamental results and topics essential to linear systems theory are emphasized. The emphasis is on time-invariant systems, both continuous- and discrete-time.

Key features and topics:

* Notes, references, exercises, and a summary and highlights section at the end of each chapter.

* Comprehensive index and answers to selected exercises at the end of the book.

* Necessary mathematical background material included in an appendix.

* Helpful guidelines for the reader in the preface.

* Three core chapters guiding the reader to an excellent understanding of the dynamical behavior of systems.

* Detailed coverage of internal and external system descriptions, including state variable, impulse response and transfer function, polynomial matrix, and fractional representations.

* Explanation of stability, controllability, observability, and realizations with an emphasis on fundamental results.

* Detailed discussion of state-feedback, state-estimation, and eigenvalue assignment.

* Emphasis on time-invariant systems, both continuous- and discrete-time. For full coverage of time-variant systems, the reader is encouraged to refer to the companion book Linear Systems, which contains more detailed descriptions and additional material, including all the proofs of the results presented here.

* Solutions manual available to instructors upon adoption of the text.

A Linear Systems Primer is geared towards first-year graduate and senior undergraduate students in a typical one-semester introductory course on systems and control. It may also serve as an excellent reference or self-study guide for electrical, mechanical, chemical, and aerospace engineers, applied mathematicians, and researchers working in control, communications, and signal processing.

Also by the authors: Linear Systems, ISBN 978-0-8176-4434-5.

"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! ...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." —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 congratulated.... Because of its mathematical sophistication and completeness the present book is highly recommended for use, both as a textbook as well as a reference." —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 systems and 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 book’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 authors’ companion book entitled A Linear Systems Primer.

Increasing complexity in engineering projects raises difficult challenges in industry and requires effective tools for correct-by-construction design or design verification. This book addresses the design of such tools for correct-by-construction synthesis of supervisors for systems and specifications represented in the discrete-event framework. The approach employed uses Petri nets as discrete-event models and structural methods for the synthesis of supervisors, and may lead to significant computational benefits.

Highlighting recent progress in the design of supervisors by structural methods, the book represents a novel contribution to the field. One of the main features of the presentation is the demonstration that structural methods can address a variety of supervisor specifications under diverse supervision settings.

Additional features of the text:

* Applications of the methods presented are emphasized by considering various concurrency assumptions as well as types of system uncontrollability and unobservability.

* Treatment of the supervision problem for decentralized settings and hybrid dynamical systems.

* A focus on both theory and practice: formal proofs are provided in a sound mathematical setting to guarantee performance and correctness; at the same time, the authors have worked out the relevant details to ensure the methods are ready to implement in software.

* Many of the presented methods have been realized in software as functions of a MATLAB toolbox, which have been used to solve many of the examples of the book.

The work is self-contained and includes necessary background on Petri nets and supervision. Requiring only basic knowledge of undergraduate-level discrete mathematics, the text is accessible to a broad audience. Researchers and developers from various engineering fields may find effective means to reduce the complexity of design problems in the discrete-event setting. Graduate students may use the work as a self-study reference, and portions of the text may be used in advanced courses on discrete-event systems.

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