L_2 Gain and Passivity Techniques in Nonlinear Control
        (second revised and enlarged edition)

        Arjan van der Schaft, University of Twente, The Netherlands.

        Springer-Verlag, Communications and Control Engineering Series,
        London, November 1999, ISBN 1 85233 073 2.

The first edition of this book appeared in the Lecture Notes on Control and
Information Sciences series, Volume 218 (1996). The 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 generalized 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 L_2-gain techniques
in nonlinear control is demonstrated, including a compact treatment of the
nonlinear H_infinity optimal control problem.

Brief Table of Contents:
1. Input-Output Stability
2. Small-gain and Passivity of Input-Output Maps
3. Dissipative Systems Theory
4. Hamiltonian Systems as Passive Systems
5. Passivity by Feedback
6. Factorizations of Nonlinear Systems
7. Nonlinear H_infinity Control
8. Hamilton-Jacobi Inequalities