L2 - Gain and Passivity Techniques in Nonlinear Control

With respect to the first edition as Volume 218 in the Lecture Notes in Con trol and Information Sciences series the basic idea of the second edition has remained the same: to provide a compact presentation of some basic ideas in the classical theory of input-output and closed-loop stability, together with a choice of contributions to the recent theory of nonlinear robust and 1foo control and passivity-based control. Nevertheless, some parts of the book have been thoroughly revised and/or expanded, in order to have a more balanced presen tation of the theory and to include some of the new developments which have been taken place since the appearance of the first edition. I soon realized, how ever, that it is not possible to give a broad exposition of the existing literature in this area without affecting the spirit of the book, which is precisely aimed at a compact presentation. So as a result the second edition still reflects very much my personal taste and research interests. I trust that others will write books emphasizing different aspects. Major changes with respect to the first edition are the following: - A new section has been added in Chapter 2 relating L2-gain and passivity via scattering, emphasizing a coordinate-free, geometric, treatment. - The section on stability in Chapter 3 has been thoroughly expanded, also incorporating some recent results presented in [182J.

Klappentext

This book gives a unified treatment of classical input-output stability theory and recent developments in nonlinear robust and passivity-based control. The synthesis between these areas is provided by the theory of dissipative systems. Specifically, the small-gain and passivity theorems and their implications for nonlinear stability and stabilization are discussed from this vantage-ground. The connection between L2-gain and passivity via scattering is detailed.BRThe passivity concepts are enriched by a generalised Hamiltonian formalism, emphasizing the close relations with modeling and control by interconnection. Feedback equivalence to a passive system and resulting stabilization strategies are discussed.BRThe potential of L2-gain techniques in nonlinear control is demonstrated, including a compact treatment of the nonlinear H optimal control problem. This book supplies the reader with a succinct, informative summary of a fundamental and rapidly developing area of nonlinear control theory.

Inhalt

Input-Output Stability.- Small-gain and Passivity of Input-Output Maps.- Dissipative Systems Theory.- Hamiltonian Systems as Passive Systems.- Passivity by Feedback.- Factorizations of Nonlinear Systems.- Nonlinear H Control.- Hamilton-Jacobi Inequalities.- Bibliography.- Index.