![]() Chapter 2 is devoted to finite-dimensional, time-continuous, time-invariant linear systems. The interest in the linear case is motivated by the theorem of stability for the first approximation. The first chapter introduces the basic notions of stability and the problem of stabilization by means of feedback. "This book is a very clear and comprehensive exposition of several aspects of linear control theory connected with the stabilizability problems. In short, this is not a book on control, but on some mathematics of control. ![]() ![]() Even if we restrict ourselves to stabilization, the book does not provide just recipes, but it fo cuses more on the ideas lying behind the recipes. In engineering practice, control-design is a very complex task in which stability is only one of the re quirements and many aspects and facets of the problem have to be taken into consideration. This book is not intended to be a text book nor a guide for control-designers. We hope that this monograph may illustrate the way in which mathematical theories do influence advanced technol ogy. These topics are important in many applications of stabilization theory. It focuses on stabilization of systems with slow and fast motions, on stabilization procedures that use only poor information about the system (high-gain stabilization and adaptive stabilization), and also on discrete time implementa tion of the stabilizing procedures. The present monograph is based mainly on results obtained by the authors. This prob lem was intensively studied during the last decades and many important results have been obtained. One of the main problems in control theory is the stabilization problem consisting of finding a feedback control law ensuring stability when the linear approximation is considered, the nat ural problem is stabilization of a linear system by linear state feedback or by using a linear dynamic controller. ![]()
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