brief paper h filtering for uncertain stochastic time delay systems with sector bounded nonlinearities in this paper we deal with the robust h filtering problem for a class of uncertain nonlinear time delay stochastic systems the system under consideration contains parameter uncertainties ito type stochastic disturbances time varying delays as well as sector bounded nonlinearities we aim at designing a full order filter such that for all admissible uncertainties nonlinearities and time delays the dynamics of the filtering error is guaranteed to be robustly asymptotically stable in the mean square while achieving the prescribed h disturbance rejection attenuation level by using the lyapunov stability theory and ito s differential rule sufficient conditions are first established to ensure the existence of the desired filters which are expressed in the form of a linear matrix inequality lmi then the explicit expression of the desired filter gains is also characterized finally a numerical example is exploited to show the usefulness of the results derived

convergence rate analysis of a multiplicative schwarz method for variational inequalities this paper derives a linear convergence for the schwarz overlapping domain decomposition method when applied to constrained minimization problems the convergence analysis is based on a minimization approach to the corresponding functional over a convex set a general framework of convergence is established for some multiplicative schwarz algorithm the abstract theory is particularly applied to some obstacle problems which yields a linear convergence for the corresponding schwarz overlapping domain decomposition method of one and two levels numerical experiments are presented to confirm the convergence estimate derived in this paper

a domain decomposition method for a kind of optimization problems in this paper we are concerned with the monotone convergence of a multiplicative method for solving a kind of optimization problems we show that the iterate sequence produced by the method converges to the solution of the problem monotonically

robust h filtering for discrete nonlinear stochastic systems with time varying delay this is the postprint version of the article the official published version can be accessed from the link below 2007 elsevier inc

uniform approximation and the circle criterion the input output maps g of causal time invariant systems are considered and a complete characterization of those maps that can be uniformly approximated by the maps of certain simple structures is given the criterion is that g must satisfy certain continuity and approximately finite memory conditions it is proved that the conditions are satisfied by the input output maps of control systems of a familiar type containing a sector nonlinearity for which the circle condition for stability is met in particular this shows that such feedback systems with inputs drawn from a certain large set of bounded functions possess arbitrarily good finite volterra series or radial basis function approximations

rate of convergence for some constraint decomposition methods for nonlinear variational inequalities some general subspace correction algorithms are proposed for a convex optimization problem over a convex constraint subset one of the nontrivial applications of the algorithms is the solving of some obstacle problems by multilevel domain decomposition and multigrid methods for domain decomposition and multigrid methods the rate of convergence for the algorithms for obstacle problems is of the same order as the rate of convergence for jump coefficient linear elliptic problems in order to analyse the convergence rate we need to decompose a finite element function into a sum of functions from the subspaces and also satisfying some constraints a special nonlinear interpolation operator is introduced for decomposing the functions

weighted max norm estimate of additive schwarz iteration scheme for solving linear complementarity problems in this paper we consider an algebraic additive schwarz iteration scheme for solving the finite dimensional linear complementarity problem that involves an m matrix the scheme contains some existing algorithms as special cases we establish monotone convergence of the iteration scheme under appropriate conditions moreover using the concept of weak regular splitting we estimate weighted max norm bounds for iteration errors thereby we show that the sequence generated by the iteration scheme converges to the unique solution of the problem without any restriction on the initial point

convergence analysis ofgeneralized schwarz algorithms for solving obstacle problems with t monotone operator this paper proves the convergence of some generalized schwarz algorithms for solvingthe obstacle problems with a t monotone operator numerical results show that the generalized schwarz algorithms converge faster than the classical schwarz algorithms

on monotone and geometric convergence of schwarz methods for two sided obstacle problems convergence of schwarz methods is discussed for certain discretizations of two sided obstacle problems monotone and especially geometrical convergence are established if the stiffness matrix is a kind of m matrix and an h independent convergence rate is proved for uniformly overlapping decomposition

convergence rate of a schwarz multilevel method for the constrained minimization of nonquadratic functionals in l badea convergence rate of a multiplicative schwarz method for strongly nonlinear inequalities v barbu i lasiecka d tiba and c varsan eds kluwer academic publishers boston 2003 the convergence of a subspace correction method applied to the constrained minimization of a functional in a general reflexive banach space has been proved provided that the convex set verifies a certain assumption this assumption is weaker than that in which the convex set is decomposed according to the space decomposition as a sum of subsets in the sobolev spaces the proposed method becomes a multiplicative schwarz method for the solution of the variational inequalities coming from the minimization of nonquadratic functionals we prove in this paper that this assumption holds for the one two and multilevel multiplicative schwarz methods in the finite element space and we explicitly write the constants in the error estimations depending on the overlapping and mesh parameters our error estimates are similar with those obtained for the minimization of quadratic functionals in l badea x c tai and j wang siam j numer anal 2003 pp 1052 1073 or with those obtained for the one obstacle problem in x c tai numer math 93 2003 pp 755 786

domain decomposition method for a parabolic variational inequality abstract in this paper we propose a domain decomposition method for the euler galerkin approximation of a parabolic variational inequality it is proved that the convergence rate of the algorithm is independent of the space meshsize h and the time stepsize

a state space approach to analysis of almost periodic nonlinear systems with sector nonlinearities the nonlinear system considered in this paper consists of two components a linear system and a time varying nonlinear element in the feedback connection and is almost periodic it is shown using a state space approach or lyapunov approach that if the well known circle criterion is satisfied then there exists an almost periodic solution which is uniformly asymptotically stable in the large furthermore it is also shown that the spectra of the almost periodic solution can be characterized by those of the input and the time varying nonlinearity

monotone multigrid methods for elliptic variational inequalities i we derive fast solvers for discrete elliptic variational inequalities of the first kind obstacle problems as resulting from the approximation of related continuous problems by piecewise linear finite elements using basic ideas of successive subspace correction we modify well known relaxation methods by extending the set of search directions extended underrelaxations are called monotone multigrid methods if they are quasioptimal in a certain sense by construction all monotone multigrid methods are globally convergent we take a closer look at two natural variants the standard monotone multigrid method and a truncated version for the considered model problems the asymptotic convergence rates resulting from the standard approach suffer from insufficient coarse grid transport while the truncated monotone multigrid method provides the same efficiency as in the unconstrained case

a generalization of the schwarz alternating method to an arbitrary number of subdomains we give a generalization of the schwarz alternating method to an arbitrary number of subdomains as applications we prove that the method converges for the main second order boundary value problems as well as for the system of linear elasticity for the dirichlet problems it is proved that the method converges geometrically and some numerical examples are given

geometry related convergence results for domain decomposition algorithms for general second order elliptic partial differential equations the schwarz alternating procedure is proved to converge at a rate independent of the aspect ratio for l shaped t shaped and c shaped domains these results cover both continuous and discrete versions of the schwarz algorithm moreover they apply to the nonoverlapping schur complement algorithms with the preconditioner proposed in chan siam j numer anal 24 1987 pp 382 390 in particular it is shown that the condition number of the preconditioned interface operator is bounded by 2 for all l shaped and t shaped domains this improves similar geometry independent convergence results for the schur complement algorithms obtained previously by chan and resasco advances in computer methods for partial differential equations vi r vichnevetsky and r s stepleman eds pp 317 322

convergence estimates for product iterative methods with applications to domain decomposition in this paper we consider iterative methods for the solution of symmetric positive definite problems on a space which are defined in terms of products of operators defined with respect to a number of subspaces the simplest algorithm of this sort has an error reducing operator which is the product of orthogonal projections onto the complement of the subspaces new normreduction estimates for these iterative techniques will be presented in an abstract setting applications are given for overlapping schwarz algorithms with many subregions for finite element approximation of second order elliptic problems

a delay dependent approach to h filtering for stochastic delayed jumping systems with sensor non linearities in this paper a delay dependent approach is developed to deal with the stochastic h filtering problem for a class of ito type stochastic time delay jumping systems subject to both the sensor non linearities and the exogenous non linear disturbances the time delays enter into the system states the sensor non linearities and the external non linear disturbances the purpose of the addressed filtering problem is to seek an h filter such that in the simultaneous presence of non linear disturbances sensor non linearity as well as markovian jumping parameters the filtering error dynamics for the stochastic time delay system is stochastically stable with a guaranteed disturbance rejection attenuation level by using ito s differential formula and the lyapunov stability theory we develop a linear matrix inequality approach to derive sufficient conditions under which the desired filters exist these conditions are dependent on the length of the time delay we then characterize the expression of the fi

multiscale young measures in almost periodic homogenization and applications we prove the existence of multiscale young measures associated with almost periodic homogenization we give applications of this tool in the homogenization of nonlinear partial differential equations with an almost periodic structure such as scalar conservation laws nonlinear transport equations hamilton jacobi equations and fully nonlinear elliptic equations motivated by the application in nonlinear transport equations we also prove basic results on flows generated by lipschitz almost periodic vector fields which are of interest in their own in our analysis an important role is played by the so called bohr compactification mathbb g n of mathbb r n this is a natural parameter space for the young measures our homogenization results provide also the asymptotic behavior for the whole set of mathbb g n translates of the solutions which is in the spirit of recent studies on the homogenization of stationary ergodic processes

weakly almost periodic functions and fourier stieltjes algebras of locally compact groups a noncompact locally compact group g is called an eberlein group if w g b g where w g is the algebra of continuous weakly almost periodic functions on g and b g is the uniform closure of the fourier stieltjes algebra of g we show that if g is a noncompact in group or a noncompact nilpotent group then w g b g contains a linear isometric copy of l in particular g is not an eberlein group on the other hand finite direct products of eucidean motion groups and by a result of w veech noncompact semisimple analytic groups with finite centers are eberlein groups 1 introduction let g be a locally compact group c g the space of bounded continuous complex valued functions on g with the sup norm w g the space of continuous weakly almost periodic w a p functions on g b g the fourier stieltjes algebra of g and b g its uniform closure in c g it is known that b g c w g and if g is compact then c g w g b g therefore in this paper g is assumed to be noncompact in his efforts to characterize w a p functions w f eberlein first raised the question whether for abelian g b g w g w rudin 24 made the initial contribution to this question by showing that b g c w g if g is abelian and contains a discrete subgroup which is not of bounded order and d ramirez 23 by studying discrete abelian groups with bounded orders together with the structure theorem for locally compact abelian groups was able to show that rudin s conclusion holds for all abelian groups see the monographs 4 and 11 for complete accounts of this result in this paper we will extend rudin ramirez result to include many nonabelian groups our main result is the following

a posteriori error analysis for a class of integral equations and variational inequalities we consider elliptic and parabolic variational equations and inequalities governed by integro differential operators of order 2s in 0 2 our main motivation is the pricing of european or american options under levy processes in particular pure jump processes or jump diffusion processes with tempered stable processes the problem is discretized using piecewise linear finite elements in space and the implicit euler method in time we construct a residual type a posteriori error estimator which gives a computable upper bound for the actual error in h s norm the estimator is localized in the sense that the residuals are restricted to the discrete non contact region numerical experiments illustrate the accuracy of the space and time estimators and show that they can be used to measure local errors and drive adaptive algorithms

on the schwarz alternating method with more than two subdomains for nonlinear monotone problems in a hilbert space an iterative process is defined which generalizes the schwarz alternating method for nonlinear monotone problems to more than two subdomains and the convergence of this process is proved in the case of the problems with the solution in a convex of h 0 1 omega it is proved that the method converges geometrically numerical results are given concerning the problem of elastic plastic torsion of prismatic bars and the problem of seepage of fluids through porous media

convergence rate analysis of an asynchronous space decomposition method for convex minimization we analyze the convergence rate of an asynchronous space decomposition method for constrained convex minimization in a reflexive banach space this method includes as special cases parallel domain decomposition methods and multigrid methods for solving elliptic partial differential equations in particular the method generalizes the additive schwarz domain decomposition methods to allow for asynchronous updates it also generalizes the bpx multigrid method to allow for use as solvers instead of as preconditioners possibly with asynchronous updates and is applicable to nonlinear problems applications to an overlapping domain decomposition for obstacle problems are also studied the method of this work is also closely related to relaxation methods for nonlinear network flow accordingly we specialize our convergence rate results to the above methods the asynchronous method is implementable in a multiprocessor system allowing for communication and computation delays among the processors

convergence analysis of p1 finite element method for free boundary problems on non overlapping subdomains abstract the paper applies a conforming p1 finite element method to general variational inequalities derived from free boundary problems the domain of the free boundary problem can be properly split into two non overlapping subdomains where the free boundary is located in only one subdomain the variational inequality is reduced to a partial differential equation in the subdomain which does not contain the free boundary but still keeps its original form in the other subdomain therefore the original variational inequality can be discretized separately with p1 finite element in different subdomains a non overlapping domain decomposition method is introduced to solve these two discretized sub problems by p1 finite element method iteratively while a robin type boundary condition is utilized for the data transfer on the common boundary we show that the sequence of such finite element solutions converges to the discretized solution of the original problem application to a free seepage problem verifies the theory

polynomial fuzzy model based control systems stability analysis via approximated membership functions considering sector nonlinearity of control input this paper presents the stability analysis of polynomial fuzzy model based pfmb control systems in which both the polynomial fuzzy model and the polynomial fuzzy controller are allowed to have their own set of premise membership functions in order to address the input nonlinearity the control signal is considered to be bounded by a sector with nonlinear bounds these nonlinear lower and upper bounds of the sector are constructed by combining local bounds using fuzzy blending such that local information of input nonlinearity can be taken into account with the consideration of imperfectly matched membership functions and input nonlinearity the applicability of the pfmb control scheme can be further enhanced to facilitate the stability analysis a general form of approximated membership functions representing the original ones is introduced as a result approximated membership functions can be brought into the stability analysis leading to relaxed stability conditions the sum of squares approach is employed to obtain the stability conditions based on lyapunov stability theory simulation examples are presented to demonstrate the feasibility of the proposed method

an additive schwarz method for variational inequalities this paper proposes an additive schwarz method for variational inequalities and their approximations by finite element methods the schwarz domain decomposition method is proved to converge with a geometric rate depending on the decomposition of the domain the result is based on an framework of convergence analysis established for general variational inequalities in hilbert spaces

the two scale convergence method applied to generalized besicovitch spaces the twoscale convergence method has proved to be a very useful tool for dealing with periodic homogenization problems in the present paper we develop this theory to generalized besicovitch spaces

homogenization of a stochastic nonlinear reaction diffusion equation with a large reaction term the almost periodic framework abstract homogenization of a stochastic nonlinear reaction diffusion equation with a large nonlinear term is considered under a general besicovitch almost periodicity assumption on the coefficients of the equation we prove that the sequence of solutions of the said problem converges in probability towards the solution of a rather different type of equation namely the stochastic nonlinear convection diffusion equation which we explicitly derive in terms of appropriate functionals we study some particular cases such as the periodic framework and many others this is achieved under a suitable generalized concept of convergence for stochastic processes