Pedersen ideals of tensor products of nonunital C*-algebras

We show that positive elements of a Pedersen ideal of a tensor product can be approximated in a particularly strong sense by sums of tensor products of positive elements. This has a range of applications to the structure of tracial cones and related topics, such as the Cuntz-Pedersen space or the Cuntz semigroup. For example, we determine the cone of lower semicontinuous traces of a tensor product in terms of the traces of the tensor factors, in an arbitrary C*-tensor norm. We show that the positive elements of a Pedersen ideal are sometimes stable under Cuntz equivalence. We generalize a result of Pedersen's by showing that certain classes of completely positive maps take a Pedersen ideal into a Pedersen ideal. We provide theorems that in many cases compute the Cuntz semigroup of a tensor product.Comment: circulated as preprint 2017

Control of distributed delay systems with uncertainties: a generalized Popov theory approach

summary:The paper deals with the generalized Popov theory applied to uncertain systems with distributed time delay. Sufficient conditions for stabilizing this class of delayed systems as well as for $\gamma$-attenuation achievement are given in terms of algebraic properties of a Popov system via a Liapunov–Krasovskii functional. The considered approach is new in the context of distributed linear time-delay systems and gives some interesting interpretations of $H^\infty$ memoryless control problems in terms of Popov triplets and associated objects. The approach is illustrated via numerical examples. Dedicated to Acad. Vlad Ionescu, in memoriam

SUR LA STABILISATION DES SYSTEMES A RETARD (THEORIE ET APPLICATIONS)

GRENOBLE1-BU Sciences (384212103) / SudocSudocFranceF

On closed-loop stability for mechanical systems with input delays

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On closed-loop stability for mechanical systems with input delays

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Models of Air Traffic Merging Techniques: Evaluating Performance of Point Merge

new technique, Point Merge, for merging aircraft without vectoring in terminal areas (TMA), is modelled, and used in fast-time simulatio ns. Four arrival traffic streams are merged for landing on a single runway. A method for designing fast-time models of vectoring and Point Merge is proposed and validated using real-time simulation trajectories. Relative performances of fast-time simulations of t he corresponding models are compared. Interactions with departure traffic are also assess ed. Results show the Point Merge model reduces: mean controller task load (20±1%), the number of instructions to pilots (~30%), and fuel consumption (170±14 kg), compared with vectoring

Towards Performance Requirements for Airborne Spacing- A Sensitivity Analysis of Spacing Accuracy

The objective of this air traffic management study was to analyse the trade-off between time spacing accuracy and corresponding control effort in a potential future application of airborne separation assistance systems (ASAS). The ASAS application airborne spacing sequencing and merging was simulated in fast-time. Lead aircraft speed profiles were generated using complete descent profiles from real-time experiments. For validation purposes, three metrics were derived from real-time experiments: time spacing error (accuracy), frequency of speed adjustments (control activity), and cumulative airspeed variations (control cost). Four experimental parameters were varied: automatic and manual speed control, spacing dead-zone, guidance law dynamics time constant and initial time spacing error. A trade-off between the metrics was found for a sequence of two aircraft by comparing their variation with the experimental parameters. Corresponding ‘minimum’ performance requirements for the metrics are proposed: (i) time spacing error - mean less than 1.5s with 0.5 to 85% of the values between -4 and +4s (automatic mode), and mean less than 2.5s with 0.5 to 85% of the values between -6 and +6s (manual mode), (ii) frequency of speed adjustments - mean less than 1 action per minute (manual mode) and (iii) cumulative airspeed variations - mean less than 10 knots (automatic and manual modes). These requirements form a basis for investigating sequences longer than two aircraft where chain propagation effects may lead to additional constraints

Delay effects and dynamical compensation for time-delay systems

International audienceIn this paper we develop an 'observer-based H∞ controller' for linear time delay systems. The main contribution of the paper is to provide with a closed loop stability analysis for the general case when the system time delay is unknown. Our analyze is based on some model transformation and on a comparison principle. This allows us to get delay dependent stabilizing conditions. We derive conditions which improve (or recover) previous results. Comments on the conservatism of the presented criteria are given. The approach makes use of appropriate Liapunov-Krasovskii functionals and the obtained criteria are expressed in terms of linear matrix inequalities. A numerical example illustrates this method

Sur la stabilisation robuste des systèmes neutres.

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