Proceedings Article10.1109/ACC.1997.609642
Robust performance and structured singular value computation by quantifier elimination
Bassam Bamieh
- 04 Jun 1997
- Vol. 6, pp 3972-3973
TL;DR: It is shown how one can use quantifier elimination techniques to provide a test for whether the H/sup /spl infin// norm is less than one.
read more
Abstract: We consider the problem of computing the robust performance norm in H/sup /spl infin// or equivalently, the complex structured singular value. This problem is equivalent to that of computing the H/sup /spl infin// norm of a function of several complex variables. We show how one can use quantifier elimination techniques to provide a test for whether the H/sup /spl infin// norm is less than one. These techniques can be viewed as a generalization of the use of Sturm's theorem to compute H/sup /spl infin// norms in the one variable case.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
References
The complex structured singular value
Andrew Packard,John Doyle +1 more
TL;DR: A tutorial introduction to the complex structured singular value (μ) is presented, with an emphasis on the mathematical aspects of μ.
1.5K
A bisection method for computing the H ∞ norm of a transfer matrix and related problems
TL;DR: The bisection method is far more efficient than algorithms which involve a search over frequencies, and the usual problems associated with such methods (such as determining how fine the search should be) do not arise.
489
On robust stability with structured time-invariant perturbations
Bassam Bamieh,Mohammed Dahleh +1 more
- 16 Dec 1992
TL;DR: In this article, the authors considered the robust stability for uncertain systems described in terms of multiple scalar structured time-invariant perturbations, which are norm bounded, and the role of the type of perturbation norm plays in the robustness conditions.
9
A necessary and sufficient condition for robust BIBO stability
Munther A. Dahleh,Yoshito Ohta +1 more
TL;DR: In this article, the necessary and sufficient conditions for robustly stabilizing a class of plants characterized by a known linear shift invariant plant with additive perturbations of the form of possibly nonlinear, time varying l ∞ -stable operators were obtained.
On robust stability with structured time-variant perturbations
Bassam Bamieh,Mohammed Dahleh +1 more
TL;DR: In this paper, the authors considered the problem of robust stability for uncertain systems described in terms of multiple scalar structured time-invariant perturbations, which are norm-bounded.