Brockett R.W. Finite Dimensional Linear Systems

John Wiley & Sons, 1970. - 129 pages.This book is based on a one-semester course on dynamical systems given in the Electrical Engineering Department at the Massachusetts Institute of Technology over the last five years. The students have been mostly electrical engineers in their first year of graduate school, but some students in aeronautics, economics, and mathematics have also attended. The topics covered form the core for advanced work in such fields of study as optimal control, estimation, stability, electrical networks, and the control of distributed systems. My objective in this course is to provide a solid foundation for learning about dynamical systems rather than to develop any special expertise.
The particular subject matter chosen for discussion has been picked not only because of the ease with which it can be applied in specific system-theoretic problems, but also because of its importance in engineering analysis in general. Thus in one way or another, many of the standard topics of applied mathematics are touched upon-solubility of linear systems of equations, ordinary differential equations, calculus of variations, and basic ideas of vector analysis. These arc discussed in the context of linear systems. The prerequisites are modest; the book can be read by students who are familiar with basic mathematical notation and who have a little experience with vector-matrix manipulation, provided that they have the patience for some detailed argumentation. To make the book more widely accessible, considerable background material on linear algebra is included in summary form.