Arjan van der Schaft

(Author)

L2-Gain and Passivity Techniques in Nonlinear Control (2017)Hardcover - 2017, 15 December 2016

L2-Gain and Passivity Techniques in Nonlinear Control (2017)
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Part of Series
Communications and Control Engineering
Part of Series
Communications and Control Engineering (Hardcover)
Print Length
321 pages
Language
English
Publisher
Springer
Date Published
15 Dec 2016
ISBN-10
3319499912
ISBN-13
9783319499918

Description

This standard text gives a unified treatment of passivity and L2-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 L2-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 L2-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 L2-gain techniques in 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.

- L2-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.

Product Details

Author:
Arjan van der Schaft
Book Edition:
2017
Book Format:
Hardcover
Country of Origin:
NL
Date Published:
15 December 2016
Dimensions:
23.39 x 15.6 x 2.06 cm
ISBN-10:
3319499912
ISBN-13:
9783319499918
Language:
English
Location:
Cham
Pages:
321
Publisher:
Weight:
653.17 gm

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