Topic
Uniform norm
About: Uniform norm is a research topic. Over the lifetime, 1760 publications have been published within this topic receiving 23519 citations. The topic is also known as: supremum norm & infinity norm.
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01 Dec 1984
TL;DR: In this paper, an error bound for reduced order models obtained from internally balanced realizations is derived, where the error bound is that the infinity norm of the frequency response of the difference between the full and reduced-order models is bounded by twice the sum of the balanced grammian's singular values that correspond to the truncated states of a balanced realization.
Abstract: An error bound for reduced order models obtained from internally balanced realizations is derived. The bound is that the infinity norm of the frequency response of the difference between the full and reduced order models is bounded by twice the sum of the balanced grammian's singular values that correspond to the truncated states of the balanced realization. The importance of a frequency weighted model reduction and the infinity norm for control system applications is discussed. A frequency weighted balanced realization which depends on specified input and output model reduction weightings is defined. Results for an example are compared using the weighted and unweighted balancing model reduction techniques.
731 citations
451 citations
338 citations
TL;DR: In this article, the leading term of this Hilbert function as n -f oo is given in terms of the height of X in the lattice I(L?n) of integral sections in the space J7(Lon) of real sections with supremum norm.
Abstract: p 5~~~~~~~~~~~~~~~~~~u integers is defined to count the volume of the lattice I(L?n) of integral sections in the space J7(Lon) of real sections with supremum norm We want to prove that the leading term of this Hilbert function as n -f oo is given in terms of the height of X in as ? 1 This is known as a theorem of Gillet and Soule [GS2] if X has a regular generic fiber Beside this known result, our proof uses Hironaka's theorem on resolutions of singularities and Minkowski's theorem on successive minima By Hironaka's theorem, we may construct
320 citations
TL;DR: In this paper, the tightest possible bound has been obtained for the absolute magnitude of the Euclidean 2 or infinity norm of the time-domain response of a multioutput system to certain classes of input disturbance.
Abstract: Some norms are derived for convolution and Hankel operators associated with linear, time-invariant systems. In certain cases, these norms are shown to be identical. The tightest possible bound has been obtained for the absolute magnitude of the Euclidean 2 or infinity norm of the time-domain response of a multioutput system to certain classes of input disturbance. >
245 citations