design of robust static output feedback for large scale systems the design of static output feedback is of fundamental importance in control theory in this note we propose a new approach to this problem based on linear matrix inequalities a distinguishing feature of the method is its ability to handle large scale problems with additive nonlinearities the resulting control is robust with respect to uncertainties and can incorporate several types of information structure constraints the effectiveness of the proposed strategy is demonstrated by application to a practical large scale system

periodic solutions of some infinite dimensional hamiltonian systems associated with non linear partial difference equations ii this is our second paper devoted to the study of some non linear schrodinger equations with random potential we study the non linear eigenvalue problems corresponding to these equations we exhibit a countable family of eigenfunctions corresponding to simple eigenvalues densely embedded in the band tails contrary to our results in the first paper the results established in the present paper hold for an arbitrary strength of the non linear cubic term in the non linear schrodinger equation

geodesics and commensurability classes of arithmetic hyperbolic 3 manifolds this sharpens 10 where it was shown that the complex length spectrum of m determines its commensurability class suppose m is an arithmetic hyperbolic 3 manifold which is not commensurable to m theorem 1 1 implies ql m 6 ql m though by example 2 1 below it is possible that one of ql m or ql m contains the other by the length formulas recalled in 2 1 and 2 2 each element of ql m ql m is a rational multiple of the logarithm of a real algebraic number as noted by prasad and rapinchuk in 9 the gelfond schneider theorem 1 implies that a ratio of such logarithms is transcendental if it is irrational thus if ql m ql m then is transcendental for all non zero ql m recently prasad and rapinchuk have shown in 9 that if m is an arithmetic hyperbolic manifold of even dimension then ql m and the commensurability class of m determine one another in addition they have shown that this is not always true for arithmetic hyperbolic 5 manifolds however they have announced a proof that for all locally symmetric spaces associated to a specified absolutely simple lie group there are only finitely many commensurability classes of arithmetic lattices giving rise to a given rational length spectrum it is known see 4 pp 415 417 that for closed hyperbolic manifolds the spectrum of the laplace beltrami operator action on l2 m counting multiplicities determines the set of lengths of closed geodesics on m without counting multiplicities hence theorem 1 1 implies

constructive fractional moment criteria for localization in random operators abstract we present a family of finite volume criteria which cover the regime of exponential decay for the fractional moments of green functions of operators with random potentials such decay is a technically convenient characterization of localization for it is known to imply spectral localization absence of level repulsion dynamical localization and a related condition which plays a significant role in the quantization of the hall conductance in two dimensional fermi gases the constructive criteria also preclude fast power law decay of the green functions at mobility edges

a nekhoroshev type theorem for hamiltonian systems with infinitely many degrees of freedom we study the propagation of lattice vibrations in models of disorder ed classical anharmonic crystals using classical perturbation theory with an optimally chosen remainder term i e a nekhoroshev type scheme we are able to show that vibrations corresponding to localized initial conditions do essentially not propagate through the crystal up to times larger than any inverse power of the strength of the anharmonic couplings

a new proof of localization in the anderson tight binding model we give a new proof of exponential localization in the anderson tight binding model which uses many ideas of the frohlich martinelli scoppola and spencer proof but is technically simpler particularly the probabilistic estimates

output feedback negative imaginary synthesis under structural constraints the negative imaginary property is a property that many practical systems exhibit this paper is concerned with the negative imaginary synthesis problem for linear time invariant systems by output feedback control sufficient conditions are developed for the design of static output feedback controllers dynamic output feedback controllers and observer based feedback controllers based on the design conditions a numerical algorithm is suggested to find the desired controllers structural constraints can be imposed on the controllers to reflect the practical system constraints also the separation principle is shown to be valid for the observer based design finally three numerical examples are presented to illustrate the efficiency of the developed theory

localization for a class of one dimensional quasi periodic schrodinger operators we prove for small and satisfying a certain diophantine condition the operator h varepsilon 2 delta frac 1 2 pi cos 2 pi j alpha theta j in mathbb z has pure point spectrum for almost all a similar result is established at low energy for h frac d 2 dx 2 k 2 cos 2 pi x cos 2 pi alpha x theta providedk is sufficiently large

sufficient conditions for finite time stability and stabilization of nonlinear quadratic systems in this paper we deal with the finite time stability problem for quadratic systems such class of systems plays an important role in the modeling of a wide class of nonlinear processes electrical robotic biological etc the main results of the paper consist of two sufficient conditions for finite time stability analysis and finite time stabilization via static state feedback both conditions are given in terms of the feasibility of a convex optimization problem involving linear matrix inequalities a numerical example illustrates the applicability of the proposed technique

absence of diffusion in the anderson tight binding model for large disorder or low energy we prove that the green s function of the anderson tight binding hamiltonian decays exponentially fast at long distances on v with probability 1 we must assume that either the disorder is large or the energy is sufficiently low our proof is based on perturbation theory about an infinite sequence of block hamiltonians and is related to kam methods

bounded sobolev norms for klein gordon equations under non resonant perturbation in this paper we prove anderson localization for the klein gordon operator on the circle x1d54b under non resonant perturbations furthermore using the result we show that the sobolev norms of solutions to the corresponding klein gordon equations remain bounded for all time

constructive proof of localization in the anderson tight binding model we prove that for large disorder or near the band tails the spectrum of the anderson tight binding hamiltonian with diagonal disorder consists exclusively of discrete eigenvalues the corresponding eigenfunctions are exponentially well localized these results hold in arbitrary dimension and with probability one in one dimension we recover the result that all states are localized for arbitrary energies and arbitrarily small disorder our techniques extend to other physical systems which exhibit localization phenomena such as infinite systems of coupled harmonic oscillators or random schrodinger operators in the continuum

localization at large disorder and at extreme energies an elementary derivation the work presents a short proof of localization under the conditions of either strong disorder 0 or extreme energies for a wide class of self adjoint operators with random matrix elements acting inl 2 spaces a prototypical example is the discrete schrodinger operatorh u 0 x v x onz d d 1 withu 0 x a specified background potential and v x generated as random variables the general results apply to operators with replaced by a non local self adjoint operatort whose matrix elements satisfy y t x y s const uniformly inx for somes 1 localization means here that within a specified energy range the spectrum ofh is of the pure point type or equivalently the wave functions do not spread indefinitely under the unitary time evolution generated byh the effect is produced by strong disorder in either the potential or in the off diagonal matrix elementst x y under rapid decay oft x y the corresponding eigenfunctions are also proven to decay exponentially the method is based on resolvent techniques the central technical ideas include the use of low moments of the resolvent kernel i e g e x y s withs small enough 1 to avoid the divergence caused by the distribution s cauchy tails and an effective use of the simple form of the dependence ofg e x y on the individual matrix elements ofh in elucidating the implications of the fundamental equation h e g e x x 0 x x0 this approach simplifies previous derivations of localization results avoiding the small denominator difficulties which have been hitherto encountered in the subject it also yields some new results which include localization under the following sets of conditions i potentials with an inhomogeneous non random partu 0 x ii the bethe lattice iii operators with very slow decay in the off diagonal terms t x y 1 x y d e and iv localization produced by disordered boundary conditions

spectral behavior of quasi periodic potentials spectral properties of schrodinger operators of the typeh v where is the laplacian v a quasiperiodic potential and a coupling constant are developed v is taken to be finite sum of exponentials with generic frequencies for small a strong stability is shown on the other hand examples in the finite diffeence case are given for which a transition in the type of spectrum occurs as is increased

brief paper a note on control of a class of discrete time stochastic systems with distributed delays and nonlinear disturbances this paper is concerned with the state feedback control problem for a class of discrete time stochastic systems involving sector nonlinearities and mixed time delays the mixed time delays comprise both discrete and distributed delays and the sector nonlinearities appear in the system states and all delayed states the distributed time delays in the discrete time domain are first defined and then a special matrix inequality is developed to handle the distributed time delays within an algebraic framework an effective linear matrix inequality lmi approach is proposed to design the state feedback controllers such that for all admissible nonlinearities and time delays the overall closed loop system is asymptotically stable in the mean square sense sufficient conditions are established for the nonlinear stochastic time delay systems to be asymptotically stable in the mean square sense and then the explicit expression of the desired controller gains is derived a numerical example is provided to show the usefulness and effectiveness of the proposed design method

on the problem of dynamical localization in the nonlinear schrodinger equation with a random potential we prove a dynamical localization in the nonlinear schrodinger equation with a random potential for times of the order of o 2 w here is the strength of the nonlinear ity

metal insulator transition for the almost mathieu operator we prove that for diophantine and almost every the almost mathieu operator h n n 1 ni 1 cos 2 n n exhibits localization for 2 and purely absolutely continuous spectrum for 2

analytic solutions of nonlinear elliptic equations on rectangular tori abstract in this paper we consider the nonlinear elliptic equations on rectangular tori using methods in the study of kam theory and anderson localization we prove that these equations admit many analytic solutions

counting and effective rigidity in algebra and geometry the purpose of this article is to produce effective versions of some rigidity results in algebra and geometry on the geometric side we focus on the spectrum of primitive geodesic lengths resp complex lengths for arithmetic hyperbolic 2 manifolds resp 3 manifolds by work of reid this spectrum determines the commensurability class of the 2 manifold resp 3 manifold we establish effective versions of these rigidity results by ensuring that for two incommensurable arithmetic manifolds of bounded volume the length sets resp the complex length sets must disagree for a length that can be explicitly bounded as a function of volume we also prove an effective version of a similar rigidity result established by the second author with reid on a surface analog of the length spectrum for hyperbolic 3 manifolds these effective results have corresponding algebraic analogs involving maximal subfields and quaternion subalgebras of quaternion algebras to prove these effective rigidity results we establish results on the asymptotic behavior of certain algebraic and geometric counting functions which are of independent interest

anderson localization for time quasi periodic random schrodinger and wave equations we prove that at large disorder with large probability and for a corresponding set of diophantine frequencies of large measure anderson localization in d is stable under localized time quasi periodic perturbations by proving that the associated quasi energy operator has pure point spectrum the main tools are the frohlich spencer mechanism for the random component and the bourgain goldstein schlag mechanism for the quasi periodic component this paper paves the way for the construction of time quasi periodic kam type of solutions of non linear random schrodinger equations in bw

large time behavior of the lp norm of schrodinger semigroups abstract letv 0 v c0 rv with v 3 be such that h 1 2 v 0 but for any e 0 1 2 1 e v is not positive we determine the exact rate of divergence of the norm of e th as a map from l to l a number of related problems are discussed

brief paper stability and stabilization of aperiodic sampled data control systems using robust linear matrix inequalities stability analysis of an aperiodic sampled data control system is considered for application to networked and embedded control the stability condition is described in a linear matrix inequality to be satisfied for all possible sampling intervals although this condition is numerically intractable a tractable sufficient condition can be constructed with the mean value theorem special attention is paid to tightness of the sufficient condition for less conservative stability analysis a region dividing technique for the reduction of conservatism and generalization to stabilization are also discussed an example demonstrates the efficacy of the approach

technical communique static output feedback control under information structure constraints an important challenge in the static output feedback control context is to provide an isolated gain matrix possessing a zero nonzero structure mainly in problems presenting information structure constraints although some previous works have contributed some relevant results to this issue a fully satisfactory solution has not yet been achieved up to now in this note by using a linear matrix inequality approach and based on previous results given in the literature we present an efficient methodology which permits us to obtain an isolated static output feedback gain matrix having simultaneously a zero nonzero structure imposed a priori

spectrally similar incommensurable 3 manifolds reid has asked whether hyperbolic manifolds with the same geodesic length spectrum must be commensurable building toward a negative answer to this question we construct examples of hyperbolic 3 manifolds that share an arbitrarily large portion of the length spectrum but are not commensurable more precisely for every n 0 we construct a pair of incommensurable hyperbolic 3 manifolds nn and nn whose volume is approximately n and whose length spectra agree up to length n both nn and nn are built by gluing two standard submanifolds along a complicated pseudo anosov map ensuring that these manifolds have a very thick collar about an essential surface the two gluing maps differ by a hyper elliptic involution along this surface our proof also involves a new commensurability criterion based on pairs of pants

structurally constrained controller synthesis for general proper plants with application to vehicle platooning abstractthis paper considers the problem of synthesizing a static output feedback sof subject to arbitrary information structure constraints in particular the plants can be non strictly proper in such a case the existing methods are hardly applicable except few special cases a general approach that significantly differs from the existing methods is proposed that is able to deal with the most general case with the feature that both finite frequency and full frequency h infinity performance specifications can be addressed in a unified manner sufficient solvability conditions are derived in terms of a set of finite frequency positive real and strictly positive real conditions of linear matrix inequalities lmis form some frequency dependent matrices are introduced into the design with the merit of making the conditions less restrictive several numerical examples are given that demonstrate the efficacy of the proposed approach including applications to vehicle platooning

pure point spectrum of the floquet hamiltonian for the quantum harmonic oscillator under time quasi periodic perturbations we prove that the 1 d quantum harmonic oscillator is stable under spatially localized time quasi periodic perturbations on a set of diophantine frequencies of positive measure this proves a conjecture raised by enss veselic in their 1983 paper ev in the general quasi periodic setting the motivation of the present paper also comes from construction of quasi periodic solutions for the corresponding nonlinear equation

spectrum and continuum eigenfunctions of schrodinger operators we consider schrodinger operators h 1 2 v for a large class of potentials v we show that if h e has a polynomially bounded solution then e is in the spectrum of h this is accomplished by proving that the spectrum of h as an operator on l 2 is identical to its spectrum as an operator on the weighted l 2 space l 2