A necessary and sufficient LMI condition for stability of 2D mixed continuous-discrete-time systems

WeA10 Regular Session: Linear Systems I, Paper WeA10.6This paper addresses the problem of establishing stability of 2D mixed continuous-discrete-time systems. Traditional stability analysis for 2D systems gives a sufficient condition based on 2D version of a Lyapunov equation. Here, a linear matrix inequality (LMI) condition is proposed that extends these results by introducing complex Lyapunov functions depending polynomially on a parameter and by exploiting the Gram matrix method. It is shown that this condition is sufficient for 2D exponential stability for any chosen degree of the Lyapunov function candidate, and it is also shown that this condition is also necessary for a sufficiently large degree. Moreover, an a priori bound on the degree required for achieving necessity is given. Some numerical examples illustrate the proposed methodology.published_or_final_versio

Mean winds of the mesosphere and lower thermosphere at 52° N in the period 1988?2000

International audienceA meteor radar in the UK (near 52° N) has been used to measure the mean winds of the mesosphere/lower-thermosphere (MLT) region over the period 1988?2000. The seasonal course and interannual variability is characterised and comparisons are made with a number of models. Annual mean wind trends were found to be + 0.37 ms-1 yr-1 for the zonal component and + 0.157 ms-1 yr-1 for the meridional component. Seasonal means revealed significant trends in the case of meridional winds in spring ( + 0.38 ms-1 yr-1) and autumn ( + 0.29 ms-1 yr-1), and zonal winds in summer ( + 0.48 ms-1 yr-1) and autumn ( + 0.38 ms-1 yr-1). Significant correlation coefficients, R, between the sunspot number and seasonal mean wind are found in four instances. In the case of the summer zonal winds, R = + 0.732; for the winter meridional winds, R = - 0.677; for the winter zonal winds, R = - 0.472; and for the autumn zonal winds R = + 0.508

Avalanches and the Renormalization Group for Pinned Charge-Density Waves

The critical behavior of charge-density waves (CDWs) in the pinned phase is studied for applied fields increasing toward the threshold field, using recently developed renormalization group techniques and simulations of automaton models. Despite the existence of many metastable states in the pinned state of the CDW, the renormalization group treatment can be used successfully to find the divergences in the polarization and the correlation length, and, to first order in an $\epsilon = 4-d$ expansion, the diverging time scale. The automaton models studied are a charge-density wave model and a ``sandpile'' model with periodic boundary conditions; these models are found to have the same critical behavior, associated with diverging avalanche sizes. The numerical results for the polarization and the diverging length and time scales in dimensions $d=2,3$ are in agreement with the analytical treatment. These results clarify the connections between the behaviour above and below threshold: the characteristic correlation lengths on both sides of the transition diverge with different exponents. The scaling of the distribution of avalanches on the approach to threshold is found to be different for automaton and continuous-variable models.Comment: 29 pages, 11 postscript figures included, REVTEX v3.0 (dvi and PS files also available by anonymous ftp from external.nj.nec.com in directory /pub/alan/cdwfigs

Ground-State Roughness of the Disordered Substrate and Flux Line in d=2

We apply optimization algorithms to the problem of finding ground states for crystalline surfaces and flux lines arrays in presence of disorder. The algorithms provide ground states in polynomial time, which provides for a more precise study of the interface widths than from Monte Carlo simulations at finite temperature. Using $d=2$ systems up to size $420^2$, with a minimum of $2 \times 10^3$ realizations at each size, we find very strong evidence for a $\ln^2(L)$ super-rough state at low temperatures.Comment: 10 pages, 3 PS figures, to appear in PR

Statistical Topography of Glassy Interfaces

Statistical topography of two-dimensional interfaces in the presence of quenched disorder is studied utilizing combinatorial optimization algorithms. Finite-size scaling is used to measure geometrical exponents associated with contour loops and fully packed loops. We find that contour-loop exponents depend on the type of disorder (periodic ``vs'' non-periodic) and they satisfy scaling relations characteristic of self-affine rough surfaces. Fully packed loops on the other hand are unaffected by disorder with geometrical exponents that take on their pure values.Comment: 4 pages, REVTEX, 4 figures included. Further information can be obtained from [email protected]

Monte Carlo Dynamics of driven Flux Lines in Disordered Media

We show that the common local Monte Carlo rules used to simulate the motion of driven flux lines in disordered media cannot capture the interplay between elasticity and disorder which lies at the heart of these systems. We therefore discuss a class of generalized Monte Carlo algorithms where an arbitrary number of line elements may move at the same time. We prove that all these dynamical rules have the same value of the critical force and possess phase spaces made up of a single ergodic component. A variant Monte Carlo algorithm allows to compute the critical force of a sample in a single pass through the system. We establish dynamical scaling properties and obtain precise values for the critical force, which is finite even for an unbounded distribution of the disorder. Extensions to higher dimensions are outlined.Comment: 4 pages, 3 figure

Energetics and geometry of excitations in random systems

Methods for studying droplets in models with quenched disorder are critically examined. Low energy excitations in two dimensional models are investigated by finding minimal energy interior excitations and by computing the effect of bulk perturbations. The numerical data support the assumptions of compact droplets and a single exponent for droplet energy scaling. Analytic calculations show how strong corrections to power laws can result when samples and droplets are averaged over. Such corrections can explain apparent discrepancies in several previous numerical results for spin glasses.Comment: 4 pages, eps files include

Computational Complexity of Determining the Barriers to Interface Motion in Random Systems

The low-temperature driven or thermally activated motion of several condensed matter systems is often modeled by the dynamics of interfaces (co-dimension-1 elastic manifolds) subject to a random potential. Two characteristic quantitative features of the energy landscape of such a many-degree-of-freedom system are the ground-state energy and the magnitude of the energy barriers between given configurations. While the numerical determination of the former can be accomplished in time polynomial in the system size, it is shown here that the problem of determining the latter quantity is NP-complete. Exact computation of barriers is therefore (almost certainly) much more difficult than determining the exact ground states of interfaces.Comment: 8 pages, figures included, to appear in Phys. Rev.