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.

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A. J. van der Schaft

Springer London : Imprint : Springer

Springer London Ltd

Springer Nature

Communications and control engineering, London, ©2000

United Kingdom and Ireland, United Kingdom

Springer Nature, London, 2012

2, 20121206

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sm43274335

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With respect to the first edition as Volume 218 in the Lecture Notes in ConƯ 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 presenƯ 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, howƯ 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

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. The 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. The 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.

Front Matter....Pages i-xii
Input-Output Stability....Pages 1-9
Small-gain and Passivity of Input-Output Maps....Pages 11-29
Dissipative Systems Theory....Pages 31-61
Hamiltonian Systems as Passive Systems....Pages 63-123
Passivity by Feedback....Pages 125-136
Factorizations of Nonlinear Systems....Pages 137-161
Nonlinear H ∞ Control....Pages 163-192
Hamilton-Jacobi Inequalities....Pages 193-227
Back Matter....Pages 229-248

2013-08-01