paper nonlinear adaptive model following control the use of discontinuous control in adaptive model following continuous control systems with nonlinear time varying plant is described the first approach is based on the theory of variable structure systems hyperstability theory is the basis of the second scheme the third one results by combining the previous approaches the link among the three approaches is explored by studying the error dynamics practical implementation and applications are discussed

robust control of cascaded and individually feedback linearizable nonlinear systems abstract feedback linearization technique is applied to design robust controllers for a class of nonlinear uncertain systems every system in the class is a series connection of finite number of nonlinear subsystems which are individually feedback linearizable and have significant but matched nonlinear functional uncertainties the key difference between this work and existing robust results is that the matching conditions and the existence of feedback linearization transformation are only required individually for each subsystem a constructive robust control design procedure is proposed for the unique control in the overall system the procedure is conceptually simple and contains three steps first perform input output feedback linearization for all individual subsystems second design fictitious robust controllers for inputs of each subsystem as if the subsystem had an independent control finally a mapping is developed which maps the individual fictitious controls recursively into the unique control of the overall system since neither the matching conditions nor feedback linearization are required for the overall system this becomes the broadest class of nonlinear uncertain or known systems for which a robust regular tracking control can be constructed using feedback linearization method global stability of the overall system is always guaranteed

regulating constraint obedience for fuzzy mechanical systems based on beta measure and a general lyapunov function we consider an uncertain mechanical system the uncertainty includes the initial condition and system parameter the uncertain parameter in the system is possibly fast time varying the only known information about the uncertainty is that it lies in a fuzzy set the mechanical system is to follow a set of constraints which may include many engineering applications even in the presence of uncertainty for this purpose we propose a beta measure for constraint obedience which reflects how much this constraint is obeyed based on a very general lyapunov function a control scheme is proposed to render a twofold performance guaranteed and optimal in the guaranteed phase the beta measure is assured to be uniformly bounded and uniformly ultimately bounded regardless of the actual value of the uncertainty in the optimal phase a fuzzy theoretic based performance by which both the average beta measure and control effort are considered is minimized as a result the control serves the practical engineering purposes the mechanical system is guaranteed to follow the desired task with the minimum cost this paper is part of a unique endeavor to cast both the descriptions of the uncertainty and desired performance index into a fuzzy framework

adaptive robust control of uncertain systems with measurement noise abstract a class of dynamical systems with time varying uncertainty is considered the nominal portion i e the portion without uncertainty of the system is stabilizable the uncertainty is either assumed to satisfy the matching condition or is close to matching moreover the uncertainty is to be cone bounded the bound is however unknown the control design is only based on the deterministic properties related to the bound of uncertainty the feedback information is the state with measurement noise

robust control design for a class of mismatched uncertain nonlinear systems we consider the robust control design problem for a class of nonlinear uncertain systems the uncertainty in the system may be due to parameter variations and or nonlinearity it may be possibly fast time varying the system does not satisfy the so called matching condition under a state transformation which is based on the possible bound of the uncertainty a robust control scheme can be designed the control renders the uncertain system practically stable furthermore the uniform ultimate boundedness ball and uniform stability ball can be made arbitrarily small by suitable choice of design parameters

an improved razumikhin type theorem and its applications an improved razumikhin type theorem is established and the advantage of the established theorem for reducing conservatism is discussed for a class of time delay systems a simple asymptotic stability condition is deduced as an application of the established theorem two illustrative examples are given to show the superiority of the results to those in the literature

global stabilization of nonlinear systems with a class of unmatched uncertainties abstract global and asymptotic stabilization of uncertain dynamical systems which violate the matching conditions is investigated a class of unmatched uncertainties called equivalently matched uncertainties is defined a robust controller is proposed to stabilize the uncertain system asymptotically in the large provided that the nominal system is uniformly asymptotically stable and that the unmatched uncertainties are equivalently matched the required information about uncertain dynamics in the system is merely that the uncertainties are bounded in euclidean norm by known functions of the system state

strong and weak error estimates for elliptic partial differential equations with random coefficients we consider the problem of numerically approximating the solution of an elliptic partial differential equation with random coefficients and homogeneous dirichlet boundary conditions we focus on the case of a lognormal coefficient and deal with the lack of uniform coercivity and uniform boundedness with respect to the randomness this model is frequently used in hydrogeology we approximate this coefficient by a finite dimensional noise using a truncated karhunen loeve expansion we give estimates of the corresponding error on the solution both a strong error estimate and a weak error estimate that is an estimate of the error commited on the law of the solution we obtain a weak rate of convergence which is twice the strong one in addition we give a complete error estimate for the stochastic collocation method in this case where neither coercivity nor boundedness is stochastically uniform to conclude we apply these results of strong and weak convergence to two classical cases of covariance kernel choices the case of an exponential covariance kernel on a box and the case of an analytic covariance kernel yielding explicit weak and strong convergence rates

quasi monte carlo integration for affine parametric elliptic pdes local supports and product weights we analyze convergence rates of first order quasi monte carlo qmc integration with randomly shifted lattice rules and for higher order interlaced polynomial lattice rules for a class of countably parametric integrands that result from linear functionals of solutions of linear elliptic diffusion equations with affine parametric uncertain coefficient function a x y bar a x sum j geq 1 y j psi j x in a bounded domain d subset mathbb r d extending the result in f y kuo c schwab and i h sloan siam j numer anal 50 2012 pp 3351 3374 where psi j was assumed to have global support in the domain d we assume in the present paper that supp psi j is localized in d and that we have control on the overlaps of these supports under these conditions we prove dimension independent convergence rates in 1 2 1 of randomly shifted lattice rules with product weights and corresponding higher order convergence rates by higher order interlaced polynomial lattice rule

covariance regularity and mathcal h h matrix approximation for rough random fields in an open bounded domain mathrm d subset mathbb r n d rn with smooth boundary partial mathrm d d or on a smooth closed and compact riemannian n manifold mathcal m subset mathbb r n 1 m rn 1 we consider the linear operator equation a u f au f where a is a boundedly invertible strongly elliptic pseudodifferential operator of order r in mathbb r r r with analytic coefficients covering all linear second order elliptic pdes as well as their boundary reductions here f in l 2 omega h t f l2 ht is an h t ht valued random field with finite second moments with h t ht denoting the isotropic sobolev space of not necessarily integer order t modelled on the domain mathrm d d or manifold mathcal m m respectively we prove that the random solution s covariance kernel k u a 1 otimes a 1 k f ku a 1 a 1 kf on mathrm d times mathrm d d d resp mathcal m times mathcal m m m is an asymptotically smooth function provided that the covariance function k f kf of the random data is a schwartz distributional kernel of an elliptic pseudodifferential operator as a consequence numerical mathcal h h matrix calculus allows the deterministic approximation of singular covariances k u ku of the random solution u a 1 f in l 2 omega h t r u a 1f l2 ht r in mathrm d times mathrm d d d text resp mathcal m times mathcal m resp m m with work versus accuracy essentially equal to that for the mean field approximation with splines of fixed order mathrm d d text resp mathcal m resp m overcoming the curse of dimensionality in this case

robust model tracking control for a class of nonlinear plants we propose a new model following control scheme for a class of nonlinear plants the feedback control signal is a continuous function of all its arguments it is shown that this scheme guarantees that tracking error remains bounded and tends to a neighborhood of the origin with a rate not inferior to an exponential one furthermore it allows the designer to arbitrarily prescribe the rate of convergence and the size of the set of ultimate boundedness

further analysis of multilevel monte carlo methods for elliptic pdes with random coefficients we consider the application of multilevel monte carlo methods to elliptic pdes with random coefficients we focus on models of the random coefficient that lack uniform ellipticity and boundedness with respect to the random parameter and that only have limited spatial regularity we extend the finite element error analysis for this type of equation carried out in charrier et al siam j numer anal 2013 to more difficult problems posed on non smooth domains and with discontinuities in the coefficient for this wider class of model problem we prove convergence of the multilevel monte carlo algorithm for estimating any bounded linear functional and any continuously frechet differentiable non linear functional of the solution we further improve the performance of the multilevel estimator by introducing level dependent truncations of the karhunen loeve expansion of the random coefficient numerical results complete the paper

qmc integration for lognormal parametric elliptic pdes local supports and product weights we analyze convergence rates of quasi monte carlo qmc quadratures for countably parametric solutions of linear elliptic partial differential equations pde in divergence form with log gaussian diffusion coefficient based on the error bounds in nichols and kuo j complex 30 4 444 468 2014 https doi org 10 1016 j jco 2014 02 004 we prove for representations of the gaussian random field pde input with locally supported basis functions and for continuous piecewise polynomial finite element discretizations in the physical domain novel qmc error bounds in weighted spaces with product weights that exploit localization of supports of the basis elements representing the input gaussian random field in this case the cost of the fast component by component algorithm for constructing the qmc points scales linearly in terms of the integration dimension the qmc convergence rate mathcal o n 1 delta independent of the parameter space dimension s is achieved under weak summability conditions on the expansion coefficients

global robust stabilization of nonlinear cascaded systems this paper gives a sufficient condition for a class of nonlinear cascaded systems to be globally stabilizable via state feedback in the presence of uncertainty which does not necessarily satisfy the so called matching condition the authors result is an extension of the former stabilization results which treated systems without uncertainty in the sense that the uncertainty is taken into account

robust control by two lyapunov functions a new method of designing a robust control law is proposed for a general class of non linear or linear systems with bounded uncertainties the method uses the property that the lyapunov function is not unique for a stable or stabilizable system it is shown that the proposed control law normally guarantees the stability of the system if there are two lyapunov functions whose null sets have a trivial intersection the null set of a lyapunov function is defined to be the set in state space in which the product of the transpose of the system input matrix and the gradient of the lyapunov function is equal to zero the robust control results impose no restriction on the structure and size of the input unrelated uncertainties moreover it is shown that asymptotic stabilization of the nominal system is not necessarily required in this method

continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems we consider a dynamic system containing uncertain elements only the set of possible values of these uncertainties is known based on this information a class of state feedback controls is proposed in order to guarantee uniform ultimate boundedness of every system response within an arbitrarily small neighborhood of the zero state these feedback controls are continuous functions of the state

on the stabilization and observation of nonlinear uncertain dynamic systems the problem of stabilization and observation of uncertain and or nonlinear dynamic systems for which matching conditions are not satisfied is investigated no statistical description of uncertain elements is assumed the uncertain and or nonlinear quantities are described only in terms of bounds on their possible sizes stabilizing feedback controllers and observers are proposed whose design is based on the constructive use of lyapunov functions and the bellman gronwall lemma

stabilization of uncertain distributed parameter systems the stabilization of uncertain systems governed by an evolution equation in a real hilbert space is studied the uncertain systems under consideration are described by state equations in which both the state and input operators depend upon uncertain parameters exponential stability is achieved by the suitable choice of state feedback control the proofs are based upon perturbation analysis of semigroup and lyapunov theory a number of examples are given to illustrate the approach

robustness of uncertain systems in the absence of matching assumptions abstract we consider a class of uncertain dynamical systems containing uncertain elements these may be due to model parameter uncertainty input disturbance and measurement noise we require no a priori information on the uncertain elements except that their restraint sets are assumed to be known and compact this paper describes a general approach for designing controls to assure practical stability in the absence of matching assumptions which most previous results have needed the result is applicable to non linear systems a specialization to linear systems is then given and a comparison is made with previous work

bibo stabilization of stochastic delay systems with uncertainty employing the razumikhin technique we present several criteria of input to bounded state stabilization and bounded input bounded output stabilization in mean square for nonlinear and quasi linear stochastic control systems with time varying delay and time varying uncertainties

criteria for robust absolute stability of time varying nonlinear continuous time systems the present paper establishes results for the robust absolute stability of a class of nonlinear continuous time systems with time varying matrix uncertainties of polyhedral type and multiple time varying sector nonlinearities by using the variational method and the lyapunov second method criteria for robust absolute stability are obtained in different forms for the given class of systems specifically the parametric classes of lyapunov functions are determined which define the necessary and sufficient conditions of robust absolute stability the piecewise linear lyapunov functions of the infinity vector norm type are applied to derive an algebraic criterion for robust absolute stability in the form of solvability conditions of a set of matrix equations several simple sufficient conditions of robust absolute stability are given which become necessary and sufficient for special cases two examples are presented as applications of the present results to a particular second order system and to a specific class of systems with time varying interval matrices in the linear part

one approach to the control of uncertain dynamical systems we present a controller design methodology for uncertain systems which is based on the constructive use of lyapunov stability theory the uncertainties which are deterministic are characterized by certain structural conditions and known as well as unknown bounds as a consequence of the lyapunov approach the methodology is not restricted to linear or time invariant systems the robustness of these controllers in the presence of singular perturbations is considered the situation in which the full state of the system is not available for measurement is also considered as are other generalizations

chirality of wavefunctions for three coalescing levels the analytic structure in the vicinity of three coalescing eigenvalues ep3 of a matrix problem is investigated it is argued that the three eigenfunctions also coalescing at the ep3 invoke a true chiral behaviour in the vicinity of the ep3 and that they can be related to a three dimensional helix the orientation of the helix depends on the distribution of the widths of the three levels in the vicinity of the ep3

linear and nonlinear stabilizing continuous controllers of uncertain dynamical systems including state delay the problem of robust stabilization of a class of time varying dynamical systems with disturbance uncertain parameters and a bounded time varying state delay is considered two classes of stabilizing continuous controllers are proposed the proposed controllers can guarantee the existence of the solution to the dynamical system in the usual sense and can also be directly implemented in the practical control problems moreover since the proposed controllers are completely independent of the time delay which is only assumed to be any nonnegative bounded and continuous function the results developed in this note are applicable to a class of dynamical systems with uncertain time delays finally a numerical example is given to demonstrate the validity of the results

on quadratic stability of systems with structured uncertainty this paper considers the problem of stability robustness with respect to a class of nonlinear time varying perturbations which are bounded in a component wise rather than aggregated manner a family of robustness bounds is parameterized in terms of a non singular symmetric matrix it is shown that the problem of computing the largest robustness bound over the set of non singular symmetric matrices can be approximated by a smooth minimization problem over a compact set a convergent algorithm for computing an optimal robustness bound is proposed in the form of a gradient flow

exponential stability criteria of uncertain systems with multiple time delays the exponential stability with convergence rate of uncertain linear systems with multiple time delays is studied in this paper using the characteristic function of linear time delay system stability criteria are derived to guarantee stability sufficient conditions are also obtained for exponential stability of uncertain parametric systems with multiple time delays for two dimensional time invariant system with multiple time delays the proposed stability criteria are shown to be less conservative than those in the literature numerical examples are given to illustrate the validity of our new stability criteria

multiple surface sliding control of a class of uncertain nonlinear systemsm we develop a multiple surface sliding control for a class of single input single output nonlinear systems whose uncertainties do not satisfy the standard matching condition a coordinate dependence condition on the uncertainty bound is assumed a computed normal form is defined to handle such uncertainties instead of the normal form used in conventional input output linearization a control algorithm which can be applied to global tracking problems has been developed and evaluated for a benchmark example

robust control for fuzzy dynamical systems uniform ultimate boundedness and optimality we propose a new approach for the control design of fuzzy dynamical systems the system may contain uncertainty which includes unknown parameter and input disturbance the uncertainty lies within a prescribed fuzzy set the control structure is deterministic and hence not if then rule based the desired controlled system performance includes uniform boundedness and uniform ultimate boundedness in addition we propose a quadratic cost index which reflects the fuzzy system performance we then formulate a control parameter design problem as a constrained optimization problem it is proven that the global solution to this problem always exists and is unique the closed form solution and the closed form minimum cost are derived

technical results for the study of robustness of lagrange stability abstract we study the robustness of boundedness of solutions of nonlinear dynamical systems a sufficient coordinate free technical condition on the characterization of unmodelled effects is given this characterization with some analogy with the input to state stability of 16 has the potential to encompass most classical uncertainties in this context we establish lagrange stability results which look very much like a small gain theorem we illustrate the use of these technical results in the robust stabilization problem by a class of interconnected systems

fast algorithms for component by component construction of rank 1 lattice rules in shift invariant reproducing kernel hilbert spaces we reformulate the original component by component algorithm for rank 1 lattices in a matrix vector notation so as to highlight its structural properties for function spaces similar to a weighted korobov space we derive a technique which has construction cost o snlog n in contrast with the original algorithm which has construction cost o sn 2 herein s is the number of dimensions and n the number of points taken prime in contrast to other approaches to speed up construction our fast algorithm computes exactly the same quantity as the original algorithm the presented algorithm can also be used to construct randomly shifted lattice rules in weighted sobolev spaces

the optical singularities of birefringent dichroic chiral crystals using a new formalism involving projection from the sphere of directions to the stereographic plane and associated complex variables explicit formulae are obtained for the two refractive indices and polarizations in optically anisotropic crystals that are both dichroic absorbing and chiral optically active this enables three types of polarization singularity to be classified and explored singular axes which are degeneracies where the two refractive indices are equal and which for a transparent non chiral crystal condense pairwise onto the optic axes c points where the polarization is purely circular right or left handed with topological index 1 or and whose positions are independent of the chirality and l lines where the polarization is purely linear dividing direction space into regions with right and left handedness a local model captures essential features of the general theory interference figures generated by slabs of crystal viewed directly or through a polarizer and or analyser enable the singularities to be displayed directly

output feedback control of uncertain coupled systems the stabilization of uncertain dynamical systems on n that admit a decomposition into two coupled subsystems of dimension nc and nr respectively is studied we refer to the nc dimensional sybsystem as the reduced order system and to the nr dimensional subsystem as the residual system the overall n dimensional system is termed the full system the prototype for which is a mechanical model arising in the study of the active control of structures each subsystem is modelled by a differential equation with a linear nominal part and a nonlinear perturbation of a specified class the output available for feedback purposes is an nc valued linear combination of the state components of the full system and is subject to bounded measurement noise with known bound an output feedback strategy is described and sufficient conditions are obtained for the existence of a calculable global uniform compact attractor containing the state origin for controlled systems of this class

improved quantitative measures of robustness for multivariable systems asymptotically stable linear systems subject to unstructured time varying perturbations are considered allowable perturbation bounds are obtained such that the perturbed systems remain stable these bounds are derived iteratively by means of adjusting a sequence of lyapunov matrices in comparison with existing methods less conservative quantitative measures of robustness are obtained

on robustness and stabilization of linear systems with delayed nonlinear perturbations in this paper by employing a razumikhin type theorem a robust stability criterion for a class of linear systems subject to delayed time varying nonlinear perturbations is given then stabilization of a class of linear systems subject to mismatched delayed time varying nonlinear perturbations by linear controller is considered for such systems conditions which ensure closed loop asymptotic stability are given numerical examples are given to illustrate the results

improved exponential stability for time varying systems with nonlinear delayed perturbations in this paper a new sufficient delay dependent exponential stability condition for a class of linear time varying systems with nonlinear delayed perturbations is derived by using an improved lyapunov krasovskii functional the proposed exponential stability conditions are formulated in terms of the solution of lyapunov differential equations the approach allows for computation of the bounds that characterize the exponential stability rate of convergence of the solution compared with existing results our conditions are shown to be less conservative numerical examples are given to illustrate the effectiveness of the obtained conditions

a novel optimal robust control design of fuzzy mechanical systems we first investigate the fundamental properties of the mechanical system related to the control design then a new optimal robust control is proposed for mechanical systems with fuzzy uncertainty fuzzy set theory is used to describe the uncertainty in the mechanical system the desirable system performance is deterministic assuring the bottom line as well as fuzzy enhancing the cost consideration the proposed control is deterministic and is not the usual if then rule based the resulting controlled system is uniformly bounded and uniformly ultimately bounded proved via the lyapunov minimax approach a performance index the combined cost which includes average fuzzy system performance and control effort is proposed based on the fuzzy information the optimal design problem associated with the control can then be solved by minimizing the performance index the resulting control design is systematic and is able to guarantee the deterministic performance as well as minimizing the cost in the end a mechanical system is chosen for demonstration

fuzzy dynamical system approach for a dual parameter hybrid order robust control design abstract robust control for uncertain dynamical systems is considered the uncertainty is assumed to be bounded and the fuzzy set theory is adopted to describe the bound a new dual parameter hybrid order robust control design is then proposed in two steps first a class of robust controls is designed taking the advantage of the flexibility in choosing the order and a design parameter the controls are deterministic and are not if then fuzzy rules based deterministic performance including uniform boundedness and uniform ultimate boundedness for the controlled systems is guaranteed second a fuzzy set theoretic based performance index consisting of average and steady state system performance and control cost is proposed a constrained optimization problem is formulated with the intension of minimizing the performance index the objective of the optimization problem is to search for the optimal choice of dual parameters that minimizes the performance index we show that the solution to the optimization problem always exists as a result the resulting control design achieves two concurrent goals guaranteeing deterministic performance as well as minimizing the performance index the theory is illustrated by an unmanned aerial vehicle uav system control design

robust constrained control for vibration suppression of mismatched systems abstract almost all undesirable vibrations in technical systems are caused by unknown or uncertain excitations in cases where these vibrations need to be actively attenuated it is very often not possible to equip the system for that purpose with enough actuators also in general necessary control actions via these actuators cannot be employed over a desired range because of their boundedness we propose a control scheme that allows for these control deficiencies no matter how small the bounds of the controllers are and how many actuators are implemented the scheme is based on lyapunov stability theory it relates to robustness vis a vis unknown but bounded excitations in addition to the controller design via lyapunov theory a stability analysis is carried out to compute the ball of ultimate boundedness for a certain class of lyapunov functions to demonstrate the effectiveness of the control we consider a mechanical system with 2 degrees of freedom where the masses are elastically coupled the unknown excitation acts on one of these masses two controllers are compared particularly with respect to attenuation of vibrations

design of softer robust nonlinear control laws abstract we show that the lyapunov function used in backstepping feedback designs for uncertain nonlinear systems leads to unnecessarily hard control laws having undesirable high gain properties we present a new lyapunov function and use it to design softer control laws which exhibit the high gain properties to a much lesser extent we show that the soft designs eliminate the chattering exhibited by the hard designs and achieve the same or better performance with less control effort

robust stabilization of a class of nonlinear time delay systems the problem of robust stabilization for a class of uncertain dynamic systems with multiple delayed state perturbations is considered it is assumed that perturbations of the time delayed sections are not bounded by first order linear functions but bounded by high order functions with unknown gains and the time delay considered is time varying two classes of controllers are proposed when the time derivative of each time varying time delay is less than 1 a class of adaptive state feedback controllers are proposed based on lyapunov krasovskii method which can render the closed loop systems uniformly ultimately bounded stable novel nonlinear feedback controllers are developed by employing razumikhin lemma and the controller also can render the closed loop systems stable in the sense of uniform ultimate boundedness finally several examples are given to show the potential of the proposed techniques

a new class of stabilizing controllers for uncertain dynamical systems this paper is concerned with the problem of designing a stabilizing controller for a class of uncertain dynamical systems the vector of uncertain parameters q cdot is time varying and its values q t lie within a prespecified bounding set q in r p furthermore no statistical description of q cdot is assumed and the controller is shown to render the closed loop system practically stable in a so called guaranteed sense that is the desired stability properties are assured no matter what admissible uncertainty q cdot is realized within the perspective of previous research in this area this paper contains one salient feature the class of stabilizing controllers which we characterize is shown to include linear controllers when the nominal system happens to be linear and time invariant in contrast in much of the previous literature see for example 1 2 7 and 9 a linear system is stabilized via nonlinear control another feature of this paper is the fact that the

robust control of nonlinear uncertain systems without generalized matching conditions a novel procedure called recursive interlacing procedure is proposed for designing globally stabilizing robust control the procedure introduces new interlacing steps and combines them with the existing recursive or backstepping design it is shown by examining all possible third order vector systems that the procedure is applicable to systems not satisfying any of the existing structural conditions that is to systems in which uncertainties are potentially anywhere and of any bounding function by its nature the procedure is not limited to systems of any specific order it either produces stabilizing control or reveals certain measure of unstabilizability and it includes recursive design as a special case

quasi monte carlo finite element methods for elliptic pdes with lognormal random coefficients in this paper we analyze the numerical approximation of diffusion problems over polyhedral domains in mathbb r d rd d 1 2 3 d 1 2 3 with diffusion coefficient a varvec x omega a x given as a lognormal random field i e a varvec x omega exp z varvec x omega a x exp z x where varvec x x is the spatial variable and z varvec x cdot z x is a gaussian random field the analysis presents particular challenges since the corresponding bilinear form is not uniformly bounded away from 0 0 or infty over all possible realizations of a a focusing on the problem of computing the expected value of linear functionals of the solution of the diffusion problem we give a rigorous error analysis for methods constructed from 1 standard continuous and piecewise linear finite element approximation in physical space 2 truncated karhunen loeve expansion for computing realizations of a a leading to a possibly high dimensional parametrized deterministic diffusion problem and 3 lattice based quasi monte carlo qmc quadrature rules for computing integrals over parameter space which define the expected values the paper contains novel error analysis which accounts for the effect of all three types of approximation the qmc analysis is based on a recent result on randomly shifted lattice rules for high dimensional integrals over the unbounded domain of euclidean space which shows that under suitable conditions the quadrature error decays with mathcal o n 1 delta o n 1 with respect to the number of quadrature points n n where delta 0 0 is arbitrarily small and where the implied constant in the asymptotic error bound is independent of the dimension of the domain of integration

stability analysis for a class of functional differential equations and applications abstract the problem of lyapunov stability for functional differential equations in hilbert spaces is studied the system to be considered is non autonomous and the delay is time varying known results on this problem are based on the gronwall inequality yielding relative conservative bounds on nonlinear perturbations in this paper using more general lyapunov krasovskii functional neither model variable transformation nor bounding restriction on nonlinear perturbations is required to obtain improved conditions for the global exponential stability of the system the conditions given in terms of the solution of standard riccati differential equations allow to compute simultaneously the two bounds that characterize the stability rate of the solution the proposed method can be easily applied to some control problems of nonlinear non autonomous control time delay systems

proximity of degeneracies and chiral points for complex 2 2 matrices m points of degeneracy d and chiral points c where the eigenvectors are circularly polarized coincide whenm is symmetric and often lie close together when m is not symmetric this proximity is explained statistically by averaging over an ensemble in which the elements of m are random complex numbers the standard deviation of the separation between c and d points is less than half the separation of the two d points if the departure from symmetry is treated as a perturbation of strength e t he separation between c and d points is of order e 2 the probability distribution of the separation is calculated

quantitative measures of robustness for systems including delayed perturbations asymptotically stable linear systems subject to delayed time varying and nonlinear perturbations are considered razumikhin type theorems are used to obtain easy to compute bounds on the perturbations so that the systems remain stable results indicate that if delayed perturbations are included then the bound is reduced as compared to the one for nondelayed perturbations however in certain cases previously obtained bounds for the nondelayed perturbations guarantee stability even when delayed perturbations are in effect

quasi monte carlo finite element methods for a class of elliptic partial differential equations with random coefficients in this paper quasi monte carlo qmc methods are applied to a class of elliptic partial differential equations pdes with random coefficients where the random coefficient is parametrized by a co

on ultimate boundedness control of uncertain systems in the absence of matching assumptions this paper describes an approach to ultimate boundedness control under hypotheses less stringent than heretofore required instead of imposing the so called matching conditions of previous authors a certain decomposition of the dynamics is performed the resulting decomposed system has two parts a matched portion and a mismatched portion a certain measure of mismatch m is defined and it is shown that effective control is possible as long as m does not exceed some critical mismatch threshold m it is seen that this threshold depends on the choice of feedback hence it becomes possible to investigate the tradeoffs between the size of the mismatch threshold and the sizes of the feedback gains which achieve the desired ultimate boundedness of solutions