L@#2@#-gain analysis of nonlinear systems and nonlinear state feedback Hl control

Arjan van der Schaft

doi:10.1109/9.256331

L@#2@#-gain analysis of nonlinear systems and nonlinear state feedback Hl control

Arjan van der Schaft

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Abstract

Previously obtained results on L2-gain analysis of smooth nonlinear systems are unified and extended using an approach based on Hamilton-Jacobi equations and inequalities, and their relation to invariant manifolds of an associated Hamiltonian vector field. On the basis of these results a nonlinear analog is obtained of the simplest part of a state-space approach to linear H∞ control, namely the state feedback H optimal control problem. Furthermore, the relation with H∞ control of the linearized system is dealt with

Original language	Undefined
Pages (from-to)	770-784
Number of pages	0
Journal	IEEE transactions on automatic control
Volume	37
Issue number	6
DOIs	https://doi.org/10.1109/9.256331
Publication status	Published - 1992

Keywords

IR-29970
METIS-140604

Access to Document

10.1109/9.256331

00256331

Cite this

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title = "L@\#2@\#-gain analysis of nonlinear systems and nonlinear state feedback Hl control",

abstract = "Previously obtained results on L2-gain analysis of smooth nonlinear systems are unified and extended using an approach based on Hamilton-Jacobi equations and inequalities, and their relation to invariant manifolds of an associated Hamiltonian vector field. On the basis of these results a nonlinear analog is obtained of the simplest part of a state-space approach to linear H∞ control, namely the state feedback H optimal control problem. Furthermore, the relation with H∞ control of the linearized system is dealt with",

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AU - van der Schaft, Arjan

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AB - Previously obtained results on L2-gain analysis of smooth nonlinear systems are unified and extended using an approach based on Hamilton-Jacobi equations and inequalities, and their relation to invariant manifolds of an associated Hamiltonian vector field. On the basis of these results a nonlinear analog is obtained of the simplest part of a state-space approach to linear H∞ control, namely the state feedback H optimal control problem. Furthermore, the relation with H∞ control of the linearized system is dealt with

KW - IR-29970

KW - METIS-140604

U2 - 10.1109/9.256331

DO - 10.1109/9.256331

M3 - Article

SN - 0018-9286

VL - 37

SP - 770

EP - 784

JO - IEEE transactions on automatic control

JF - IEEE transactions on automatic control

IS - 6

ER -