Book reviews

Let us first leaf through the table of contents of this book. Chapter 1 reviews Laplace transforms and basic impulse response and input-output concepts. Chapter 2 uses analog computer simulation as a starting point for the study of realizations and their relationship to input-output behavior. This chapter includes controllability and observability, realizations and the solution of linear time-invariant state equations; it works simultaneously in discrete and continuous time, but is restricted to scalar (singleinput-single-output) systems. Chapter 3 introduces state feedback for pole placement and linear-quadratic design, while Chapter 4 introduces observers and direct transfer function design through polynomial equations; both chapters are also restricted to the scalar case. In Chapter 5, some algebraic ideas are presented, including linear subspaces. Chapter 6, 150 pages long, retraces the steps of Chapter 2, but for the more complex multivariable systems. The matrix fraction description is the basic representation used here; the required background in polynomial matrices is covered, and the input-output and internal (state) descriptions are well related. Chapter 7 does for multivariable systems what Chapter 3 does for the scalar case. The role of eigenvector selection in the state feedback problem is given particular prominence and yields a rather novel approach to the linear-quadratic problem. Chapter 8 is devoted to the polynomial matrix description introduced by Rosenbrock. Chapter 9 presents a few results on linear, time-varying systems, while Chapter 10 sketches developments in other areas of linear systems. There is an appendix with some useful facts from matrix theory.