robust d stability for linear uncertain discrete time delay systems we propose criteria which guarantee robust pole location within a specified circular region for a linear uncertain discrete time delay system the perturbations are treated with structured and unstructured information examples are given to demonstrate the result

pole assignment robustness in a specified disk abstract a sufficient condition is proposed to guarantee robust pole location within a specified circular region for a linear uncertain system the explicit bounds on linear time invariant perturbations with highly structured information are obtained under these allowable highly structured perturbations both stability robustness and certain performance robustness will thus be ensured the merit of the proposed new approach is demonstrated by a given example where the results achieved are much better than the ones reported recently

robustness of eigenvalue clustering in various regions of the complex plane for perturbed systems abstract sufficient conditions of robust eigenvalue clustering for perturbed systems are presented if all the eigenvalues of the nominal system are located in a specified region of the complex plane then the proposed sufficient conditions guarantee that all the eigenvalues of the perturbed system remain inside the same region the characteristics of a linear dynamical system are influenced by the eigenvalue locations therefore through the study of eigenvalue clustering more features about perturbed systems such as stability margin performance robustness and so on can be investigated it is emphasized that the proposed perturbation bounds for robust eigenvalue clustering in a specified region can be applied to both continuous and discrete time systems three illustrative examples are given to show the applicability of the proposed theorems

eulerian lagrangian theory of transport in space time nonstationary velocity fields exact nonlocal formalism by conditional moments and weak approximation a unified eulerian lagrangian theory is presented for the transport of a conservative solute in a random velocity field that satisfies locally v x t f x t where f x t is a random function including sources and or the time derivative of head solute concentration satisfies locally the eulerian equation c x t t j x t g x t where j x t is advective solute flux and g x t is a random source independent of f x t we consider the prediction of c x t and j x t by means of their unbiased ensemble moments c x t and j x t conditioned as implied by the subscript on local hydraulic measurements through the use of the latter in obtaining a relatively smooth unbiased estimate x t of v x t these predictors satisfy c x t v t j x t g x t where j x t x t c x t q x t and q x t is a dispersive flux we show that q is given exactly by three space time convolution integrals of conditional lagrangian kernels with q with c and with c for a broad class of v x t fields including fractals this implies that q x t is generally nonlocal and non fickian rendering c x t non gaussian the direct contribution of random variations in f to q depends on c rather than on c we elucidate the nature of the above kernels discuss conditions under which the convolution of and c becomes pseudo fickian with a lagrangian dispersion tensor similar to that derived in 1921 by taylor recall a 1952 result by batchelor which yields an exact expression for c at early time use the latter to conclude that linearizations which predict that c bifurcates at early time when the probability density function of v is unimodal cannot be correct propose instead a weak approximation which leads to a nonlinear integro differential equation for c due to an instantaneous point source and which improves with the quantity and quality of hydraulic data demonstrate that the weak approximation is analogous to the direct interaction closure of turbulence theory offer non fickian and pseudo fickian weak approximations for the second conditional moment of the concentration prediction error demonstrate that it yields the so called two particle covariance as a special case conclude that the conditional variance of c does not become infinite merely as a consequence of disregarding local dispersion and discuss how to estimate explicitly the cumulative release of a contaminant across a compliance surface together with the associated estimation error

poisson and compound poisson approximations in conventional and nonconventional setups it was shown in kifer israel j math 2013 that for any subshift of finite type considered with a gibbs invariant measure the numbers of multiple recurrencies to shrinking cylindrical neighborhoods of almost all points are asymptotically poisson distributed here we not only extend this result to all psi mixing shifts with countable alphabet but actually show that for all points the distributions of these numbers are asymptotically close either to poisson or to compound poisson distributions it turns out that for all nonperiodic points a limiting distribution is always poisson while at the same time for periodic points there may be no limiting distribution at all unless the shift invariant measure is bernoulli in which case the limiting distribution always exists thus we describe essentially completely limiting distributions of multiple recurrence numbers in this setup as a corollary we obtain also that the first occurence time of the multiple recurrence event is asymptotically exponentially distributed most of the results are new also for the widely studied single recurrencies case see for instance haydn and vaienti discret contin dyn syst a 10 589 616 2004 probab theory relat fields 144 517 542 2009 abadi and saussol stoch process appl 121 314 323 2011 abadi and vergne nonlinearity 21 2871 2885 2008 as well

the compound poisson limit ruling periodic extreme behaviour of non uniformly hyperbolic dynamics we prove that the distributional limit of the normalised number of returns to small neighbourhoods of periodic points of certain non uniformly hyperbolic dynamical systems is compound poisson the returns to small balls around a fixed point in the phase space correspond to the occurrence of rare events or exceedances of high thresholds so that there is a connection between the laws of return times statistics and extreme value laws the fact that the fixed point in the phase space is a repelling periodic point implies that there is a tendency for the exceedances to appear in clusters whose average sizes is given by the extremal index which depends on the expansion of the system at the periodic point we recall that for generic points the exceedances in the limit are singular and occur at poisson times however around periodic points the picture is different the respective point processes of exceedances converge to a compound poisson process so instead of single exceedances we have entire clusters of exceedances occurring at poisson times with a geometric distribution ruling its multiplicity the systems to which our results apply include general piecewise expanding maps of the interval rychlik maps maps with indifferent fixed points manneville pomeau maps and benedicks carleson quadratic maps

generalized bounded variation and applications to piecewise monotonic transformations we prove the quasi compactness of the perron frobenius operator of piecewise monotonic transformations when the inverse of the derivative is holder continuous or more generally of bounded p variation

on the computation of the extremal index for time series the extremal index is a quantity introduced in extreme value theory to measure the presence of clusters of exceedances in the dynamical systems framework it provides important information about the dynamics of the underlying systems in this paper we provide a review of the meaning of the extremal index in dynamical systems depending on the observables used this quantity can inform on local properties of attractors such as periodicity stability and persistence in phase space or on global properties such as the lyapunov exponents we also introduce a new estimator of the extremal index and show its relation with those previously introduced in the statistical literature we reserve a particular focus to the systems perturbed with noise as they are a good paradigm of many natural phenomena different kind of noises are investigated in the annealed and quenched situations applications to climate data are also presented

robustness of regional pole placement for uncertain continuous time implicit systems in this note under assumptions that the nominal linear implicit system is regular impulse free with all its generalized eigenvalues lying inside some specified regions sufficient conditions are proposed to preserve the assumed properties when structured perturbations are added into the nominal system explicit bounds on perturbations with different structures are given in terms of the spectral radii of some nonnegative matrices

an evolution strategy method for computing eigenvalue bounds of interval matrices in this paper a modified method by means of an evolution strategy es is introduced for computing eigenvalue bounds of interval matrices then a sufficient condition theorem of the evolutionary strategy is presented which guarantees the convergence in probability of the method the numerical examples show the method can effectively yield accurate bounds for interval eigenvalues

stochastic diagrammatic analysis of groundwater flow in heterogeneous porous media the diagrammatic approach is an alternative to standard analytical methods for solving stochastic differential equations governing groundwater flow with spatially variable hydraulic conductivity this approach uses diagrams instead of abstract symbols to visualize complex multifold integrals that appear in the perturbative expansion of the stochastic flow solution and reduces the original flow problem to a closed set of equations for the mean and the covariance functions diagrammatic analysis provides an improved formulation of the flow problem over conventional first order series approximations which are based on assumptions such as constant mean hydraulic gradient infinite flow domain and neglect of cross correlation terms this formulation includes simple schemes like finite order diagrammatic perturbations that account for mean gradient trends and boundary condition effects as well as more advanced schemes like diagrammatic porous media description operators which contain infinite order correlations in other words diagrammatic analysis covers not only the cases where low order diagrams lead to good approximations of flow but also those situations where low order perturbation is insufficient and a more sophisticated analysis is needed diagrams lead to a nonlocal equation for the mean hydraulic gradient in terms of which necessary conditions are formulated for the existence of an effective hydraulic conductivity three dimensional flow in an isotropic bounded domain with dirichlet boundary conditions is considered and an integral equation for the mean hydraulic head is derived by means of diagrams this formulation provides an explicit expression for the boundary effects within the three dimensional flow domain in addition to these theoretical results the numerical performance of the diagrammatic approach is tested and useful insight is obtained by means of one dimensional flow examples where the exact stochastic solutions are available

analysis of stability robustness for generalized state space systems with structured perturbations abstract a new approach is proposed to analyze the stability robustness of generalized state space systems with structured perturbations the presented method is computationally simple to use and can easily be calculated by computer as far as we are aware this paper seems to be the first one to solve the robust stability problems for generalized state space systems with structured uncertainties the robust stability problem of generalized state space systems is more complicated than that of regular state space systems because it needs consideration of not only stability robustness but also system regularity and impulse elimination the latter two ones need not be considered in regular state space systems

back to balls in billiards we consider a billiard in the plane with periodic configuration of convex scatterers this system is recurrent in the sense that almost every orbit comes back arbitrarily close to the initial point in this paper we study the time needed to get back in an e ball about the initial point in the phase space and also for the position in the limit when e 0 we establish the existence of an almost sure convergence rate and prove a convergence in distribution for the rescaled return times

limiting entry and return times distribution for arbitrary null sets we describe an approach that allows us to deduce the limiting return times distribution for arbitrary sets to be compound poisson distributed we establish a relation between the limiting return times distribution and the probability of the cluster sizes where clusters consist of the portion of points that have finite return times in the limit where random return times go to infinity in the special case of periodic points we recover the known polya aeppli distribution which is associated with geometrically distributed cluster sizes we apply this method to several examples the most important of which is synchronisation of coupled map lattices for the invariant absolutely continuous measure we establish that the returns to the diagonal is compound poisson distributed where the coefficients are given by certain integrals along the diagonal

robustness of discrete systems under structured uncertainties we give a sufficient condition for the robust stability of the discrete system x k 1 f e x k where the perturbation e is bounded e u a necessary and sufficient condition is derived in the case where f is a positive or a negative matrix and u f the stability of interval matrices is also considered numerical examples are given for illustration

asymptotic limit law for the close approach of two trajectories in expanding maps of the circle given two pointsx y s 1 randomly chosen independently by a mixing absolutely continuous invariant measure of a piecewise expanding and smooth mapf of the circle we consider for each e 0 the point process obtained by recording the timesn 0 such that f n x f n y e with the further assumption that the density of is bounded away from zero we show that when e tends to zero the above point process scaled by e 1 converges in law to a marked poisson point process with constant parameter measure this parameter measure is given explicity by an average on the rate of expansion off

new robustness bounds for discrete systems with random perturbations some new stochastic stability robustness bounds for state space models are reported nominally exponentially stable discrete time systems are assumed to be subject to random parameter perturbations and novel bounds are obtained on the maximum variances of these random perturbations to maintain stability robustness the methods employed in the analysis are the existing ones used in the deterministic framework after transforming the stochastic robustness problem to a deterministic one the results are compared with each other and with the exact stability region in an example

stability analysis of interval matrices continuous and discrete systems this paper considers the stability properties of dynamical interval systems two new methods of determining an upper bound on interval perturbations are presented one of the methods is applicable to both continuous and discrete systems

a quasi linear theory of non fickian and fickian subsurface dispersion 1 theoretical analysis with application to isotropic media a theory is presented which accounts for nonlinearity caused by the deviation of plume particles from their mean trajectory in three dimensional statistically homogeneous but anisotropic porous media under an exponential covariance of log hydraulic conductivities existing linear theories predict that in the absence of local dispersion transverse dispersivities tend asymptotically to zero as fickian conditions are reached according to our new quasi linear theory these dispersivities ascend to peak values and then diminish gradually toward nonzero fickian asymptotes which are proportional to y4 when the log hydraulic conductivity variance y2 is much less than 1 all existing theories agree that in isotropic media the asymptotic longitudinal dispersivity is proportional to y2 when y2 1 and all are nominally restricted to mildly heterogeneous media in which this inequality is satisfied however the quasi linear theory appears to be less prone to error than linear theories when extended to strongly heterogeneous media because it deals with the above nonlinearity without formally limiting y2 it predicts that when y 1 in isotropic media both the longitudinal and transverse dispersivities ascend monotonically toward fickian asymptotes proportional to y

the use of field theoretic methods for the study of flow in a heterogeneous porous medium the effects of heterogeneities on the steady state flow of a single fluid in a porous medium are examined it is argued that incomplete knowledge of the permeability requires the use of a stochastic model of the system it is shown that the problem may be written as a field theory which allows a perturbation series to be expressed by diagrammatic means this allows the calculation of effective permeability the mean pressure and the pressure variance the method as well as recovering familiar results gives a formal means of improving the approximation and approaching more complex systems

robust stability and performance analysis for the system with linear dependent perturbations abstract in this paper the sufficient conditions of the robust stability and robust performance for both continuous time and discrete time systems with structured perturbations are obtained using the matrix measure based approach using the derived results along with the lyapunov based approach several results for determining the robust criterion for the control system with time varying perturbations are also obtained numerical examples have been given to illustrate the effectiveness of the proposed results it shows that the proposed approach is less conservative than those proposed in the previous literature

assessing the stability of linear time invariant continuous interval dynamic systems it is known that stability analysis of linear time invariant dynamic systems under parameter uncertainties can be equated to estimating the range of the eigenvalues of matrices whose elements are intervals in this note first the problem of finding tight outer bounds on the eigenvalue ranges is considered a method for computing such bounds is suggested which consists essentially of setting up and solving a system of n mildly nonlinear algebraic equations n being the size of the interval matrix investigated the main result of the note however is a method for determining the right end point of the exact eigenvalue ranges the latter makes use of the outer bounds it is applicable if certain computationally verifiable monotonicity conditions are fulfilled the methods suggested can be applied for robust stability analysis of both continuous and discrete time systems numerical examples illustrating the applicability of the new methods are also provided

the compound poisson distribution and return times in dynamical systems previously it has been shown that some classes of mixing dynamical systems have limiting return times distributions that are almost everywhere poissonian here we study the behaviour of return times at periodic points and show that the limiting distribution is a compound poissonian distribution we also derive error terms for the convergence to the limiting distribution we also prove a very general theorem that can be used to establish compound poisson distributions in many other settings

prediction of steady state flow in nonuniform geologic media by conditional moments exact nonlocal formalism effective conductivities and weak approximation we consider the effect of measuring randomly varying local hydraulic conductivities k x on one s ability to predict steady state flow within a bounded domain driven by random source and boundary functions more precisely we consider the prediction of local hydraulic head h x and darcy flux q x by means of their unbiased ensemble moments h x and q x conditioned on measurements of k x these predictors satisfy a deterministic flow equation in which q x x h x r x where x is a relatively smooth unbiased estimate of k x and r x is a residual flux we derive a compact integral expression for r x which is rigorously valid for a broad class of k x fields including fractals it demonstrates that q x is nonlocal and non darcian so that an effective hydraulic conductivity does not generally exist we show analytically that under uniform mean flow the effective conductivity may be a scalar a symmetric or a nonsymmetric tensor or a set of directional scalars which do not form a tensor we demonstrate numerically that in two dimensional mean radial flow it may increase from the harmonic mean of k x near interior and boundary sources to the geometric mean far from such sources for cases where r x can neither be expressed nor approximated by a local expression we propose a weak integral approximation closure which appears to work well in media with pronounced heterogeneity and improves as the quantity and quality of k x measurements increase the nonlocal deterministic flow equation can be solved numerically by standard methods our theory shows clearly how the scale of grid discretization should relate to the scale quantity and quality of available data after providing explicit approximations for the second moments of head and flux prediction errors we conclude by discussing practical methods to compute x from noisy measurements of k x and to calculate required second moments of the associated estimation errors when k x is lognormal

necessary and sufficient conditions for stability of time varying discrete interval matrices sufficient conditions for the stability of time varying discrete interval systems are presented the spectral radius of the maximum absolute matrix of all interval matrices is employed as opposed to utilizing the matrix norm or lyapunov theorem for special cases our result becomes a necessary and sufficient condition for stability furthermore the proposed conditions are inclusive of the previous results of stability of time invariant interval systems

extremes and local dependence in stationary sequences extensions of classical extreme value theory to apply to stationary sequences generally make use of two types of dependence restriction a a weak mixing condition restricting long range dependence b a local condition restricting the clustering of high level exceedances

robust control analysis and design for discrete time singular systems abstract in this paper we propose a simple approach to analyse stability robustness of discrete time singular systems under structured perturbations the developed robustness criteria are then applied to solve robust regional pole assignment problems of singular systems a robust control design algorithm via state feedback is also given the robust stability problem of singular systems is more complicated than that of regular systems not only stability robustness but system regularity and impulse elimination should be considered simultaneously since the results of robust control and analysis for singular systems is not available in the literature as much as other fields the paper may be viewed as a complementary result in this field although only discrete time case is discussed several results can be directly applied to continuous time systems as well

on the stability properties of polynomials with perturbed coefficients given a polynomial p c s s n t 1 s n 1 t n 0 which is hurwitz or p d z z n t 1 z n 1 t n 0 which has zeros only within or on the unit circle it is of interest to know how much the coefficients t j can be perturbed while preserving the stability properties in this note a method is presented for obtaining the largest hypersphere centered at t t t 1 t n containing only polynomials which are stable

a method for estimating upper and lower bounds of eigenvalues of closed loop systems with uncertain parameters using the convex model theory the vibration control problem of structures with uncertain parameters is discussed which is approximated by a deterministic one a method for estimating the upper and lower bounds of eigenvalues of the closed loop systems is presented by combining the matrix perturbation and optimization the present method is applied to a vibration system to illustrate the application the numerical results show that the present method is effective

interval finite element method for dynamic response of closed loop system with uncertain parameters in practical engineering it is difficult to obtain all possible solutions of dynamic responses with sharp bounds even if an optimum scheme is adopted where there are many uncertain parameters in this paper using the interval finite element ife method and precise time integration pti method we discuss the dynamic response of vibration control problem of structures with interval parameters with matrix perturbation theory and interval arithmetic the algorithm for estimating upper and lower bounds of dynamic response of the closed loop system is developed directly from the interval parameters two numerical examples are given to illustrate the application of the present method the example 1 is used to show the applicability of the present method the example 2 is used to show the validity of the present method by comparing the results with those obtained by the classical random perturbation method copyright 2006 john wiley sons ltd