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- Title
A small gain type result with respect to the induced L<sub>∞</sub> norm.
- Authors
Stoica, Adrian-Mihail; Yaesh, Isaac
- Abstract
The aim of this paper is to present a small gain type result with respect to the L1 or induced L∞ norm of stable systems. This norm representing the peak-to-peak gain obtained for magnitude bounded inputs is determined using a method based on invariant ellipsoids. A version of Bounded Real Lemma providing necessary and sufficient conditions of boundedness of this norm is derived. Further, based on the necessary conditions of this result a Small Gain Theorem with respect to the induced L∞ norm is proved.
- Subjects
SMALL-gain theorem (Mathematics); STABILITY theory; MATHEMATICAL bounds; ELLIPSOIDS; INVARIANTS (Mathematics); MATHEMATICAL proofs
- Publication
Mathematics in Engineering, Science & Aerospace (MESA), 2013, Vol 4, Issue 3, p207
- ISSN
2041-3165
- Publication type
Article