L2-Gain and Passivity Techniques in Nonlinear Control

Arjan van der Schaft

doi:10.1007/3-540-76074-1

L2-Gain and Passivity Techniques in Nonlinear Control

Arjan van der Schaft

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Abstract

The aim of these lecture notes is to provide a synthesis between classical input-output and closed-loop stability theory, in particular the small-gain and passivity theorems, and recent work on nonlinear H( and passivity-based control. The treatment of the theory of dissipative systems is the main aspect of these lecture notes. Fundamentals of passivity techniques are summarised, and it is shown that the passivity properties of different classes of physical systems can be unified within a generalised Hamiltonian framework. Key developments in linear robust control theory are extended to the nonlinear context using L2-gain techniques. An extensive treatment of nonlinear H( control theory is presented, emphasising its main structural features. Since the application of L2-gain techniques relies on solving Hamilton-Jacobi inequalities the structure of their solution sets and conditions for solvability are derived.

Original language	English
Place of Publication	Berlin
Publisher	Springer
Number of pages	168
ISBN (Electronic)	978-3-540-70689-2
ISBN (Print)	978-3-540-76074-0
DOIs	https://doi.org/10.1007/3-540-76074-1
Publication status	Published - 1996

Publication series

Name	Lecture Notes in Control and Information Sciences 218
Publisher	Springer
Volume	218
ISSN (Print)	0170-8643
ISSN (Electronic)	1610-7411

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10.1007/3-540-76074-1

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AB - The aim of these lecture notes is to provide a synthesis between classical input-output and closed-loop stability theory, in particular the small-gain and passivity theorems, and recent work on nonlinear H( and passivity-based control. The treatment of the theory of dissipative systems is the main aspect of these lecture notes. Fundamentals of passivity techniques are summarised, and it is shown that the passivity properties of different classes of physical systems can be unified within a generalised Hamiltonian framework. Key developments in linear robust control theory are extended to the nonlinear context using L2-gain techniques. An extensive treatment of nonlinear H( control theory is presented, emphasising its main structural features. Since the application of L2-gain techniques relies on solving Hamilton-Jacobi inequalities the structure of their solution sets and conditions for solvability are derived.

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L2-Gain and Passivity Techniques in Nonlinear Control

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