Interval observers for linear time-invariant systems with disturbances

International audienceIt is shown that, for any time-invariant exponentially stable linear system with additive disturbances, time-varying exponentially stable interval observers can be constructed. The technique of construction relies on the Jordan canonical form that any real matrix admits and on time-varying changes of coordinates for elementary Jordan blocks which lead to cooperative linear systems. The approach is applied to detectable linear systems

Twisted Electromagnetic Modes and Sagnac Ring-Lasers

A new approximation scheme, designed to solve the covariant Maxwell equations inside a rotating hollow slender conducting cavity (modelling a ring-laser), is constructed. It is shown that for well-defined conditions there exist TE and TM modes with respect to the longitudinal axis of the cavity. A twisted mode spectrum is found to depend on the integrated Frenet torsion of the cavity and this in turn may affect the Sagnac beat frequency induced by a non-zero rotation of the cavity. The analysis is motivated by attempts to use ring-lasers to measure terrestrial gravito-magnetism or the Lense-Thirring effect produced by the rotation of the Earth.Comment: LaTeX 31 pages, 3 Figure

The VPOS: a vast polar structure of satellite galaxies, globular clusters and streams around the Milky Way

It has been known for a long time that the satellite galaxies of the Milky Way (MW) show a significant amount of phase-space correlation, they are distributed in a highly inclined Disc of Satellites (DoS). We have extended the previous studies on the DoS by analysing for the first time the orientations of streams of stars and gas, and the distributions of globular clusters within the halo of the MW. It is shown that the spatial distribution of MW globular clusters classified as young halo clusters (YH GC) is very similar to the DoS, while 7 of the 14 analysed streams align with the DoS. The probability to find the observed clustering of streams is only 0.3 per cent when assuming isotropy. The MW thus is surrounded by a vast polar structure (VPOS) of subsystems (satellite galaxies, globular clusters and streams), spreading from Galactocentric distances as small as 10 kpc out to 250 kpc. These findings demonstrate that a near-isotropic infall of cosmological sub-structure components onto the MW is essentially ruled out because a large number of infalling objects would have had to be highly correlated, to a degree not natural for dark matter sub-structures. The majority of satellites, streams and YH GCs had to be formed as a correlated population. This is possible in tidal tails consisting of material expelled from interacting galaxies. We discuss the tidal scenario for the formation of the VPOS, including successes and possible challenges. The potential consequences of the MW satellites being tidal dwarf galaxies are severe. If all the satellite galaxies and YH GCs have been formed in an encounter between the young MW and another gas-rich galaxy about 10-11 Gyr ago, then the MW does not have any luminous dark-matter substructures and the missing satellites problem becomes a catastrophic failure of the standard cosmological model.Comment: 21 pages, 8 figures, 2 tables. Accepted for publication in MNRAS. An animation of Figure 5 can be found at http://youtu.be/nUwxv-WGfH

Twistor Theory and Differential Equations

This is an elementary and self--contained review of twistor theory as a geometric tool for solving non-linear differential equations. Solutions to soliton equations like KdV, Tzitzeica, integrable chiral model, BPS monopole or Sine-Gordon arise from holomorphic vector bundles over T\CP^1. A different framework is provided for the dispersionless analogues of soliton equations, like dispersionless KP or $SU(\infty)$ Toda system in 2+1 dimensions. Their solutions correspond to deformations of (parts of) T\CP^1, and ultimately to Einstein--Weyl curved geometries generalising the flat Minkowski space. A number of exercises is included and the necessary facts about vector bundles over the Riemann sphere are summarised in the Appendix.Comment: 23 Pages, 9 Figure

Regelungstheorie

The workshop “Regelungstheorie” (control theory) covered a broad variety of topics that were either concerned with fundamental mathematical aspects of control or with its strong impact in various fields of engineering

The role of the ventral intraparietal area (VIP/pVIP) in parsing optic flow into visual motion caused by self-motion and visual motion produced by object-motion

Retinal image motion is a composite signal that contains information about two behaviourally significant factors: self-motion and the movement of environmental objects. It is thought that the brain separates the two relevant signals, and although multiple brain regions have been identified that respond selectively to the composite optic flow signal, which brain region(s) perform the parsing process remains unknown. Here, we present original evidence that the putative human ventral intraparietal area (pVIP), a region known to receive optic flow signals as well as independent self-motion signals from other sensory modalities, plays a critical role in the parsing process and acts to isolate object-motion. We localised pVIP using its multisensory response profile, and then tested its relative responses to simulated object-motion and self-motion stimuli; results indicated that responses were much stronger in pVIP to stimuli that specified object-motion. We report two further observations that will be significant for the future direction of research in this area; firstly, activation in pVIP was suppressed by distant stationary objects compared to the absence of objects or closer objects. Secondly, we describe several other brain regions that share with pVIP selectivity for visual object-motion over visual self-motion as well as a multisensory response