This standard text gives a unified treatment of passivity and L 2 -gain theory for nonlinear state space systems, preceded by a compact treatment of classical passivity and small-gain theorems for nonlinear input-output maps. The synthesis between passivity and L 2 -gain theory 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 standpoint. The connection between L 2 -gain and passivity via scattering is detailed.

Feedback equivalence to a passive system and resulting stabilization strategies are discussed. The passivity concepts are enriched by a generalised Hamiltonian formalism, emphasising the close relations with physical modeling and control by interconnection, and leading to novel control methodologies going beyond passivity.

The potential of L 2 -gain techniquesin nonlinear control, including a theory of all-pass factorizations of nonlinear systems, and of parametrization of stabilizing controllers, is demonstrated. The nonlinear H-infinity optimal control problem is also treated and the book concludes with a geometric analysis of the solution sets of Hamilton-Jacobi inequalities and their relation with Riccati inequalities for the linearization.

· **** L 2 -Gain and Passivity Techniques in Nonlinear Control (third edition) is thoroughly updated, revised, reorganized and expanded. Among the changes, readers will find:

· **** updated and extended coverage of dissipative systems theory

· **** substantial new material regarding converse passivity theorems and incremental/shifted passivity · **** coverage of recent developments on networks of passive systems with examples

· **** a completely overhauled and succinct introduction to modeling and control of port-Hamiltonian systems, followed by an exposition of port-Hamiltonian formulation of physical network dynamics · updated treatment of all-pass factorization of nonlinear systems

The book provides graduate students and researchers in systems and control with a compact presentation of a fundamental and rapidly developing area of nonlinear control theory, illustrated by a broad range of relevant examples stemming from different application areas.

Enriches understanding of a fundamental and rapidly developing area of nonlinear control theory Explains the small-gain and passivity theorems and their implications for stability and stabilization Expands on earlier editions with new examples of port-Hamiltonian network dynamics and coverage of converse and incremental/shifted passivity Includes supplementary material: sn.pub/extras

Autorentext
Gjerrit Meinsma received his graduate degree in Applied Mathematics from the University of Twente (Enschede, the Netherlands) in 1989. Four years later, at the same university, he obtained his Ph.D. degree. His postdoctoral work was done at the University of Newcastle with the Electrical Engineering Department. In 1997 he returned to the University of Twente where he now holds a position of senior lecturer. His research interests are in mathematical systems and control theory, and mathematics in general. He has written around 75 papers. In the last 10 years he focuses more on teaching. Arjan van der Schaft received his undergraduate and Ph.D. degrees in Mathematics from the University of Groningen, the Netherlands, in 1979 and 1983, respectively. In 1982 he joined the Department of Applied Mathematics, University of Twente, Enschede, where he was appointed as a full professor in Mathematical Systems and Control Theory in 2000. In 2005 he returned to Groningen as a full professor in Mathematics. He is Fellow of the Institute of Electrical and Electronics Engineers (IEEE) and Fellow of the International Federation of Automatic Control (IFAC), and invited semi-plenary speaker at the International Congress of Mathematicians (2006). His research interests include mathematical systems theory, nonlinear control, geometric modeling of multi-physics systems, and hybrid systems. His present focus is on network modeling and control of physical systems and their formulation as port-Hamiltonian systems, and applications in complex engineering systems, power networks, and systems biology.

Inhalt
Chapter 1: Input-Output Stability.- Chapter 2: Small-Gain and Passivity of InputOutput Maps.- Chapter 3: Dissipative Systems Theory.- Chapter 4: Passivity.- Chapter 5: Passivity by Feedback.- Chapter 6: Port-Hamiltonian Systems.- Chapter 7: Port-Hamiltonian Network Dynamics.- Chapter 8: L 2 -Gain and the Small Gain Theorem.- Chapter 9: Factorizations of Nonlinear Systems.- Chapter 10: Nonlinear H-infinity Control.-Chapter 11: Hamilton-Jacobi Inequalities.