Control and Cybernetics Linear Systems

There exist many good books on linear systems. I wish to mention here only some of them: L. Among these volumes the book by P.J. Antsaklis and A.M. Michel occupies a special place. It is an interesting and original introduction to modern control systems theory. It contains also many interesting problems from advanced systems theory. According to the authors the primary aim of the book is the following: " The primary aim of this text is to provide an understanding of (.. .) fundamentals by emphasizing mathematical descriptions of systems and their properties. Our goal was to clearly present the fundamental concepts of system theory in a self-contained text ". The goal was reached and performed by the authors in an excellent way. The book consist of a preface, seven chapters and an appendix. Chapter 1 is devoted to mathematical descriptions of linear continuous-time and discrete-time finite-dimensional systems. The chapter starts with preliminaries from the calculus, analysis and linear algebra. Next, the initial-value problems, determined by systems of first-order nonlinear ordinary differential equations are introduced. Conditions for the existence and uniqueness of solutions are established. The linearization of nonlinear systems, the solutions of linear state equations, the method of successive approximation, the response of a linear system to an input, given initial states, are discussed. The internal and external behavior of a system input-output descriptions of linear systems, the convolution integral for continuous-time system and the convolution sum for discrete-time systems are also presented. In Chapter 2 the response of linear system is addressed. First, some mathematical background from linear algebra and matrix theory are given. Linear subspaces of vector spaces, linear independence of a set of vectors, bases of vectors spaces, linear transformations defined on vectors spaces, the representations