H

An H-function with complex parameters is defined by a Mellin-Barnes type integral. Necessary and sufficient conditions under which the integral defining the H-function converges absolutely are established. Some properties, special cases, and an application to integral transforms are given

H-function with complex parameters II: evaluation

Sufficient conditions for computation of the H-functions with complex parameters by means of residues are derived and some examples are given

Asymptotic behavior of a 2D overhead crane with input delays in the boundary control

International audienceThe paper investigates the asymptotic behavior of a 2D overhead crane with input delays in the boundary control. A linear boundary control is proposed. The main feature of such a control lies in the fact that it solely depends on the velocity but under the presence of time-delays. We end-up with a closed-loop system where no displacement term is involved. It is shown that the problem is well-posed in the sense of semigroups theory. LaSalle's invariance principle is invoked in order to establish the asymptotic convergence for the solutions of the system to a stationary position which depends on the initial data. Using a resolvent method, it is proved that the convergence is indeed of polynomial type as long as the delay term satisfies a smallness condition. Lastly, non-convergence results are put forward in the case when such a condition on the delay term is not fulfilled

© Hindawi Publishing Corp. H-FUNCTION WITH COMPLEX PARAMETERS II: EVALUATION

Abstract. Sufficient conditions for computation of the H-functions with complex parameters by means of residues are derived and some examples are given. 2000 Mathematics Subject Classification. Primary 33C60. 1