Bounded Real Lemma for Structured Noncommutative Multidimensional Linear Systems and Robust Control

Authors:
Joseph A. Ball;Gilbert Groenewald;Tanit Malakorn
Affiliations:
Department of Mathematics, Virginia Tech, Blacksburg, Virginia 24061-0123;Department of Mathematics, North West University, Potchefstroom, South Africa 2520;Department of Electrical and Computer Engineering, Naresuan University, Phitsanulok, Thailand 65000
Venue:
Multidimensional Systems and Signal Processing
Year:
2006

Citing 4
Cited 1

Robust and optimal control

Robust and optimal control
Robust stability under mixed time-varying, time-invariant and parametric uncertainty

Automatica (Journal of IFAC)
Stability and Robustness of Multivariable Feedback Systems

Stability and Robustness of Multivariable Feedback Systems
Structured Noncommutative Multidimensional Linear Systems

SIAM Journal on Control and Optimization

Noncommutative rational functions, their difference-differential calculus and realizations

Multidimensional Systems and Signal Processing

Quantified Score

Hi-index	0.00

Visualization

Abstract

We obtain a standard Bounded Real Lemma and a strict Bounded Real Lemma for the class of input/state/output linear systems with evolution along a free semigroup recently introduced by the authors. As an application we show the equivalence of this result with a recent result from robust control theory: the structured 驴-singular value of an operator (taken in a certain uniform sense) is equal to its upper bound computed via diagonal scalings in case the structured singular value is taken with respect to the collection of time-varying perturbations given by a linear-fractional model.