Input-to-state stability of Lur’e systems

An input-to-state stability theory, which subsumes results of circle criterion type, is developed in the context of continuous-time Lur’e systems. The approach developed is inspired by the complexified Aizerman conjecture.</p

High resolution modelling of the North Icelandic Irminger Current (NIIC)

International audienceThe northward inflow of Atlantic Water through Denmark Strait ? the North Icelandic Irminger Current (NIIC) ? is simulated with a numerical model of the North Atlantic and Arctic Ocean. The model uses the technique of adaptive grid refinement which allows a high spatial resolution (1 km horizontal, 10 m vertical) around Iceland. The model is used to assess time and space variability of volume and heat fluxes for the years 1997?2003. Passive tracers are applied to study origin and composition of NIIC water masses. The NIIC originates from two sources: the Irminger Current, flowing as part of the sub-polar gyre in 100?500 m depth along the Reykjanes Ridge and the shallow Icelandic coastal current, flowing eastward on the south Icelandic shelf. The ratio between the deep and shallow branch is 0.7/0.2 Sv. The NIIC continues as a warm and saline branch northward through Denmark Strait where it entrains large amounts of polar water due to the collision with the southward flowing East Greenland Current. Tracer model results indicate that north of Denmark Strait at Hornbanki section (at 21°30' W from 66°40' N to 67°30' N), the NIIC is composed of 43% water masses of Atlantic origin (AW) originating from the south and 57% entrained polar or Arctic water masses (PW) coming from the north. After passing Denmark Strait, the NIIC follows the coast line north-eastward where it influences the hydrography of north Icelandic waters. Volume and heat transport is highly variable and depends strongly on the wind field north of Denmark Strait. Highest monthly mean transport rates at Hornbanki occur in summer (0.75 Sv) when northerly winds are weak, lowest transport is observed in winter (0.35 Sv). Summer heat flux rates (14 TW) can be even three times higher than in winter (4 TW). Strong variability can also be observed on the interannual scale. In particular the winter 2002/2003 showed anomalous high transport and heat flux rates. During the period 1997 to 2003 decreasing northerly winds caused an increase of the NIIC volume and heat transport by 30%, leading to a warming of North Icelandic shelf by around 0.5K

Transfer Functions of Infinite-Dimensional Systems: Positive Realness and Stabilization

We consider a general class of operator-valued irrational positive-real functions with an emphasis on their frequency-domain properties and the relation with stabilization by output feedback. Such functions arise naturally as the transfer functions of numerous infinite-dimensional control systems, including examples specified by PDEs. Our results include characterizations of positive realness in terms of imaginary axis conditions, as well as characterizations in terms of stabilizing output feedback, where both static and dynamic output feedback are considered. In particular, it is shown that stabilizability by all static output feedback operators belonging to a sector can be characterized in terms of a natural positive-real condition and, furthermore, we derive a characterization of positive realness in terms of a mixture of imaginary axis and stabilization conditions. Finally, we introduce concepts of strict and strong positive realness, prove results which relate these notions and analyse the relationship between the strong positive realness property and stabilization by feedback. The theory is illustrated by examples, some arising from controlled and observed partial differential equations