U-Pb SHRIMP zircon dating of high-grade rocks from the Upper Allochthonous Terrane of Bragança and Morais Massifs (NE Portugal); geodynamic consequences

Bragança and Morais Massifs are part of the mega-klippen ensemble of NW Iberia, comprising a tectonic pile of four allochthonous units stacked above the Central-Iberian Zone autochthon. On top of this pile, the Upper Allochthonous Terrane (UAT) includes different high-grade metamorphic series whose age and geodynamic meaning are controversial. Mafic granulites provided U–Pb zircon ages at 399±7 Ma, dating the Variscan emplacement of UAT. In contrast,U–Pb zircon ages of ky- and hb-eclogites, felsic/intermediate HP/HT-granulites and orthogneisses (ca. 500–480 Ma) are identical to those of gabbros (488 ± 10 Ma) and Grt-pyroxenites (495 ± 8 Ma) belonging to a mafic/ultramafic igneous suite that records upper mantle melting and mafic magma crustal underplating at these times. Gabbros intrude the high-grade units of UAT and did not underwent the HP metamorphic event experienced by eclogites and granulites. These features and the zircon dates resemblance among different lithologies, suggest that extensive age resetting of older events may have been correlative with the igneous suite emplacement/crystallisation. Accordingly, reconciliation of structural, petrological and geochronological evidence implies that the development and early deformation of UAT high-grade rocks should be ascribed to an orogenic cycle prior to ≈500 Ma. Undisputable dating of this cycle is impossible, but the sporadic vestiges of Cadomian ages cannot be disregarded. The ca. 500–480 Ma time-window harmonises well with the Lower Palaeozoic continental rifting that trace the VariscanWilson Cycle onset and the Rheic Ocean opening. Subsequent preservation of the high heat-flowregime, possibly related to the Palaeotethys back-arc basin development (ca. 450–420 Ma), would explain the 461 ± 10 Ma age yielded by some zircon domains in felsic granulites, conceivably reflecting zircon dissolution/ recrystallisation till Ordovician times, long before the Variscan paroxysm (ca. 400–390 Ma). This geodynamic scenario suggests also that UAT should have been part of Armorica before its emplacement on top of Iberia after Palaeotethys closure.

Discrete-time positive periodic systems with state and control constraints

The aim of this paper is to provide an efficient control design technique for discrete-time positive periodic systems. In particular, stability, positivity and periodic invariance of such systems are studied. Moreover, the concept of periodic invariance with respect to a collection of boxes is introduced and investigated with connection to stability. It is shown how such concept can be used for deriving a stabilizing state-feedback control that maintains the positivity of the closed-loop system and respects states and control signals constraints. In addition, all the proposed results can be efficiently solved in terms of linear programming.