adaptive grid generation from harmonic maps on reimannian manifolds abstract in this paper we describe a new method for generation of solution adaptive grids based on harmonic maps on riemannian manifolds the reliability of the method is assured by an existence and uniqueness theorem for one to one maps between multidimensional multiconnected domains we formulate an adaptive riemannian metric consistent with this theorem several examples demonstrating application of the developed procedure are provided

optimal robust filtering with time varying parameter uncertainty stochastic linear systems subject to time varying parameter uncertainties affecting both system dynamics and noise statistics are considered a linear filter is used to estimate a linear combination of the states of the system when the filter is given the stabilizing solution of a suitable riccati equation is shown to yield an upper bound for the covariance of the estimator error the main problem addressed in the paper is the design of an optimal robust filter that minimizes such a covariance bound necessary conditions are given for the existence of an optimal reduced order robust filter as well as necessary and sufficient conditions for the full order case the computation of the optimal filter calls for the solution of a riccati equation that generalizes the standard riccati equation for the kalman filtering problem a numerical example is provided in which the new filter is compared with both the kalman and h filters

decentralized finite time h filtering for interconnected markovian jump system with interval mode dependent delays this paper concerns with the problem of finite time h filtering for a class of interconnected markovian jump system with mode dependent delays in the interconnection sufficient conditions guaranteeing the interconnected markovian jump systems to be finite time bounded are established by constructing an augmented lyapunov krasovskii functional the obtained conditions are delay range dependent and mode dependent based on the results the decentralized filter is proposed to guarantee the finite time bounded and h performance of the resulting augmented system for admissible disturbances the desired filter parameters can be obtained via solving a group of linear matrix inequalities lmis finally a numerical example is employed to illustrate the effectiveness of the proposed methods

robust state estimation for perturbed continuous systems with circular pole and error variance constraints in this paper the problem of circular pole and variance constrained state estimator design is studied for perturbed linear continuous time systems the system under consideration is subject to unstructured time invariant norm bounded parameter perturbations in both the state and measurement matrices the problem we address is the design of a state estimator such that for all admissible time invariant perturbations the poles of the steady state filtering matrix are assigned inside a prespecified circular region and the variance of the estimation error of each state is not more that the individual prespecified value simultaneously an algebraic riccati like matrix inequality approach is proposed to solve the above problem specifically the existence conditions and an explicit expression for the desired estimators are obtained furthermore an illustrative example is presented to demonstrate the effectiveness of the proposed design procedure

a finite volume element scheme with a monotonicity correction for anisotropic diffusion problems on general quadrilateral meshes abstract we construct a finite volume element scheme with a monotonicity correction for anisotropic diffusion problems on general quadrilateral meshes where the strict convexity restriction on the meshes is removed the main contributions of this paper include three aspects firstly the classical finite volume element c fve method is extended to severely distorted quadrilateral meshes even with concave cells by virtue of a new overlapping dual partition and a new gradient approximation in fact the choice of this dual partition and gradient approximation is also conducive to the construction of a monotone scheme secondly a new monotonicity correction is suggested based on which we obtain a monotone finite volume element m fve method the resulting m fve method still keeps the local conservation and is easy for implementation finally we analyze theoretically the truncation error and the monotonicity for this scheme besides the existence of a solution to this nonlinear scheme is proved by applying the brouwer s fixed point theorem numerical results demonstrate that the m fve method has the approximate second order accuracy and preserves well the positivity of the solution for both isotropic and anisotropic diffusion problems on severely distorted quadrilateral meshes

a comparison of implicit time integration methods for nonlinear relaxation and diffusion several time integration methods for nonlinear systems are compared all of the time discretizations are based on the method but differ in their treatment of the implicit nonlinear terms one method converges the implicit nonlinear terms to a small tolerance and is often referred to as nonlinearly consistent nc newton s method or its approximation newton krylov is used to converge the nonlinearities the other methods considered are linearized and comparisons are made for a relaxation problem and a radiation diffusion problem the linearized one step method that uses the full jacobian is shown to have similar accuracy as nc methods the lagged linearization method and an extension that is second order accurate are also studied a trunction error analysis complements the numerical results for the relaxation problem it is shown that each of the second order accurate linearized methods may be more accurate than an nc method depending on the degree of nonlinearity in the problem for the radiation diffusion problem in general the nc method is most accurate and allows a larger time step however the linearized methods perfom surprisingly well

a criterion for the equivalence of formal singularities we prove a generalization of the finite determinacy theorem for isolated singularities the maximal ideal occuring in the finite determinacy theorem is replaced by any ideal annihilating the first cotangent cohomology of a formal singularity over a noetherian ring an analogous result holds for finitely generated modules as an application we give a criterion for the algebraizability of formal singularities and modules

robust h sub 2 h sub spl infin filtering for linear systems with error variance constraints in this correspondence we consider the robust h sub 2 h sub spl infin filtering problem for linear perturbed systems with steady state error variance constraints the purpose of this multiobjective problem is to design a linear filter that does not depend on the parameter perturbations such that the following three performance requirements are simultaneously satisfied 1 the filtering process is asymptotically stable 2 the steady state variance of the estimation error of each state is not more than the individual prespecified value 3 the transfer function from exogenous noise inputs to error state outputs meets the prespecified h sub spl infin norm upper bound constraint we show that in both continuous and discrete time cases the addressed filtering problem can effectively be solved in terms of the solutions of a couple of algebraic riccati like equations inequalities we present both the existence conditions and the explicit expression of desired robust filters an illustrative numerical example is provided to demonstrate the flexibility of the proposed design approach

on designing observers for time delay systems with non linear disturbances in this paper the observer design problem is studied for a class of time delay non linear systems the system under consideration is subject to delayed state and non linear disturbances the time delay is allowed to be time varying and the non linearities are assumed to satisfy global lipschitz conditions the problem addressed is the design of state observers such that for the admissible time delay as well as non linear disturbances the dynamics of the observation error is globally exponentially stable an effective algebraic matrix inequality approach is developed to solve the non linear observer design problem specifically some conditions for the existence of the desired observers are derived and an explicit expression of desired observers is given in terms of some free parameters a simulation example is included to illustrate the practical applicability of the proposed theory

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

h optimal control part 2 solution for controllers abstract the problem is considered of bounding the h norm of the transfer function t y1u1 relating the output y 1 to the input u 1 for the feedback configuration shown in fig 1 subject to the closed loop system being internally stable a new criterion for internal stability is derived in terms of the q parameterization where q k i p22 k 1 by means of such a stability theory it is shown that the h control problem can be decomposed into two one sided model matching problems of the form considered in part 1 hung 1989 of the paper a closed form state space solution with a tight mcmillan degree bound is obtained for h optimal or suboptimal controllers an iterative algorithm for obtaining the h optimal controller is provided computationally the algorithm requires the solution of only two algebraic riccati equations in each iteration for which the upper bound on t y1u1 is adjusted

robust kalman filtering for discrete time varying uncertain systems with multiplicative noises in this paper a robust finite horizon kalman filter is designed for discrete time varying uncertain systems with both additive and multiplicative noises the system under consideration is subject to both deterministic and stochastic uncertainties sufficient conditions for the filter to guarantee an optimized upper bound on the state estimation error variance for admissible uncertainties are established in terms of two discrete riccati difference equations a numerical example is given to show the applicability of the presented method

robust spl hscr sub spl infin filtering for continuous time varying uncertain systems with deterministic input signals many dynamical systems involve not only process and measurement noise signals but also parameter uncertainty and known input signals when spl lscr sub 2 or spl hscr sub spl infin filters that were designed based on a nominal model of the system are applied the presence of parameter uncertainty will not only affect the noise attenuation property of the filter but also introduce a bias proportional to the known input signal and the latter may be very appreciable we introduce a finite horizon robust spl hscr sub spl infin filtering method that provides a guaranteed spl hscr sub spl infin bound for the estimation error in the presence of both parameter uncertainty and a known input signal this method is developed by using a game theoretic approach and the results generalize those obtained for cases without parameter uncertainty or without a known input signal it is also demonstrated via an example that the proposed method provides significantly improved signal estimates

moving mesh methods based on moving mesh partial differential equations several versions of a moving mesh method are developed based on a mesh spatial smoothing technique and on the moving mesh pdes derived in a previous paper these versions are quite simple and easy to program they are applied to three bench mark one dimensional problems which show different solution behaviour the numerical results clearly demonstrate that the present methods are capable of accurately tracking rapid spatial and temporal transitions

steady state kalman filtering with an h error bound abstract an estimator design problem is considered which involves both l 2 least squares and h worst case frequency domain aspects specifically the goal of the problem is to minimize an l 2 state estimation error criterion subject to a prespecified h constraint on the state estimation error the h estimation error constraint is embedded within the optimization process by replacing the covariance lyapunov equation by a riccati equation whose solution leads to an upper bound on the l 2 state estimation error the principal result is a sufficient condition for characterizing fixed order i e full and reduced order estimators with bounded l 2 and h estimation error the sufficient condition involves a system of modified riccati equations coupled by an oblique projection i e idempotent matrix when the h constraint is absent the sufficient condition specializes to the l 2 state estimation result given in 2

on balanced approximations for time integration of multiple time scale systems the effect of various numerical approximations used to solve linear and nonlinear problems with multiple time scales is studied in the framework of modified equation analysis mea first mea is used to study the effect of linearization and splitting in a simple nonlinear ordinary differential equation ode and in a linear partial differential equation pde several time discretizations of the ode and pde are considered and the resulting truncation terms are compared analytically and numerically it is demonstrated quantitatively that both linearization and splitting can result in accuracy degradation when a computational time step larger than any of the competing fast time scales is employed many of the issues uncovered on the simple problems are shown to persist in more realistic applications specifically several differencing schemes using linearization and or time splitting are applied to problems in nonequilibrium radiation diffusion magnetohydrodynamics and shallow water flow and their solutions are compared to those using balanced time integration methods

the fast adaptive composite grid fac method for elliptic equation the fast adaptive composite grid fag method is a systematic process for solving differential boundary value problems fac uses global and local uniform grids both to define the composite grid problem and to interact for its fast solution it can with little added cost substantially improve accuracy of the coarse grid solution and is very suitable for vector and parallel computation this paper develops both the theoretical and practical aspects of fac as it applies to elliptic problems 1 introduction the need for local resolution in physical models occurs frequently in practice special local features of the forcing function operator coefficients boundary and boundary conditions can demand resolution in restricted regions of the domain that is much finer than the required global resolution it is important that the discretization and solution processes account for this locally that is that the local phenomena do not precipitate a dramatic increase in the overall computation unfortunately this objective of efficiently adapting to local features is often in conflict with the solution process equation solvers can degrade or even fail to apply in the presence of varying discretization scales data structures that account for irregular grids can be cumbersome the computer architecture may not be able to effectively account for grid irregularity e g vectorizability may be inhibited etc in fact even the discretization process itself may find difficulty with this objective for finite differences it is problematic to develop accurate difference formulae for irregular grids for finite elements this objective is reflected in the substantial overhead costs needed to automate the discretization the fast adaptive composite grid method fac 11 is a discretization and solution method designed to achieve efficient local resolution by constructing the

filtering for nonlinear genetic regulatory networks with stochastic disturbances in this paper the filtering problem is investigated for nonlinear genetic regulatory networks with stochastic disturbances and time delays where the nonlinear function describing the feedback regulation is assumed to satisfy the sector condition the stochastic perturbation is in the form of a scalar brownian motion and the time delays exist in both the translation process and the feedback regulation process the purpose of the addressed filtering problem is to estimate the true concentrations of the mrna and protein specifically we are interested in designing a linear filter such that in the presence of time delays stochastic disturbances as well as sector nonlinearities the filtering dynamics of state estimation for the stochastic genetic regulatory network is exponentially mean square stable with a prescribed decay rate lower bound beta by using the linear matrix inequality lmi technique sufficient conditions are first derived for ensuring the desired filtering performance for the gene regulatory model and the filter gain is then characterized in terms of the solution to an lmi which can be easily solved by using standard software packages a simulation example is exploited in order to illustrate the effectiveness of the proposed design procedures

practical aspects of formulation and solution of moving mesh partial differential equations moving mesh partial differential equations mmpdes are used in the mmpde moving mesh method to generate adaptive moving meshes for the numerical solution of time dependent problems how mmpdes are formulated and solved is crucial to the efficiency and robustness of the method in this paper several practical aspects of formulating and solving mmpdes are studied they include spatial balance scaling invariance effective control of mesh concentration bounds on time steps multiple sub steps and two level mesh movement numerical results are also given c 2001 academic press

a parameter dependent approach to robust h_ infty filtering for time delay systems this paper is concerned with the problem of robust h infin filtering for linear continuous time systems with polytopic parameter uncertainties and time varying delay in the state we utilize the polynomially parameter dependent idea to solve the robust h infin filtering problem with new linear matrix inequality conditions obtained for the existence of admissible filters these conditions are developed based on homogeneous polynomially parameter dependent matrices of arbitrary degree the delay dependence and polynomial parameter dependence guarantee the proposed approach to be potentially less conservative which is shown via a numerical example

design of low order linear phase iir filters via orthogonal projection this paper presents an indirect linear phase iir filter design technique based on a reduction of linear phase fir filters the desired filter is obtained by minimizing the l sub 2 norm of the difference between the original fir filter and the lower order iir filter we first establish a relationship between the hankel singular values of the discarded part of the fir filter and the l sub 2 norm of the corresponding filter approximation error based on model truncation this result motivates us to propose a simple finite search method that will achieve better approximation results than commonly used truncation methods such as the balanced truncation bt and the impulse response gramian irg methods we then develop an iterative algorithm for finding an optimal iir filter based on a matrix projection of the original fir filter the convergence of the proposed algorithm is established filters designed using the proposed algorithm are compared with those obtained by other techniques with respect to the amplitude response and group delay characteristics in the passband numerical examples show that the proposed algorithm offers the best performance

h sub infinity minimum error state estimation of linear stationary processes a state estimator is derived which minimizes the h sub infinity norm of the estimation error power spectrum matrix two approaches are presented the first achieves the optimal estimator in the frequency domain by finding the filter transfer function matrix that leads to an equalizing solution the second approach establishes a duality between the problem of h sub infinity filtering and the problem of unconstrained input h sub infinity optimal regulation using this duality previously published results for the latter regulation problem are applied which lead to an optimal filter that possess the structure of the corresponding kalman filter the two approaches usually lead to different results they are compared by a simple example which also demonstrates a clear advantage of the h sub infinity estimate over the conventional l sub 2 estimate

input to state stable nonlinear filtering for a class of continuous time delayed nonlinear systems this paper investigates the input to state stable iss nonlinear filtering problem for a class of continuous time delayed nonlinear systems with external disturbance a new delay dependent nonlinear iss filter is established through available measurements to estimate the states of delayed nonlinear systems such that the filtering error system is both exponentially and input to state stable for any bounded external disturbance the design of the nonlinear iss filter for these nonlinear systems is achieved by solving a linear matrix inequality lmi which can be easily facilitated by using standard numerical packages an illustrative example is given to demonstrate the effectiveness of the proposed filter

finite escapes and convergence properties of guaranteed cost robust filters the design of robust filters for linear time varying systems subject to parameter perturbations is considered the design is based on the minimization of an upper bound for the error covariance the computation of the filter matrices calls for the solution of a pair of differential riccati equations parameterized by a scalar design parameter the main results of the paper concern the asymptotic properties of the filter when it is applied to time invariant systems differently from the standard kalman filter the robust filter may abruptedly cease to exist owing to the presence of finite escape times in the associated riccati equations nevertheless provided that the parameter perturbations do not affect the unstable dynamics convergence to a stable steady state filter can always be ensured by properly adjusting the scalar design parameter since such an adjustment might deteriorate the steady state performance a time varying strategy for the tuning of the scalar parameter is developed in order to guarantee both convergence and performance

robust h sub 2 filtering for uncertain systems with measurable inputs this paper deals with the robust minimum variance filtering problem for linear time varying systems subject to a measurable input and to norm bounded parameter uncertainty in the state and or the output matrices of the state space model the problem addressed is the design of linear filters having an error variance with a guaranteed upper bound for any allowed uncertainty and any input of bounded energy three types of input signals are considered a signal that is a priori known for the whole time interval an unknown signal of very large bandwidth that is perfectly measured on line and a large bandwidth signal that is measured ahead of time in a fixed preview time interval both the time varying finite horizon and stationary infinite horizon cases are treated

decentralized adaptive neural control for high order stochastic nonlinear strongly interconnected systems with unknown system dynamics abstract this paper studies the problem of decentralized adaptive neural backstepping control for a class of high order stochastic nonlinear systems with unknown strongly interconnected nonlinearity during the control of the high order nonlinear interconnected systems only one adaptive parameter is used to overcome the over parameterization problem and radial basis function rbf neural networks are employed to tackle the difficulties brought about by completely unknown system dynamics and stochastic disturbances in addition to address the problem arising from high order strongly interconnected nonlinearities with full states of the overall system the variable separation technique is introduced based on the monotonically increasing property of the bounding functions next a decentralized adaptive neural control method is proposed based on lyapunov stability theory in which the controller is designed to decrease the number of learning parameters it is shown that the designed controller can ensure that all the signals in the closed loop system are 4 moment or 2 moment semi globally uniformly ultimately bounded sguub and the tracking error converges to a small neighborhood of the origin finally two simulation examples are offered to illustrate the effectiveness of the proposed control scheme

robust kalman filtering for continuous time lag systems the linear continuous time kalman filter for a class of time lag systems with norm bounded uncertain parameters is considered we investigate the conditions for linear delayless state estimator such that the estimation error covariance is guaranteed to lie within a prescribed bound for all admissible uncertainties it is proven that a robust kalman filter algorithm can be determined in terms of two riccati equations involving scalar parameters the developed theory is illustrated by numerical simulation

a linear matrix inequality approach to robust h sub spl infin filtering we consider the robust h sub spl infin filtering problem for a general class of uncertain linear systems described by the so called integral quadratic constraints iqcs this problem is important in many signal processing applications where noise nonlinearity quantization errors time delays and unmodeled dynamics can be naturally described by iqcs the main contribution of this paper is to show that the robust h spl infin filtering problem can be solved using linear matrix inequality lmi techniques which are numerically efficient owing to recent advances in convex optimization the paper deals with both continuous and discrete time uncertain linear systems

robust kalman filtering for uncertain systems abstract this paper studies the problem of kalman filter design for uncertain systems the system under consideration is subjected to time varying norm bounded parameter uncertainties in both the state and measurement matrices the problem we address is the design of a state estimator such that the covariance of the estimation error is guaranteed to be within a certain bound for all admissible uncertainties a riccati equation approach is proposed to solve the above problem furthermore a suboptimal covariance upper bound can be computed by a convex optimization

robust filter design with time varying parameter uncertainty and error variance constraints in this paper we consider the design of robust filters for linear continuous and discrete time systems subjected to timevarying parameter uncertainties and estimation error variance constraints the problem addressed is the design of robust filters which do not depend on uncertainty such that for all admissible time varying parameter perturbations the variance of the estimation error of each state is guaranteed to be not more than the individual prespecified upper bound in both continuous and discrete time cases it is shown that the computation of the filter matrices calls for the solution of a pair of algebraic riccati equations specifically the existence conditions and the explicit expression of the desired filters are obtained furthermore two illustrative examples are presented to demonstrate the effectiveness of the proposed design procedure

variational mesh adaptation isotropy and equidistribution we present a new approach for developing more robust and error oriented mesh adaptation methods specifically assuming that a regular in cell shape and uniform in cell size computational mesh is used as is commonly done in computation we develop a criterion for mesh adaptation based on an error function whose definition is motivated by the analysis of function variation and local error behavior for linear interpolation the criterion is then decomposed into two aspects the isotropy or conformity and uniformity or equidistribution requirements each of which can be easier to deal with the functionals that satisfy these conditions approximately are constructed using discrete and continuous inequalities a new functional is finally formulated by combining the functionals corresponding to the isotropy and uniformity requirements the features of the functional are analyzed and demonstrated by numerical results in particular unlike the existing mesh adaptation functionals the new functional has clear geometric meanings of minimization a mesh that has the desired properties of isotropy and equidistribution can be obtained by properly choosing the values of two parameters the analysis presented in this article also provides a better understanding of the increasingly popular method of harmonic mapping in two dimensions

robust h exponential filtering for uncertain stochastic time delay systems with markovian switching and nonlinearities in this paper we deal with the robust h exponential filtering problem for a class of uncertain stochastic time delay systems with markovian switching and nonlinear disturbances the system under consideration involves parameter uncertainties ito type stochastic disturbances markovian jump parameters unknown nonlinear disturbances as well as time varying delays which vary in a range and dependent on the mode of the operation the aim of this problem is to design a markovian jump exponential filter such that the filtering error system is robustly stochastically exponentially mean square stable and a prescribed h disturbance attenuation level is guaranteed novel delay range dependent sufficient conditions are proposed to guarantee the existence of the desired robust exponential filter which are derived in terms of linear matrix inequalities lmis then the explicit expression of the desired filter parameters is characterized an illustrative numerical example is provided to demonstrate the effectiveness of the proposed method

technical communique robust h observer design of linear state delayed systems with parametric uncertainty the discrete time case in this note we consider the problem of h observer design for a class of uncertain linear discrete time systems with delayed state and parameter uncertainties the goal of this problem is to design a linear state observer such that for the positive integer state time delay and all admissible norm bounded parameter uncertainties the observation process remains robustly stable and the transfer function from exogenous disturbances to error state outputs meets the prespecified h norm upper bound constraint the observer structure does not depend on the parameter uncertainties a simple effective algebraic methodology is developed to derive the conditions for the existence of the desired robust h observers and the analytical expression of these observers is then characterized in terms of the matrix riccati like equations inequalities we provide a numerical example to demonstrate the validity and the applicability of the proposed approach

optimal linear filtering under parameter uncertainty this paper addresses the problem of designing a guaranteed minimum error variance robust filter for convex bounded parameter uncertainty in the state output and input matrices the design procedure is valid for linear filters that are obtained from the minimization of an upper bound of the error variance holding for all admissible parameter uncertainty the results provided generalize the ones available in the literature to date in several directions first all system matrices can be corrupted by parameter uncertainty and the admissible uncertainty may be structured assuming the order of the uncertain system is known the optimal robust linear filter is proved to be of the same order as the order of the system in the present case of convex bounded parameter uncertainty the basic numerical design tools are linear matrix inequality lmi solvers instead of the riccati equation solvers used for the design of robust filters available in the literature to date the paper that contains the most important and very recent results on robust filtering is used for comparison purposes in particular it is shown that under the same assumptions our results are generally better as far as the minimization of a guaranteed error variance is considered some numerical examples illustrate the theoretical results

on the almost sure and mean square exponential convergence of some stochastic observers it is pointed out that linear observers used for estimating the state of the discrete time stochastic parameter systems are both almost surely and mean square ms exponentially convergent under the same conditions guaranteeing mean square convergence in addition to the mean square convergence properties of linear observers constructed for mean square stable stochastic parameter systems they also possess an almost sure exponential convergence property and the rate of ms convergence is exponential this rate depends on the parameters used in the design

filtering and smoothing in an h sup infinity setting the problems of filtering and smoothing are considered for linear systems in an h sup infinity setting i e the plant and measurement noises have bounded energies are in l sub 2 but are otherwise arbitrary two distinct situations for the initial condition of the system are considered the initial condition is assumed known in one case while in the other the initial condition is not known but the initial condition the plant and measurement noise are in some weighted ball of r sup n xl sub 2 finite horizon and infinite horizon cases are considered necessary and sufficient conditions are presented for the existence of estimators both filters and smoothers that achieve a prescribed performance bound and algorithms that result in performance within the bounds are developed in case of smoothers the optimal smoother is also presented the approach uses basic quadratic optimization theory in a time domain setting as a consequence of which both linear time varying and time invariant systems can be considered with equal ease in the smoothing problem for linear time varying systems one considers only the finite horizon case

variational mesh adaptation ii error estimates and monitor functions the key to the success of a variational mesh adaptation method is to define a proper monitor function which controls mesh adaptation in this paper we study the choice of the monitor function for the variational adaptive mesh method developed in the previous work j comput phys 174 2001 924 two types of monitor functions scalar matrix and non scalar matrix ones are defined based on asymptotic estimates of interpolation error obtained using the interpolation theory of finite element methods the choice of the adaptation intensity parameter is also discussed for each of these monitor functions asymptotic bounds on interpolation error are obtained for adaptive meshes that satisfy the regularity and equidistribution conditions two dimensional numerical results are given to verify the theoretical findings

robust stabilization of uncertain linear systems quadratic stabilizability and h sup infinity control theory the problem of robustly stabilizing a linear uncertain system is considered with emphasis on the interplay between the time domain results on the quadratic stabilization of uncertain systems and the frequency domain results on h sup infinity optimization a complete solution to a certain quadratic stabilization problem in which uncertainty enters both the state and the input matrices of the system is given relations between these robust stabilization problems and h sup infinity control theory are explored it is also shown that in a number of cases if a robust stabilization problem can be solved via lyapunov methods then it can be also be solved via h sup infinity control theory based methods

robust minimum variance filtering this paper deals with the robust minimum variance filtering problem for linear systems subject to norm bounded parameter uncertainty in both the state and the output matrices of the state space model the problem addressed is the design of linear filters having an error variance with a guaranteed upper bound for any allowed uncertainty two methods for designing robust filters are investigated the first one deals with constant parameter uncertainty and focuses on the design of steady state filters that yield an upper bound to the worst case asymptotic error variance this bound depends on an upper bound for the power spectrum density of a signal at a specific point in the system and it can be made tighter if a tight bound on the latter power spectrum can be obtained the second method allows for time varying parameter uncertainty and for general time varying systems and is more systematic we develop filters with an optimized upper bound for the error variance for both finite and infinite horizon filtering problems

a moving mesh finite difference method for equilibrium radiation diffusion equations an efficient moving mesh finite difference method is developed for the numerical solution of equilibrium radiation diffusion equations in two dimensions the method is based on the moving mesh partial differential equation approach and moves the mesh continuously in time using a system of meshing partial differential equations the mesh adaptation is controlled through a hessian based monitor function and the so called equidistribution and alignment principles several challenging issues in the numerical solution are addressed particularly the radiation diffusion coefficient depends on the energy density highly nonlinearly this nonlinearity is treated using a predictor corrector and lagged diffusion strategy moreover the nonnegativity of the energy density is maintained using a cutoff method which has been known in literature to retain the accuracy and convergence order of finite difference approximation for parabolic equations numerical examples with multi material multiple spot concentration situations are presented numerical results show that the method works well for radiation diffusion equations and can produce numerical solutions of good accuracy it is also shown that a two level mesh movement strategy can significantly improve the efficiency of the computation

robustness of exponential stability of stochastic differential delay equations regard the stochastic differential delay equation dx t a a t b b t spl tau x t spl tau dt g t x t x t spl tau dw t as the result of the effects of uncertainty stochastic perturbation and time lag to a linear ordinary differential equation x spl dot t a b x t assume the linear system is exponentially stable in this paper we characterize how much the uncertainty stochastic perturbation and time lag the linear system can bear such that the stochastic delay system remains exponentially stable the result can also be extended to nonlinear systems

numerical analysis of time integration errors for nonequilibrium radiation diffusion numerical analysis of time integration errors for nonequilibrium radiation diffusion is considered two first order implicit time integration methods are studied asymptotic analysis and modified equation analysis are applied to both time integration methods numerical experiments are used to highlight the results of the analysis asymptotic analysis is used to highlight the source of temperature spiking when a hot radiation wave propagates into a cold material modified equation analysis is used to provide insight into the thermal wave speed coming from the two different first order methods

robust state estimation for uncertain neural networks with time varying delay the robust state estimation problem for a class of uncertain neural networks with time varying delay is studied in this paper the parameter uncertainties are assumed to be norm bounded based on a new bounding technique a sufficient condition is presented to guarantee the existence of the desired state estimator for the uncertain delayed neural networks the criterion is dependent on the size of the time varying delay and on the size of the time derivative of the time varying delay it is shown that the design of the robust state estimator for such neural networks can be achieved by solving a linear matrix inequality lmi which can be easily facilitated by using some standard numerical packages finally two simulation examples are given to demonstrate the effectiveness of the developed approach

the extended kalman filter as an exponential observer for nonlinear systems we analyze the behavior of the extended kalman filter as a state estimator for nonlinear deterministic systems using the direct method of lyapunov we prove that under certain conditions the extended kalman filter is an exponential observer i e the dynamics of the estimation error is exponentially stable furthermore we discuss a generalization of the kalman filter with exponential data weighting to nonlinear systems

stability analysis and observer design for neutral delay systems this paper deals with the observer design problem for a class of linear delay systems of the neutral type the problem addressed is that of designing a full order observer that guarantees the exponential stability of the error dynamic system an effective algebraic matrix equation approach is developed to solve this problem in particular both the observer analysis and design problems are investigated by using the singular value decomposition technique and the generalized inverse theory sufficient conditions for a neutral type delay system to be exponentially stable are first established then an explicit expression of the desired observers is derived in terms of some free parameters furthermore an illustrative example is used to demonstrate the validity of the proposed design procedure

robust h sub 2 h sub spl infin state estimation for systems with error variance constraints the continuous time case the paper is concerned with the state estimator design problem for perturbed linear continuous time systems with h sub spl infin norm and variance constraints the perturbation is assumed to be time invariant and norm bounded and enters into both the state and measurement matrices the problem we address is to design a linear state estimator such that for all admissible measurable perturbations the variance of the estimation error of each state is not more than the individual prespecified value and the transfer function from disturbances to error state outputs satisfies the prespecified h sub spl infin norm upper bound constraint simultaneously existence conditions of the desired estimators are derived in terms of riccati type matrix inequalities and the analytical expression of these estimators is also presented a numerical example is provided to show the directness and effectiveness of the proposed design approach

robust filtering for a class of stochastic uncertain nonlinear time delay systems via exponential state estimation we investigate the robust filter design problem for a class of nonlinear time delay stochastic systems the system under study involves stochastics unknown state time delay parameter uncertainties and unknown nonlinear disturbances which are all often encountered in practice and the sources of instability the aim of this problem is to design a linear delayless uncertainty independent state estimator such that for all admissible uncertainties as well as nonlinear disturbances the dynamics of the estimation error is stochastically exponentially stable in the mean square independent of the time delay sufficient conditions are proposed to guarantee the existence of desired robust exponential filters which are derived in terms of the solutions to algebraic riccati inequalities the developed theory is illustrated by numerical simulation

the cutoff method for the numerical computation of nonnegative solutions of parabolic pdes with application to anisotropic diffusion and lubrication type equations the cutoff method which cuts off the values of a function less than a given number is studied for the numerical computation of nonnegative solutions of parabolic partial differential equations a convergence analysis is given for a broad class of finite difference methods combined with cutoff for linear parabolic equations two applications are investigated linear anisotropic diffusion problems satisfying the setting of the convergence analysis and nonlinear lubrication type equations for which it is unclear if the convergence analysis applies the numerical results are shown to be consistent with the theory and in good agreement with existing results in the literature the convergence analysis and applications demonstrate that the cutoff method is an effective tool for use in the computation of nonnegative solutions cutoff can also be used with other discretization methods such as collocation finite volume finite element and spectral methods and for the computation of positive solutions