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

Multidimensional Systems and Signal Processing - Tập 17 - Trang 119-150 - 2006
Joseph A. Ball1, Gilbert Groenewald2, Tanit Malakorn3
1Department of Mathematics, Virginia Tech, Blacksburg, Virginia
2Department of Mathematics, North West University, Potchefstroom, South Africa
3Department of Electrical and Computer Engineering, Naresuan University, Phitsanulok, Thailand

Tóm tắt

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 μ-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.

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