Feedback and Stabilization

The introductory Sections 1.2 to 1.5, which the reader is advised to review at this point, motivated the search for feedback laws to control systems. One is led then to the general study of the effect of feedback and more generally to questions of stability for linear and nonlinear systems. This Chapter develops basic facts about linear feedback and related topics in the algebraic theory of control systems including a proof of the Pole-Shifting Theorem described in Chapter 1, as well as an elementary introduction to Lyapunov’s direct method and a proof of a “linearization principle” for stability. Some more “advanced” topics on nonlinear stabilization are also included, mostly to indicate some of the directions of current research.