Nonlinear \(H_ \infty\) almost disturbance decoupling
type: Item
instance of: scholarly article
title: Nonlinear \(H_ \infty\) almost disturbance decoupling
zbMATH Open document ID: 0822.93028
DOI: 10.1016/0167-6911(94)90001-9
author: Riccardo Marino
author: P. Tomei
author: Witold Respondek
author: Arjan van der Schaft
published in: Systems \& Control Letters
publication date: 1995-10-23T00:00:00Z
full work available at URL: nonlinear-hinfinity-almost-disturbance-decoupling(1d624619-7a89-400e-8129-a5da0ecfdef2).html
review text: Disturbance decoupling is the problem of finding a compensator such that the disturbance has no influence on the output of a given system. By the adjective ``almost'' one denotes the weaker problem of making this influence arbitrarily small. Here, the almost disturbance decoupling problem is related to the \(H_ \infty\) problem. The authors solve the almost disturbance decoupling problem for a class of nonlinear systems. Sufficient conditions are given provided that the control and disturbance enter the system linearly. Formulas for the controller that makes the ratio between the \(L^ 2\)-norm of the output less than a given number times the \(L^ 2\)-norm of the disturbance are given as well. Furthermore, they obtain a necessary condition for the solvability of the almost disturbance decoupling problem with stability. This last problem is a special \(H_ \infty\) problem.
Mathematics Subject Classification ID: 93B36
Mathematics Subject Classification ID: 93C73
Mathematics Subject Classification ID: 93C10
zbMATH DE Number: 683624
zbMATH Keywords: disturbance decoupling
zbMATH Keywords: \(H_ \infty\) problem
zbMATH Keywords: nonlinear
reviewed by: Hans Zwart
MaRDI profile type: Publication
OpenAlex ID: W1995735225
cites work: H/sup infinity / control for nonlinear systems with output feedback
cites work: New results and examples in nonlinear feedback stabilization
cites work: Q3200939
cites work: Disturbance attenuation and H/sub infinity /-control via measurement feedback in nonlinear systems
cites work: Systematic design of adaptive controllers for feedback linearizable systems
cites work: A positive real condition for global stabilization of nonlinear systems
cites work: Q3845518
cites work: Direct approach to almost disturbance and almost input-output decoupling
cites work: Almost disturbance decoupling for single-input single-output nonlinear systems
cites work: Q3996565
cites work: The Singular $H_\infty $ Control Problem with Dynamic Measurement Feedback
cites work: The Quadratic Matrix Inequality in Singular $H_\infty $ Control with State Feedback
cites work: Q3744013
cites work: Sufficient Lyapunov-like conditions for stabilization
cites work: Controlled invariance for hamiltonian systems
cites work: On a state space approach to nonlinear \(H_ \infty\) control
cites work: L/sub 2/-gain analysis of nonlinear systems and nonlinear state-feedback H/sub infinity / control
cites work: Almost invariant subspaces: An approach to high gain feedback design--Part I: Almost controlled invariant subspaces
description: scientific article; zbMATH DE number 683624