Although the text is designed to serve primarily the needs of graduate students, it should also prove valuable to researchers and practitioners for self-study. Many simple examples are included to clarify the material and to encourage readers to actively participate in the learning process. The exercises at the end of each chapter introduce additional supporting concepts and results and encourage readers to gain additional insight by using what was learned. The exercises also encourage readers to comment, interpret, and visualize results (e.g., responses), making use of computer programs to aid in calculations and the generation of graphical results, when appropriate.
Over the past several years, the material has been class-tested in a first-year graduate-level course on linear systems, and its development has been influenced greatly by student feedback. Although there are many ways of using this book in a course, we suggest in the following several useful guidelines. Because any course on linear systems will most likely serve students with different educational experiences from a variety of disciplines and institutions, Chapters 1 and 2 provide necessary background material and develop certain systems fundamentals. Armed with this foundation, we develop essential results on controllability and observability (Chapter 3), on state observers and state feedback (Chapter 4), and on realization of systems (Chapter 5). Chapters 6 and 7 address basic issues concerning stability (Chapter 6) and the representation of systems using polynomial matrices and matrix fractions (Chapter 7). The appendix presents supplementary material (concerning numerical aspects).
How to use this book
At the beginning of each chapter is a detailed description of the chapter’s contents, along with guidelines for readers. This material should be consulted when designing a course based on this book. In the following we give a general overview of the book’s contents, with suggested topics for an introductory, one-semester course in linear systems.From Chapter 1, covering a first course in linear systems should include the following: all the material on systems (Section 1.1); the material on initial-value problems (Sections 1.3 and 1.4); the material on systems of linear first-order ordinary differential equations (Sections 1.11, 1.12, and 1.13); the material on state equation descriptions of continuous-time systems (Section 1.14) and discrete-time systems (Section 1.15); and the material on input-output descriptions of systems (Section 1.16). The mathematical background material in Sections 1.2, 1.5 and Subsections 1.10A to 1.10C is included for review and to establish some needed notation. This material should not require formal class time. In Subsection 1.10D [dealing with existence, continuation, uniqueness, and continuous dependence (on initial conditions and parameters) of solutions of initial-value problems], the coverag
should emphasize the results and their implications rather than the proofs of those results.From Chapter 2, a first course in linear systems should include essentially all the material from the following sections: Section 2.3 (dealing with systems of linear homogeneous and nonhomogeneous first-order ordinary differential equations); Section 2.4 (dealing with systems of linear first-order ordinary differential equations with constant coefficients); and Sections 2.6 and 2.7 (which address the state equation description, the input-output description, and important properties, such with Lynn Cox, the Electrical Engineering Editor. Finally, we are both indebted to many individuals who have shaped our views of systems theory, in particular, Bill Wolovich, Brown University; Boyd Pearson, Rice University; David Mayne, Imperial College of the University of London (England); Sherman Wu, Marquette University; and Wolfgang Hahn, the Technical University of Graz (Austria).
The present printing of Linear Systems, by Birkh¨auser, is in response to many requests by colleagues from the US and around the world, who wanted to start using or continue using the book, which was out of print. Colleagues who had used the book in the classroom or as a reference, as well as our own students, identified several items that needed to be changed. These corrections, which mostly constituted minor typos, have been incorporated in the current printing of the book. This publication of Linear Systems was made possible primarily because of Tom Grasso, Birkhauser’s Computational Sciences and Engineering Editor, whom we would like to thank for his professionalism, encouragement and support.
A new companion book entitled A Linear Systems Primer is forthcoming. The Primer–based on the more complete treatment of the present Linear Systems book– contains 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 without sacrificing rigor.
Panos J. Antsaklis and Anthony N. Michel
Notre Dame, Indiana
August 2005