1,781 research outputs found
Positive trigonometric polynomials for strong stability of difference equations
We follow a polynomial approach to analyse strong stability of linear
difference equations with rationally independent delays. Upon application of
the Hermite stability criterion on the discrete-time homogeneous characteristic
polynomial, assessing strong stability amounts to deciding positive
definiteness of a multivariate trigonometric polynomial matrix. This latter
problem is addressed with a converging hierarchy of linear matrix inequalities
(LMIs). Numerical experiments indicate that certificates of strong stability
can be obtained at a reasonable computational cost for state dimension and
number of delays not exceeding 4 or 5
Stringy Space-Time Foam and High-Energy Cosmic Photons
In this review, I discuss briefly stringent tests of Lorentz-violating
quantum space-time foam models inspired from String/Brane theories, provided by
studies of high energy Photons from intense celestial sources, such as Active
Galactic Nuclei or Gamma Ray Bursts. The theoretical models predict
modifications to the radiation dispersion relations, which are quadratically
suppressed by the string mass scale, and time delays in the arrival times of
photons (assumed to be emitted more or less simultaneously from the source),
which are proportional to the photon energy, so that the more energetic photons
arrive later. Although the astrophysics at the source of these energetic
photons is still not understood, and such non simultaneous arrivals, that have
been observed recently, might well be due to non simultaneous emission as a
result of conventional physics effects, nevertheless, rather surprisingly, the
observed time delays can also fit excellently the stringy space-time foam
scenarios, provided the space-time defect foam is inhomogeneous. The key
features of the model, that allow it to evade a plethora of astrophysical
constraints on Lorentz violation, in sharp contrast to other field-theoretic
Lorentz-violating models of quantum gravity, are: (i) transparency of the foam
to electrons and in general charged matter, (ii) absence of birefringence
effects and (iii) a breakdown of the local effective lagrangian formalism.Comment: 26 pages Latex, 4 figures, uses special macros. Keynote Lecture in
the International Conference "Recent Developments in Gravity" (NEB14),
Ioannina (Greece) June 8-11 201
The Impact of Tax Uncertainty on Irreversible Investment
Tax legislation, fiscal authorities, and tax courts create tax uncertainty by frequent tax reforms and various different interpretations of the tax law. Moreover, investors generate model-specific tax uncertainty by using simplified models that anticipate the actual tax base incorrectly. I analyze the effects of stochastic taxation on investment behavior in a real options model. The investor holds an option to invest in an irreversible project with stochastic cash flows. To cover the effects of both tax base and tax rate uncertainty, the investment’s tax payment is modelled as a stochastic process. Increased tax uncertainty has an ambiguous impact on investment timing. The view that tax uncertainty depresses real investment is rejected. A higher expected tax payment delays investment. A higher tax rate on interest income affects investment timing ambiguously.tax uncertainty, capital budgeting, real options, investment incentives
Design of robust structurally constrained controllers for MIMO plants with time-delays
International audience— The structurally constrained controller design problem for linear time invariant neutral and retarded time-delay systems (TDS) is considered in this paper. The closed-loop system of the plant and structurally constrained controller is modelled by a system of delay differential algebraic equations (DDAEs). A robust controller design approach using the existing spectrum based stabilisation and the H-infinity norm optimisation of DDAEs has been proposed. A MATLAB based tool has been made available to realise this approach. This tool allows the designer to select the sub-controller input-output interactions and fix their orders. The results obtained while stabilising and optimising two TDS using structurally constrained (decentralised and overlapping) controllers have been presented in this paper
Stabilization of time-delay systems with a controlled time-varying delay and applications
International audienceWe study the stability of a linear system with a pointwise, time-varying delay. We assume that the delay varies around a nominal value in a deterministic way and investigate the influence of this variation on stability. More precisely we are interested in characterizing situations where the time-varying delay system is stable, whereas the system with constant delay is unstable. Our approach consists of relating the stability properties of a system with a fast varying point-wise delay with these of a time-invariant system with a distributed delay. Then we can use frequency domain methods to analyze the problem and to derive stability criteria. The results are first illustrated with two theoretical examples. Then, we study a model of a variable speed rotating cutting tool. Based on the developed theory, we thereby provide both a theoretical explanation and a quantitative analysis tool for the beneficial effect of a variation of the machine speed on enhancing stability properties, which was reported in the literature
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