1,006 research outputs found
New summation inequalities and their applications to discrete-time delay systems
This paper provides new summation inequalities in both single and double
forms to be used in stability analysis of discrete-time systems with
time-varying delays. The potential capability of the newly derived inequalities
is demonstrated by establishing less conservative stability conditions for a
class of linear discrete-time systems with an interval time-varying delay in
the framework of linear matrix inequalities. The effectiveness and least
conservativeness of the derived stability conditions are shown by academic and
practical examples.Comment: 15 pages, 01 figur
Logarithmic Coefficients and Generalized Multifractality of Whole-Plane SLE
We consider the whole-plane SLE conformal map f from the unit disk to the
slit plane, and show that its mixed moments, involving a power p of the
derivative modulus |f'| and a power q of the map |f| itself, have closed forms
along some integrability curves in the (p,q) moment plane, which depend
continuously on the SLE parameter kappa. The generalization of this
integrability property to the m-fold transform of f is also given. We define a
generalized integral means spectrum corresponding to the singular behavior of
the mixed moments above. By inversion, it allows for a unified description of
the unbounded interior and bounded exterior versions of whole-plane SLE, and of
their m-fold generalizations. The average generalized spectrum of whole-plane
SLE takes four possible forms, separated by five phase transition lines in the
moment plane, whereas the average generalized spectrum of the m-fold
whole-plane SLE is directly obtained from a linear map acting in that plane. We
also conjecture the form of the universal generalized integral means spectrum.Comment: 51 pages, 11 figures; considerably revised and extended version.
Sections 4 and 5 fused, Section 7 deleted. Complete proof of Theorem 1.7
given. New Figures 2, 6 and
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