synchronization of chaotic lur e systems with time delays using sampled data control the asymptotical synchronization problem is investigated for two identical chaotic lur e systems with time delays the sampled data control method is employed for the system design a new synchronization condition is proposed in the form of linear matrix inequalities the error system is shown to be asymptotically stable with the constructed new piecewise differentiable lyapunov krasovskii functional lkf different from the existing work the new lkf makes full use of the information in the nonlinear part of the system the obtained stability condition is less conservative than some of the existing ones a longer sampling period is achieved with the new method the numerical examples are given and the simulations are performed on chua s circuit the results show the superiorities and effectiveness of the proposed control method

exponential stability of impulsive systems with application to uncertain sampled data systems we establish exponential stability of nonlinear time varying impulsive systems by employing lyapunov functions with discontinuity at the impulse times our stability conditions have the property that when specialized to linear impulsive systems the stability tests can be formulated as linear matrix inequalities lmis then we consider lti uncertain sampled data systems in which there are two sources of uncertainty the values of the process parameters can be unknown while satisfying a polytopic condition and the sampling intervals can be uncertain and variable we model such systems as linear impulsive systems and we apply our theorem to the analysis and state feedback stabilization we find a positive constant which determines an upper bound on the sampling intervals for which the stability of the closed loop is guaranteed the control design lmis also provide controller gains that can be used to stabilize the process we also consider sampled data systems with constant sampling intervals and provide results that are less conservative than the ones obtained for variable sampling intervals

an iqc approach to robust stability of aperiodic sampled data systems conditions for robust stability of sampled data systems with non uniform sampling patterns and structural uncertainties are derived the problem is tackled under the integral quadratic constraint iqc framework where the aperiodic sampling operation is modelled by an delay integration operator characterization based on integral quadratic constrains iqc is identified for this operator and the iqc theory is applied to derive convex stability criteria compared to the dominating lyapunov approach where the candidate lyapunov krasovskii functionals or looped functionals need to be tailored for the systems under consideration and therefore the stability conditions need to be re derived whenever additional uncertainties are considered the proposed approach has the advantage of avoiding such endeavor numerical examples are given to illustrate this main point and effectiveness of the proposed approach

approximation of schrodinger eigenvalues and eigenfunctions by canonical perturbation theory the periodically driven quantum rotator a first order approximate formula for eigenvalues and eigenfunctions of the schrodinger operator of the periodically driven quantum rotator is given by means of the classical perturbation theory and an estimate for the remainder is provided in the nonresonant case the remainder is of order 2 while in the resonant case the remainder turns out to be of order 3 2 in the first case to what extent the procedure can be interated to higher orders is also discussed

adaptive learning in complex reproducing kernel hilbert spaces employing wirtinger s subgradients this paper presents a wide framework for non linear online supervised learning tasks in the context of complex valued signal processing the complex input data are mapped into a complex reproducing kernel hilbert space rkhs where the learning phase is taking place both pure complex kernels and real kernels via the complexification trick can be employed moreover any convex continuous and not necessarily differentiable function can be used to measure the loss between the output of the specific system and the desired response the only requirement is the subgradient of the adopted loss function to be available in an analytic form in order to derive analytically the subgradients the principles of the recently developed wirtinger s calculus in complex rkhs are exploited furthermore both linear and widely linear in rkhs estimation filters are considered to cope with the problem of increasing memory requirements which is present in almost all online schemes in rkhs the sparsification scheme based on projection onto closed balls has been adopted we demonstrate the effectiveness of the proposed framework in a non linear channel identification task a non linear channel equalization problem and a quadrature phase shift keying equalization scheme using both circular and non circular synthetic signal sources

canonical perturbation expansions to large order from classical hypervirial and hellmann feynman theorems the classical hypervirial and hellmann feynman theorems are used to formulate a perturbation theory without fourier series that can be used to generate canonical series expansions for the energies of perturbed periodic orbits for separable classical hamiltonians as in the case where these theorems are used to generate quantum mechanical rayleigh schrodinger perturbation series the method is very efficient and may be used to generate expansions to large order either numerically or in algebraic form here the method is applied to one dimensional anharmonic oscillators and radial kepler problems in all cases the classical series for energies and expectation values are seen to correspond to the expansions associated with their quantum mechanical counterparts through an appropriate action preserving classical limit as discussed by turchetti graffi and paul this action fixing is inherent in the classical hellmann feynman theorem applied to periodic orbits

sampled data synchronization analysis of markovian neural networks with generally incomplete transition rates this paper investigates the problem of sampled data synchronization for markovian neural networks with generally incomplete transition rates different from traditional markovian neural networks each transition rate can be completely unknown or only its estimate value is known in this paper compared with most of existing markovian neural networks our model is more practical because the transition rates in markovian processes are difficult to precisely acquire due to the limitations of equipment and the influence of uncertain factors in addition the time dependent lyapunov krasovskii functional is proposed to synchronize drive system and response system by applying an extended jensen s integral inequality and wirtinger s inequality new delay dependent synchronization criteria are obtained which fully utilize the upper bound of variable sampling interval and the sawtooth structure information of varying input delay moreover the desired sampled data controllers are obtained finally two examples are provided to illustrate the effectiveness of the proposed method

widely linear estimation with complex data mean square estimation of complex and normal data is not linear as in the real case but widely linear the purpose of the paper is to calculate the optimum widely linear mean square estimate and to present its main properties the advantage with respect to the linear procedure is especially analyzed

on convergence of normal forms for complex frequencies convergence of the normal form for the hamiltonian system is proven xi he yi yi he xi 1 i n where he has the form he x y h0 x eh1 x y x y rn tn and is holomorphic with respect to x y e provided n 2 and the ratio h0 x1 h0 x2 is not real

distribution of lattice points visible from the origin let be a region in the plane which contains the origin is star shaped with respect to the origin and has a piecewise c 1 boundary for each integer q 1 we consider the integer lattice points from which are visible from the origin and prove that the 1 st consecutive spacing distribution of the angles formed with the origin exists this is a probability measure supported on an interval m with m 0 its repartition function is explicitly expressed as the convolution between the square of the distance from origin function and a certain kernel

the pair correlation function of fractional parts of polynomials we investigate the pair correlation function of the sequence of fractional parts of n d n 1 2 n where d 2 is an integer and an irrational we conjecture that for badly approximable the normalized spacings between elements of this sequence have poisson statistics as n

second order analysis of improper complex random vectors and processes we present a comprehensive treatment of the second order theory of complex random vectors and wide sense stationary wss signals the main focus is on the improper case in which the complementary covariance does not vanish accounting for the information present in the complementary covariance requires the use of widely linear transformations based on these we present the eigenanalysis of complex vectors and apply it to the problem of rank reduction through principal components we also investigate joint properties of two complex vectors by introducing canonical correlations which paves the way for a discussion of the wiener filter and its rank reduced version we link the concepts of propriety and joint propriety to eigenanalysis and canonical correlation analysis respectively our treatment is extended to wss signals in particular we give a result on the asymptotic distribution of eigenvalues and examine the connection between wss proper and analytic signals

quantum mechanics as classical mechanics plus quantum corrections the cubic anharmonic oscillator the rayleigh schrodinger perturbation series for the cubic anharmonic oscillator can be formally rearranged as the classical birkhoff series plus quantum corrections proportional to successive powers of h cross 2 each of the individual quantum corrections is a convergent power series expansion with the same radius of convergence as the classical series of the corresponding term in the jeffreys wentzel kramers brillouin series

complex valued signal processing the proper way to deal with impropriety complex valued signals occur in many areas of science and engineering and are thus of fundamental interest in the past it has often been assumed usually implicitly that complex random signals are proper or circular a proper complex random variable is uncorrelated with its complex conjugate and a circular complex random variable has a probability distribution that is invariant under rotation in the complex plane while these assumptions are convenient because they simplify computations there are many cases where proper and circular random signals are very poor models of the underlying physics when taking impropriety and noncircularity into account the right type of processing can provide significant performance gains there are two key ingredients in the statistical signal processing of complex valued data 1 utilizing the complete statistical characterization of complex valued random signals and 2 the optimization of real valued cost functions with respect to complex parameters in this overview article we review the necessary tools among which are widely linear transformations augmented statistical descriptions and wirtinger calculus we also present some selected recent developments in the field of complex valued signal processing addressing the topics of model selection filtering and source separation

new insights on stability of sampled data systems with time delay abstract this paper analyses the stability of sampled data systems with time delay by employing a two sided looped functional approach some improved conditions are derived to guarantee the stability of the system under consideration then based the conditions some intrinsic relationships between sampled data period and time delay are obtained from the illustrative example being solved by the proposed approach it is observed that the results obtained are significantly better than those obtained by existing methods more importantly from the simulation being carried out it is discovered that contrary to the findings in previous studies time delays in a system may enlarge the interval of sampled data periods and accelerate the rate of convergence of the system states rather than deteriorate the system performance

quantum birkhoff gustavson normal form in some completely resonant cases abstract the goal of this paper is to present an explicit computation of the birkhoff gustavson normal form in the 1 1 1 2 and 1 3 resonances by using the concept of weyl quantization especially when it is about the first terms we use in particular the weyl symbolic calculus and the abstract theorem of the quantum birkhoff gustavson normal form in infinite dimension

convergence and equivalence results for the jensen s inequality application to time delay and sampled data systems the jensen s inequality plays a crucial role in the analysis of time delay and sampled data systems its conservatism is studied through the use of the gruss inequality it has been reported in the literature that fragmentation or partitioning schemes allow to empirically improve the results we prove here that the jensen s gap can be made arbitrarily small provided that the order of uniform fragmentation is chosen sufficiently large nonuniform fragmentation schemes are also shown to speed up the convergence in certain cases finally a family of bounds is characterized and a comparison with other bounds of the literature is provided it is shown that the other bounds are equivalent to jensen s and that they exhibit interesting well posedness and linearity properties which can be exploited to obtain better numerical results

asymptotic density of eigenvalue clusters for the perturbed landau hamiltonian we consider the landau hamiltonian i e the 2d schrodinger operator with constant magnetic field perturbed by an electric potential v which decays sufficiently fast at infinity the spectrum of the perturbed hamiltonian consists of clusters of eigenvalues which accumulate to the landau levels applying a suitable version of the anti wick quantization we investigate the asymptotic distribution of the eigenvalues within a given cluster as the number of the cluster tends to infinity we obtain an explicit description of the asymptotic density of the eigenvalues in terms of the radon transform of the perturbation potential v

the energy level spacing for two harmonic oscillators with golden mean ratio of frequencies the limit distribution of energy level spacing is studied for the system of two harmonic oscillators with generic ratio of frequencies it is proved that for any fixed generic ratio no limit distribution exists but for random with any absolutely continuous distributionp d on 0 1 a universal random limit distribution of the energy level spacing exists some properties of the random limit distribution are discussed

data aided and blind stochastic gradient algorithms for widely linear mmse mai suppression for ds cdma in this paper three novel stochastic gradient algorithms for adjustment of the widely linear wl minimum mean squared error mmse filter for multiple access interference mai suppression for direct sequence code division multiple access ds cdma are introduced and analyzed in particular we derive a data aided wl least mean square lms algorithm a blind wl minimum output energy moe algorithm and a wl blind lms blms algorithm we give analytical expressions for the steady state signal to interference plus noise ratios sinrs of the proposed wl algorithms and we also investigate their speed of convergence wherever possible comparisons with the corresponding linear adaptive algorithms are made both analytical considerations and simulations show in good agreement the superiority of the novel wl adaptive algorithms nevertheless all proposed wl algorithms require a slightly lower computational complexity than their linear counterparts

poincare contraction of su 1 1 fock bargmann structure some aspects of the contraction process so0 1 2 to poincare are studied the starting point is the choice of a suitable parametrization for the de sitterian phase space so0 1 2 so 2 approximately su 1 1 u 1 the authors show that the contraction to poincare must be realized by restricting the fock bargmann space to a specific subspace this constraint is necessary to make the divergent terms disappear in particular the classical result according to which the discrete series representation of su 1 1 contracts onto the wigner representation p m is described at a global level

blind adaptive multiuser detection the decorrelating detector and the linear minimum mean square error mmse detector are known to be effective strategies to counter the presence of multiuser interference in code division multiple access channels in particular those multiuser detectors provide optimum near far resistance when training data sequences are available the mmse multiuser detector can be implemented adaptively without knowledge of signature waveforms or received amplitudes this paper introduces an adaptive multiuser detector which converges for any initialization to the mmse detector without requiring training sequences this blind multiuser detector requires no more knowledge than does the conventional single user receiver the desired user s signature waveform and its timing the proposed blind multiuser detector is made robust with respect to imprecise knowledge of the received signature waveform of the user of interest

phase space bounds for quantum mechanics on a compact lie group let k be a compact connected lie group and k bbb c its complexification i consider the hilbert space cal h l 2 left k bbb c nu t right of holomorphic functions introduced in h1 where the parameter t is to be interpreted as planck s constant in light of l s the complex group k bbb c may be identified canonically with the cotangent bundle of k using this identification i associate to each f in cal h l 2 left k bbb c nu t right a phase space probability density the main result of this paper is theorem 1 which provides an upper bound on this density which holds uniformly over all f and all points in phase space specifically the phase space probability density is at most a t left 2 pi t right n where n dim k and a t is a constant which tends to one exponentially fast as t tends to zero at least for small t this bound cannot be significantly improved

on stability of systems with aperiodic sampling devices this technical note is concerned with stability analysis of aperiodic sampled data systems the stability problem is tackled from a pure discrete time point of view where the at sampling behavior of the system is modelled as the response of a nominal discrete time lti system in feedback interconnection with a structured uncertainty conditions under which the uncertainty is positive real pr are identified based on the pr property a number of integral quadratic constraints iqc are derived and the iqc theory is applied to derive stability conditions numerical examples are given to illustrate the effectiveness of the proposed approach

the blind widely linear minimum output energy algorithm for ds cdma systems a novel blind widely linear wl minimum output energy moe algorithm is proposed for the code division multiple access cdma receiver whereas the recently proposed wl moe algorithm is only applicable to real valued modulation the proposed receiver is applicable to complex valued modulation as well in this correspondence the blind wl moe filter is analyzed and the convergence properties of an adaptive implementation are derived the proposed algorithm dramatically outperforms nonwidely linear moe algorithms when at least one of the signals desired or interference is improper i e real valued while there is a small performance and complexity penalty relative to the previous wl moe algorithm when only real valued modulation is employed the great advantage of the proposed algorithm in being able to handle complex valued modulation such as the popular qam in most cases should outweigh this slight penalty

wirtinger based integral inequality application to time delay systems in the last decade the jensen inequality has been intensively used in the context of time delay or sampled data systems since it is an appropriate tool to derive tractable stability conditions expressed in terms of linear matrix inequalities lmis however it is also well known that this inequality introduces an undesirable conservatism in the stability conditions and looking at the literature reducing this gap is a relevant issue and always an open problem in this paper we propose an alternative inequality based on the fourier theory more precisely on the wirtinger inequalities it is shown that this resulting inequality encompasses the jensen one and also leads to tractable lmi conditions in order to illustrate the potential gain of employing this new inequality with respect to the jensen one two applications on time delay and sampled data stability analysis are provided

generalized jensen inequalities with application to stability analysis of systems with distributed delays over infinite time horizons the jensen inequality has been recognized as a powerful tool to deal with the stability of time delay systems recently a new inequality that encompasses the jensen inequality was proposed for the stability analysis of systems with finite delays in this paper we first present a generalized integral inequality and its double integral extension it is shown how these inequalities can be applied to improve the stability result for linear continuous time systems with gamma distributed delays then for the discrete time counterpart we provide an extended jensen summation inequality with infinite sequences which leads to less conservative stability conditions for linear discrete time systems with poisson distributed delays the improvements obtained by the introduced generalized inequalities are demonstrated through examples

on the diagonalization of quantum birkhoff gustavson normal form an application to quantum mechanics of one of classical perturbation theory methods the birkhoff gustavson normal form bgnf is described in the quantum case it results in the van vleck perturbation theory performed upon wick normal ordered operators algebraic aspects of this procedure and formal construction of invariants integrals of motion for a perturbed system are considered it turned out that a larger set of such operators existed in the quantum mechanics rather than in the classical one it is demonstrated that according to general results of the quantum mechanical perturbation theory the quantum bgnf may always be diagonalized and two formal processes for such diagonalization are constructed in the opposite case the classical bgnf is in general nondiagonalizable this reflects the fact that the classical perturbation theory cannot handle a system with two or more resonances possible reasons for such different behavior of two very close in spirit perturbation procedures are discussed results of the described procedure entirely performed upon the wick normal ordered operators are equivalent to those of rayleigh schrodinger perturbation expansion

predictor based sampled data exponential stabilization through continuous discrete observers the problem of stabilizing a linear continuous time system with discrete time measurements and a sampled input with a pointwise constant delay is considered in a first part we design a continuous discrete observer which converges when the maximum time interval between two consecutive measurements is sufficiently small in a second part we construct a dynamic output feedback by using a technique which is strongly reminiscent of the reduction model approach it stabilizes the system when the maximal time between two consecutive sampling instants is sufficiently small no limitation on the size of the delay is imposed and an iss property with respect to additive disturbances is established

berry s phase hannay s angle and quantum normal forms for any polynomial perturbation of the generalized harmonic oscillator the berry phase is explicitly computed in all orders of perturbation theory as a polynomial in h cross whose term of order zero is the hannay angle this construction is a direct application of the technique of quantum normal forms

some remarks on the use of time varying delay to model sample and hold circuits this note revises the so called input delay approach to the control of sampled data systems with nonuniform sampling in which the sample and hold circuit is embedded into an analog system with a time varying input delay it is shown that the conservatism in calculating the maximal admissible sampling period is reduced by about 57 if the time varying delay embedding step is omitted

stability analysis of linear coupled differential difference systems with general distributed delays we present a new approach for the stability analysis of linear coupled differential difference systems with a general distributed delay the distributed delay term in this note can contain any mathbb l 2 function which is approximated via a class of elementary functions including polynomial trigonometric exponential functions etc through the application of a new proposed integral inequality a sufficient condition for the stability of the system is derived in terms of linear matrix inequalities based on the construction of a lyapunov krasovskii functional the methods proposed in this note can handle problems that cannot be dealt using existing approaches two numerical examples are presented to show the effectiveness of our proposed stability condition

spectral statistics on zoll surfaces the subject of this article is a family of partly conjectural spectral invariants of a laplace operator with a discrete spectrum j known as its k level correlation functions k and level spacings distribution the 2 level or pair correlation function 2 for instance measures the asymptotic number of spacings i j between normalized eigenvalues i as the eigenvalues tend to infinity the normalization is so that the mean level spacing i 1 i is one these invariants have been studied by many physicists including wigner dyson and berry and are conjectured to have certain universal forms depending on the qualitative behaviour of the corresponding classical geodesic flow

nearest neighbor distances on a circle multidimensional case we study the distances called spacings between pairs of neighboring energy levels for the quantum harmonic oscillator specifically we consider all energy levels falling between e and e 1 and study how the spacings between these levels change for various choices of e particularly when e goes to infinity primarily we study the case in which the spring constant is a badly approximable vector we first give the proof by boshernitzan dyson that the number of distinct spacings has a uniform bound independent of e then if the spring constant has components forming a basis of an algebraic number field we show that when normalized up to a unit the spacings are from a finite set moreover in the specific case that the field has one fundamental unit the probability distribution of these spacings behaves quasiperiodically in loge we conclude by studying the spacings in the case that the spring constant is not badly approximable providing examples for which the number of distinct spacings is unbounded

stability of hamiltonian systems at high energy let h t p u p be the hamiltonian for a classical mechanical system of l degrees of freedom where t is an integrable hamiltonian generating quasiperiodic motion in the first l 1 degrees of freedom which has the form

the schrodinger equation and canonical perturbation theory lett0 ev be the schrodinger operator corresponding to the classical hamiltonianh0 ev whereh0 is thed dimensional harmonic oscillator with non resonant frequencies 1 d and the potentialv q1 qd is an entire function of order d 1 1 we prove that the algorithm of classical canonical perturbation theory can be applied to the schrodinger equation in the bargmann representation as a consequence each term of the rayleigh schrodinger series near any eigenvalue oft0 admits a convergent expansion in powers of of initial point the corresponding term of the classical birkhoff expansion moreover ifv is an even polynomial the above result and the kam theorem show that all eigenvalues n e oft0 ev such thatn coincides with a kam torus are given up to order e by a quantization formula which reduces to the bohr sommerfeld one up to first order terms in

local spacings along curves we investigate local spacing problems along curves via smooth maps moreover we provide explicit formulas for the nearest neighbor spacing distribution function of torsion points on elliptic curves over r and of rational points on the unit circle

widely linear versus linear blind multiuser detection with subspace based channel estimation finite sample size effects in a recent paper a s cacciapuoti et al ldquofinite sample performance analysis of widely linear multiuser receivers in ds cdma systems ieee transactions on signal processing vol 56 no 4 pp 1572 1588 apr 2008 we presented the finite sample theoretical performance comparison between linear l and widely linear wl minimum output energy moe receivers for direct sequence code division multiple access ds cdma systems worked out under the assumption that the channel impulse response of the desired user is exactly known the main scope of this paper is to extend such an analysis taking into account not only autocorrelation matrix acm estimation effects but also the accuracy of subspace based blind channel estimation ce we aim to answer the two following questions which of the two estimation processes acm or ce is the main source of degradation when implementing the receivers on the basis of a finite sample size compared with the l moe one is the finite sample wl moe receiver with blind ce capable of achieving the performance gains predicted by the theory to this goal simple and easily interpretable formulas are developed for the signal to interference plus noise ratio sinr at the output of the l and wl moe receivers with blind ce when they are implemented using either the sample acm or its eigendecomposition in addition the derived formulas which are validated by simulations allow one to recognize and discuss interesting tradeoffs between the main parameters of the ds cdma system

static output feedback stabilization necessary conditions for multiple delay controllers this note focuses on the static output feedback stabilization problem for a class of single input single output systems when the control law includes multiple distinct delays we are interested in giving necessary conditions for the existence of such stabilizing controllers illustrative examples second order system chain of integrators or chain of oscillators are presented and discussed

quantum degeneracy and classical perturbation theory the degenerate rayleigh schrodinger perturbation theory for the eigenvalues of the class of schrodinger operators s e s0 ev where s0 is the laplace beltrami operator on the one dimensional torus t1 and v is an analytic potential perturbed rotator is explicitly constructed by means of the algorithm of the classical resonant birkhoff normal form as a consequence the degenerate quantum perturbation theory tends to the classical one in the classical limit

mmse interference suppression for direct sequence spread spectrum cdma we consider interference suppression for direct sequence spread spectrum code division multiple access cdma systems using the minimum mean squared error mmse performance criterion the conventional matched filter receiver suffers from the near far problem and requires strict power control typically involving feedback from receiver to transmitter for acceptable performance multiuser detection schemes previously proposed mitigate the near far problem but are complex and require explicit knowledge or estimates of the interference parameters in this paper we present and analyze several new mmse interference suppression schemes which have the advantage of being near far resistant to varying degrees depending on their complexity and can be implemented adaptively when interference parameters are unknown and or time varying numerical results are provided that show that these schemes offer significant performance gains relative to the matched filter receiver we conclude that mmse detectors can alleviate the need for stringent power control in cdma systems and may be a practical alternative to the matched filter receiver

linear multiuser detectors for synchronous code division multiple access channels under the assumptions of symbol synchronous transmissions and white gaussian noise the authors analyze the detection mechanism at the receiver comparing different detectors by their bit error rates in the low background noise region and by their worst case behavior in a near far environment where the received energies of the users are not necessarily similar optimum multiuser detection achieves important performance gains over conventional single user detection at the expense of computational complexity that grows exponentially with the number of users it is shown that in the synchronous case the performance achieved by linear multiuser detectors is similar to that of optimum multiuser detection attention is focused on detectors whose linear memoryless transformation is a generalized inverse of the matrix of signature waveform crosscorrelations and on the optimum linear detector it is shown that the generalized inverse detectors exhibit the same degree of near far resistance as the optimum multiuser detectors the optimum linear detector is obtained

reciprocally convex approach to stability of systems with time varying delays whereas the upper bound lemma for matrix cross product introduced by park 1999 and modified by moon park kwon and lee 2001 plays a key role in guiding various delay dependent criteria for delayed systems the jensen inequality has become an alternative as a way of reducing the number of decision variables it directly relaxes the integral term of quadratic quantities into the quadratic term of the integral quantities resulting in a linear combination of positive functions weighted by the inverses of convex parameters this paper suggests the lower bound lemma for such a combination which achieves performance behavior identical to approaches based on the integral inequality lemma but with much less decision variables comparable to those based on the jensen inequality lemma

a novel approach to stability and stabilization of fuzzy sampled data markovian chaotic systems abstract this paper studies the problems of stability and stabilization of a class of markovian chaotic systems via fuzzy sampled data control different from some existing results the markovian jumping with general uncertain transition rates is considered for such systems a novel approach i e input delay dependent vector approach is proposed for the first time based on this approach an input delay dependent lyapunov krasovskii functional lkf with cubic function of input delay is successfully constructed and the convex combination technique is used with ease to derive stability and stabilization criteria compared with some existing stability and stabilization criteria for chaotic systems our results are not only less conservative but also with reduced calculation complexity finally the superiorities of proposed results are illustrated by two numerical examples

brief paper wirtinger s inequality and lyapunov based sampled data stabilization discontinuous lyapunov functionals appeared to be very efficient for sampled data systems fridman 2010 naghshtabrizi hespanha teel 2008 in the present paper new discontinuous lyapunov functionals are introduced for sampled data control in the presence of a constant input delay the construction of these functionals is based on the vector extension of wirtinger s inequality these functionals lead to simplified and efficient stability conditions in terms of linear matrix inequalities lmis the new stability analysis is applied to sampled data state feedback stabilization and to a novel sampled data static output feedback problem where the delayed measurements are used for stabilization

spectral statistics for quantized skew translations on the torus we study the spectral statistics for quantized skew translations on the torus which are ergodic but not mixing for irrational parameters it is shown explicitly that in this case the level spacing distribution and other common spectral statistics like the number variance do not exist in the semiclassical limit

level repulsion in the spectrum of two dimensional harmonic oscillators the asymptotic energy limit of the density p s of spacings between adjacent levels of the two dimensional harmonic oscillator tdho spectrum is studied it is shown that in any integer segment m m 1 containing approximately m levels of the tdho spectrum m n p s has the form wi s si where i takes on at most three values for large m p s displays strong level repulsion for irrational but it does not settle on a stationary form nor does its average over m this is in marked contrast with the behaviour of generic integrable systems for which the poisson statistics p s exp s is known to apply

a small scale density of states formula let m g be a c compact riemann manifold with classical hamiltonian h c t m assume that the corresponding quantization p1 op h is quantum completely integrable we establish an microlocal weyl law on short spectral intervals of size 2 e e 0 for various families of operators p1u u i containing p1 both in the mean and pointwise a e for u i the microlocalization refers to a small tubular neighbourhood of a non degenerate stable periodic bicharacteristic t m 0

semiclassical estimates for weyl quantisation abstract we discuss weyl quantisation for operators with holomorphic symbols in the bargmann representation as an application we extend to this class of operators the semiclassical analysis of perturbation theory as introduced by degli esposti et al ann phys 209 1991 364 392

technical communique stability and robust stability for systems with a time varying delay to concern the stability and robust stability criteria for systems with time varying delays this note uses not only the time varying delayed state x t h t but also the delay upper bounded state x email protected to exploit all possible information for the relationship among a current state x t an exactly delayed state x t h t a marginally delayed state x email protected and the derivative of the state email protected t when constructing lyapunov krasovskii functionals and some appropriate integral inequalities originally suggested by park 1999 a delay dependent stability criterion for systems with uncertain time invariant delays ieee transactions on automatic control 44 4 876 877 two fundamental criteria are provided for the cases where no bound of delay derivative is assumed and where an upper bound of delay derivative is assumed examples show the resulting criteria outperform all existing ones in the literature

an improved time delay implementation of derivative dependent feedback abstract we consider an lti system of relative degree r 2 that can be stabilized using r 1 output derivatives the derivatives are approximated by finite differences leading to a time delayed feedback we present a new method of designing and analyzing such feedback under continuous time and sampled measurements this method admits essentially larger time delay sampling period compared to the existing results and for the first time allows to use consecutively sampled measurements in the sampled data case the main idea is to present the difference between the derivative and its approximation in a convenient integral form the kernel of this integral is hard to express explicitly but we show that it satisfies certain properties these properties are employed to construct the lyapunov krasovskii functional that leads to lmi based stability conditions if the derivative dependent control exponentially stabilizes the system then its time delayed approximation stabilizes the system with the same decay rate provided the time delay for continuous time measurements or the sampling period for sampled measurements are small enough

stability of discrete time systems with time varying delays via a novel summation inequality this technical note is concerned with the stability analysis of discrete linear systems with time varying delays the novelty of the technical note comes from the consideration of a new inequality which is less conservative than the celebrated jensen inequality employed in the context of discrete time delay systems this inequality is a discrete time counterpart of the wirtinger based integral inequality that was recently employed for the improved analysis of continuous tine systems with delays however differently from the continuous time case the proof of the new inequality is not based on the wirtinger inequality the method is also combined with an efficient representation of the improved reciprocally convex combination inequality in order to reduce the conservatism induced by the lmis optimization setup the effectiveness of the proposed result is illustrated by some classical examples from the literature

stability analysis of linear systems with interval time varying delays utilizing multiple integral inequalities this paper is devoted to stability analysis of continuous time delay systems with interval time varying delays having known bounds on the delay derivatives a parameterized family of lyapunov krasovskii functionals involving multiple integral terms is introduced and novel multiple integral inequalities are utilized to derive sufficient stability condition for systems with time varying delays the efficiency of the proposed method is illustrated by numerical examples

semiclassical approximation for schrodinger operators on a two sphere at high energy let h s v be a schrodinger operator acting in l2 s with s the two dimensional unit sphere s the spherical laplacian and v a smooth potential approximate eigenfunctions and eigenvalues for h are obtained involving expansions in inverse powers of the classical angular momentum variables provided that these variables are in a region of phase space where the corresponding classical hamiltonian is nearly integrable the analysis is carried out in a bargmann representation where s becomes a quadratic expression in the sum of two quantum harmonic oscillator hamiltonians and v becomes a pseudodifferential operator

classical limit of the harmonic oscillator wigner functions in the bargmann representation writing the wigner functions of any pair of harmonic oscillator eigenstates in the bargmann representation a direct and detailed proof is given of their convergence in the sense of distributions to at the classical limit m n fixed

a uniform quantum version of the cherry theorem consider in l 2 mathbb r 2 the operator family h epsilon p 0 hbar omega epsilon f 0 p 0 is the quantum harmonic oscillator with diophantine frequency vector f 0 a bounded pseudodifferential operator with symbol decreasing to zero at infinity in phase space and epsilon in mathbb c then there exist epsilon ast 0 independent of hbar and an open set gamma subset mathbb c 2 setminus mathbb r 2 such that if epsilon epsilon ast and omega in gamma the quantum normal form near p 0 converges uniformly with respect to hbar this yields an exact quantization formula for the eigenvalues and for hbar 0 the classical cherry theorem on convergence of birkhoff s normal form for complex frequencies is recovered

technical communique delay range dependent stability for systems with time varying delay this paper is concerned with the stability analysis for systems with time varying delay in a range an appropriate type of lyapunov functionals is proposed to investigate the delay range dependent stability problem the present results may improve the existing ones due to a method to estimate the upper bound of the derivative of lyapunov functional without ignoring some useful terms and the introduction of additional terms into the proposed lyapunov functional which take into account the range of delay numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method

a quantum cherry theorem for perturbations of the plane rotator we consider on l2 t2 the schrodinger operator family l r with domain and action defined as d l h2 t2 l u 12 2 1 12 2 22 u i 1 1 2 2 u vu here r 1 2 1 2 are vectors of complex non real frequencies and v a pseudodifferential operator of order zero l represents the weyl quantization of the hamiltonian family l x 12 1 12 2 22 1 1 2 2 v x defined on the phase space r2 t2 where v x c2 r2 t2 r we prove the uniform convergence with respect to 0 1 of the quantum normal form which reduces to the classical one for 0 this result simultaneously entails an exact quantization formula for the quantum spectrum as well as a convergence criterion for the classical birkhoff normal form generalizing a well known theorem of cherry

pair correlation of sums of rationals with bounded height for each positive integer q let f q denote the farey sequence of order q we prove the existence of the pair correlation measure associated to the sum f q f q modulo 1 as q tends to infinity and compute the corresponding limiting pair correlation function

synchronization for complex dynamical networks with time delay and discrete time information the synchronization problem is studied for complex dynamical networks cdns with time delay based on discrete time communication pattern a new lyapunov functional is proposed which is positive definite at communication instants but not necessarily positive definite inside the communication intervals and can make full use of the available information about the discrete time communication pattern based on the lyapunov functional an exponential synchronization criterion is proposed to ensure the synchronization of the considered cdns the effectiveness of the developed results are shown by the numerical simulation

statistical properties of spectral fluctuations for a quantum system with infinitely many components extending the idea formulated in makino phys rev e 67 066205 2003 that is based on the berry robnik approach m v berry and m robnik j phys a 17 2413 1984 we investigate the statistical properties of a two point spectral correlation for a classically integrable quantum system the eigenenergy sequence of this system is regarded as a superposition of infinitely many independent components in the semiclassical limit we derive the level number variance lnv in the limit of infinitely many components and discuss its deviations from poisson statistics the slope of the limiting lnv is found to be larger than that of poisson statistics when the individual components have a certain accumulation this property agrees with the result from the semiclassical periodic orbit theory that is applied to a system with degenerate torus actions d biswas m azam and s v lawande phys rev a 43 5694 1991

spectral form factors of rectangle billiards the berry tabor conjecture asserts that local statistical measures of the eigenvalues j of a generic integrable quantum system coincide with those of a poisson process we prove that in the case of a rectangle billiard with random ratio of sides the sum behaves for random and n large like a random walk in the complex plane with a non gaussian limit distribution the expectation value of the distribution is zero its variance which is essentially the average pair correlation function is one in accordance with the berry tabor conjecture but all higher moments 4 diverge the proof of the existence of the limit distribution uses the mixing property of a dynamical system defined on a product of hyperbolic surfaces the berry tabor conjecture and the existence of the limit distribution for a fixed generic rectangle are related to an equidistribution conjecture for long horocycles on this product space

sampled data control for a class of linear time varying systems this paper is concerned with the sampled data control for a class of linear time varying system a classic halanay inequality is first extended to the time varying sampled data system then based on the comparison principle and the extended halanay inequality new criteria for globally uniformly exponential stability and globally uniformly asymptotic stability of the corresponding closed loop system are derived furthermore an algorithm is presented to solve the gain synthesis problem finally one example is given to show the effectiveness of the obtained results

quantum evolution and classical flow in complex phase space for a class of holomorphic perturbations of the harmonic oscillator inn degrees of freedom a local solution of the time dependent schrodinger equation in the bargmann representation is constructed which pointwise propagates to leading order in along the classical trajectories in complex phase space

convergence of a quantum normal form and a generalization of cherry s theorem we consider on the schrodinger operator family with the domain and action defined as follows where 1 2 is a vector of complex frequencies and v is a pseudodifferential operator of order zero he represents the weyl quantization of the hamiltonian family defined on the phase space where we prove the uniform convergence with respect to 0 1 of the quantum normal form which reduces to the classical one for 0 as a consequence we simultaneously obtain an exact quantization formula for the quantum spectrum as well as a convergence criterion for the classical birkhoff normal form generalizing a well known theorem of cherry

resonant harmonic oscillators and eigenvalue multiplicity explicit formulae are worked out for the eigenvalue multiplicity of a system of n independent quantum harmonic oscillators in the general case of 1 or s or n 1 resonance relations among the frequencies omega 1 omega n as a particular case we prove that even though the quantum numbers are always less than the degrees of freedom the eigenvalues are in general intrinsically degenerate only in the completely resonant case s n 1

finite time synchronization of sampled data markovian jump complex dynamical networks with additive time varying delays based on dissipative theory abstract this paper is concerned with the problem of finite time synchronization issue of sampled data markovian jump complex dynamical networks mjcdns with additive time varying delays based on dissipative theory sufficient conditions to guarantee the finite time stability of mjcdns with additive time varying delays are presented sampled data control with stochastically varying sampling periods is considered the closed loop system is not just finite time bounded but also satisfies the dissipativity conditions further we handled a nonuniform sampled data controller by utilizing the properties of kronecker product combined with the appropriate lyapunov functionals technique a novel delay dependent finite time stability of dissipativity rule is derived in terms of linear matrix inequalities lmis to ensure that the delayed complex dynamical systems to be dissipative finally numerical examples are given to represent the applicability of the proposed approach

reliable h_ infty control for discrete time fuzzy systems with infinite distributed delay in this paper the problem of reliable h control is investigated for discrete time takagi sugeno t s fuzzy systems with infinite distributed delay and actuator faults a discrete time homogeneous markov chain is used to represent the stochastic behavior of actuator faults in terms of a stochastic fuzzy lyapunov functional a sufficient condition is proposed to ensure that the resultant closed loop system is exponentially stable in the mean square sense with an h performance index based on the derived condition the reliable h control problem is solved and an explicit expression of the desired controller is also given the case of no failure in the actuator is also considered a numerical example is given to demonstrate that our results are effective and less conservative

on backwards and forwards reachable sets bounding for perturbed time delay systems linear systems with interval time varying delay and unknown but bounded disturbances are considered in this paper we study the problem of finding outer bound of forwards reachable sets and inter bound of backwards reachable sets of the system firstly two definitions on forwards and backwards reachable sets where initial state vectors are not necessary to be equal to zero are introduced then by using the lyapunov krasovskii method two sufficient conditions for the existence of i the smallest possible outer bound of forwards reachable sets and ii the largest possible inter bound of backwards reachable sets are derived these conditions are presented in terms of linear matrix inequalities with two parameters need to tuned which therefore can be efficiently solved by combining existing convex optimization algorithms with a two dimensional search method to obtain optimal bounds lastly the obtained results are illustrated by four numerical examples

third harmonic generation as a third order quasi exactly solvable system the two degrees of freedom in the usual third harmonic generation effective hamiltonian can be separated both classically and quantum mechanically into a harmonic oscillator and a nonlinear oscillator in turn the quantum hamiltonian of the nonlinear oscillator can be written as a cubic polynomial in the generators of a quasi exactly solvable lie algebra and the physically relevant eigenstates are precisely those that can be determined exactly although in general not explicitly since the standard jeffreys wentzel kramers brillouin methods are not easily applicable to general third order differential equations we use a bohr sommerfeld quantization of the classical orbits to obtain approximate explicit formulas for the corresponding quantum eigenvalues

semiclassical analysis of a quasi exactly solvable system second harmonic generation the usual second harmonic generation effective hamiltonian is shown to be equivalent to a one dimensional schrodinger operator with a sextic polynomial potential this operator belongs to the class of quasi exactly solvable models for which a finite number of eigenvalues and eigenvectors can be determined exactly a jeffreys wentzel kramers brillouin analysis provides accurate asymptotic expansions for these eigenvalues in the limit of large unperturbed energies

bessel laguerre inequality and its application to systems with infinite distributed delays by taking advantage of properties of the laguerre polynomials we propose a new inequality called bessel laguerre integral inequality which can be applied to stability analysis of linear systems with infinite distributed delays and with general kernels the matrix corresponding to the system without the delayed term or the matrix corresponding to the system with the zero delay is not necessarily assumed to be non hurwitz through a laguerre polynomials approximation of kernels the advantage of the method is that the original system is not needed to be transformed into an augmented one instead it is represented as a system with additional signals that are captured by the bessel laguerre integral inequality then we derive a set of sufficient stability conditions that is parameterized by the degree of the polynomials the particular case of gamma kernel functions can be easily considered in this analysis numerical examples illustrate the potential improvements achieved by the presented conditions with increasing the degree of the polynomial but at the price of numerical complexity

degeneracy moments for the square billiard we calculate the semiclassical asymptotics of the moments of a function that characterizes the accidental energy level degeneracies of the square billiard the results quantify the deviations from generic poisson statistics in this spectrum