rotational degeneracy of hyperbolic systems of conservation laws the purpose of the paper is to study wave patterns of hyperbolic systems in which rotational symmetry creates a specific kind of degeneracy in this situation hyperbolicity is necessarily non strict so that the elementary waves have interesting patterns the discussion is centered around a theorem on existence and uniqueness of solutions of the riemann problem we give a unified presentation of examples from continuum mechanics

an organizing center for wave bifurcation in multiphase flow models we consider a one parameter family of nonstrictly hyperbolic systems of conservation laws modeling three phase flow in a porous medium for a particular value of the parameter the model has a shock wave solution that undergoes several bifurcations upon perturbation of its left and right states and the parameter in this paper we use singularity theory and bifurcation theory of dynamical systems including melnikov s method to find all nearby shock waves that are admissible according to the viscous profile criterion we use these results to construct a unique solution of the riemann problem for each left and right state and parameter value in a neighborhood of the unperturbed shock wave solution together with previous numerical work this construction completes the solution of the three phase flow model in the bifurcation analysis the unperturbed shock wave acts as an organizing center for the waves appearing in riemann solutions

the riemann problem near a hyperbolic singularity ii this paper is interested in classifying the solutions of riemann problems for the 2 times 2 conservation laws that have homogeneous quadratic flux functions such flux functions approximate an arbitrary 2 times 2 system in a neighborhood of an isolated point where strict hyperbolicity fails here the solution for the symmetric systems in region iii of the four region classification of schaeffer and shearer is given the solution is based on the qualitative shape of the integral curves described by schaeffer and shearer and a numerical calculation of the hugoniot loci and their shock types

robust h sup spl infin filtering for uncertain markovian jump systems with mode dependent time delays this paper considers the problem of robust h sup spl infin filtering for uncertain markovian jump linear systems with time delays which are time varying and depend on the system mode the parameter uncertainties are time varying norm bounded the aim of this problem is to design a markovian jump linear filter that ensures robust exponential mean square stability of the filtering error system and a prescribed l sub 2 induced gain from the noise signals to the estimation error for all admissible uncertainties a sufficient condition for the solvability of this problem is obtained the desired filter can be constructed by solving a set of linear matrix inequalities an illustrative numerical example is provided to demonstrate the effectiveness of the proposed approach

network based robust h_infty filtering for uncertain linear systems the problem of network based robust hinfin filtering for uncertain linear systems is investigated different from the design of the traditional filter the effects of the network induced delay and data dropout on the performance of a filtering error system are considered the derived criteria for hinfin performance analysis of the filtering error system and filter design are expressed as a set of linear matrix inequalities which can be solved by using convex optimization method numerical examples show the effectiveness of the design method

novel delay dependent kalman luenberger type filter design for neutral systems this article presents a new delay dependent condition to design a kalman luenberger type filter for neutral systems where the resulting filter is such that a prescribed level is guaranteed the proposed approach is based on linear matrix inequalities and on lyapunov krasovskii theory also the gu s discretisation method and a slack matrix technique that decouples the system matrices from the lyapunov ones are applied in order to obtain less conservative results than the similar ones two numerical examples are performed to illustrate the advantage of the method proposed

a global formalism for nonlinear waves in conservation laws we introduce a unifying framework for treating all of the fundamental waves occurring in general systems ofn conservation laws fundamental waves are represented as pairs of states statisfying the rankine hugoniot conditions after trivial solutions have been eliminated by means of a blow up procedure these pairs form an n 1 dimensional manifold the fundamental wave manifold there is a distinguishedn dimensional submanifold of containing a single one dimensonal foliation that represents the rarefaction curves for all families similarly there is a foliation of itself that represent shock curves we identify othern dimensional submanifolds of that are naturally interpreted as boundaries of regions of admissible shock waves these submanifolds also have one dimensional foliations which represent curves of composite waves this geometric framework promises to simplify greatly the study of the stability and bifurcation properties

structurally stable riemann solutions abstract we study the structure of solutions of riemann problems for systems of two conservation laws such a solution comprises a sequence of elementary waves viz rarefaction and shock waves of various types shock waves are required to have viscous profiles we construct a riemann solution by solving a system of equations characterizing its component waves a riemann solution is structurally stable if the number and types of its component waves are preserved when the initial data and the flux function are perturbed under the assumption that rarefaction waves and shock states lie in the stricly hyperbolic region we characterize riemann solutions for which the definition equations have maximal rank and we prove that such solutions are structurally stable structurally stable riemann solutions cannot contain overcompressive shock waves but they can contain transitional shock waves including doubly sonic transitional shock waves including doubly sonic transitional shock waves that have not been observed before

the classification of 2 2 systems of non strictly hyperbolic conservation laws with application to oil recovery on considere un systeme 2 2 a une variable d espace u f u x 0 0 ou u u x t r 2 et f r 2 r 2 on montre que pour des equations hyperboliques des points ombilicaux sont typiquement isoles et que en un point ombilical isole df est typiquement diagonalisable on donne une classification des equations hyperboliques a points ombilicaux isoles

on the riemann problem for a prototype of a mixed type conservation law we study the system of conservation laws given by with initial value the system is elliptic when u2 v2 2 and hyperbolic when u2 v2 2 following liu s construction it is found that the system always has a weak solution which however is not necessarily unique

multiobjective output feedback control via lmi optimization this paper presents an overview of a linear matrix inequality lmi approach to the multiobjective synthesis of linear output feedback controllers the design objectives can be a mix of h sub spl infin performance h sub 2 performance passivity asymptotic disturbance rejection time domain constraints and constraints on the closed loop pole location in addition these objectives can be specified on different channels of the closed loop system when all objectives are formulated in terms of a common lyapunov function controller design amounts to solving a system of linear matrix inequalities the validity of this approach is illustrated by a realistic design example

comments on robust stabilization of a class of time delay nonlinear systems in this paper we point out an error in the above paper by nguang ibid vol 45 2000 which shows that the main result of the paper cannot stand in the paper the nguang considers the problem of robust stabilization of a class of triangular nonlinear system and develops an iterative procedure of constructing a stabilization controller based on the constructive use of appropriate lyapunov krasovskii functions however we show in this note that there is an error in the paper which leads to the failure of the iterative procedure so the conclusion cannot stand

fuzzy h_ infty filter design for a class of nonlinear discrete time systems with multiple time delays this paper studies the fuzzy hinfin filter design problem for signal estimation of nonlinear discrete time systems with multiple time delays and unknown bounded disturbances first the takagi sugeno t s fuzzy model is used to represent the state space model of nonlinear discrete time systems with time delays next we design a stable fuzzy hinfin filter based on the t s fuzzy model which guarantees asymptotic stability and a prescribed hinfin index for the filtering error system irrespective of the time delays and uncertain disturbances a sufficient condition for the existence of such a filter is established by using the linear matrix inequality lmi approach the proposed lmi problem can be efficiently solved with global convergence guarantee using convex optimization techniques such as the interior point algorithm simulation examples are provided to illustrate the design procedure of the present 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

robust mixed h_2 h_infty filtering for time delay fuzzy systems in this paper a robust mixed h2 hinfin filtering problem for continuous time fuzzy systems subject to parameter uncertainties and multiple time varying delays in state variables is addressed the uncertain systems are expressed as takagi sugeno fuzzy models with linear nominal parts and norm bounded uncertainties the main objective is to design stable filters that minimize a guaranteed cost index and achieve a prescribed hinfin performance under worst case disturbance based on lyapunov theory both delay independent and delay dependent sufficient conditions guaranteeing stability and achieving prescribed performances are stated in terms of linear matrix inequalities therefore stable filters can be obtained easily with existing convex algorithms lastly two examples are given to illustrate the proposed design methodology

degenerate hyperbolic conservation laws with dissipation reduction to and validity of a class of burgers type equations a conservation law is said to be degenerate or critical if the jacobian of the flux vector evaluated on a constant state has a zero eigenvalue in this paper it is proved that a degenerate conservation law with dissipation will generate dynamics on a long time scale that resembles burger s dynamics the case of k fold degeneracy is also treated and it is shown that it leads to a reduction to a quadratically coupled k fold system of burgers type equations validity of the reduction and existence for the reduced system is proved in the class of uniformly local spaces thereby capturing both finite and infinite energy solutions the theory is applied to some examples from stratified shallow water hydrodynamics that model the birth of hydraulic jumps

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

brief paper robust h filtering for a class of uncertain linear systems with time varying delay this paper deals with the problem of delay dependent robust h filtering for uncertain linear systems with time varying delay two cases of time varying delays are fully considered one is the time varying delay being continuous uniformly bounded while the other is the time varying delay being differentiable uniformly bounded with delay derivative bounded by a constant a stable linear filter is designed to ensure that the filtering error system is asymptotically stable with a prescribed level of h noise attenuation based on a new integral inequality delay dependent sufficient conditions for the existence of such a filter are established in terms of linear matrix inequalities lmis through deriving these conditions neither model transformation nor bounding technique for cross terms is employed moreover the relationship between the sufficient conditions for the two cases of time varying delay is disclosed finally two examples are also given to illustrate the effectiveness of the proposed methodology

robust h sub spl infin filter design of uncertain descriptor systems with discrete and distributed delays the robust h sub spl infin filtering problem for a class of continuous time uncertain linear descriptor systems with time varying discrete and distributed delays is investigated the time delays are assumed to be constant and known the uncertainties under consideration are norm bounded and possible time varying uncertainties sufficient condition for the existence of an h sub spl infin filter is expressed in terms of strict linear matrix inequalities lmis instead of using decomposition technique a unified form of lmis is proposed to show the exponential stability of the augmented systems the condition for assuring the stability of the fast subsystem is implied from the unified form of lmis which is shown to be less conservative than the characteristic equation based conditions or matrix norm based conditions the suitable filter is derived through a convex optimization problem a numerical example is given to show the effectiveness of the method

robust h sub spl infin filtering for stochastic time delay systems with missing measurements in this paper the robust hinfin filtering problem is studied for stochastic uncertain discrete time delay systems with missing measurements the missing measurements are described by a binary switching sequence satisfying a conditional probability distribution we aim to design filters such that for all possible missing observations and all admissible parameter uncertainties the filtering error system is exponentially mean square stable and the prescribed hinfin performance constraint is met in terms of certain linear matrix inequalities lmis sufficient conditions for the solvability of the addressed problem are obtained when these lmis are feasible an explicit expression of a desired robust hinfin filter is also given an optimization problem is subsequently formulated by optimizing the hinfin filtering performances finally a numerical example is provided to demonstrate the effectiveness and applicability of the proposed design approach

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

a higher order godunov method for modeling finite deformation in elastic plastic solids in this paper we develop a first order system of conservation laws for finite deformation in solids describe its characteristic structure and use this analysis to develop a second order numerical method for problems involving finite deformation and plasticity the equations of mass momentum and energy conservation in lagrangian and eulerian frames of reference are combined with kinetic equations of state for the stress and with caloric equations of state for the internal energy as well as with auxiliary equations representing equality of mixed partial derivatives of the deformation gradient particular attention is paid to the influence of a curl constraint on the deformation gradient so that the characteristic speeds transform properly between the two frames of reference next we consider models in rate form for isotropic elastic plastic materials with work hardening and examine the circumstances under which these models lead to hyperbolic systems for the equations of motion in spite of the fact that these models violate thermodynamic principles in such a way that the acoustic tensor becomes nonsymmetric we still find that the characteristic speeds are always real for elastic behavior and essentially always real for plastic response these results allow us to construct a second order godunov method for the computation of three dimensional displacement in a one dimensional material viewed in the lagrangian frame of reference we also describe a technique for the approximate solution of riemann problems in order to determine numerical fluxes in this algorithm finally we present numerical examples of the results of the algorithm

h filter design for discrete delay systems a new parameter dependent approach this article revisits the problem of h filtering for discrete time systems with a time varying delay in the state and parameter uncertainties residing in a polytope by utilising the polynomially parameter dependent idea a new filter design procedure is proposed which formulates the existence of admissible robust h filters into a set of linear matrix inequalities these conditions are developed based on homogeneous polynomially parameter dependent matrices of an arbitrary degree as the degree grows test of increasing precision is obtained providing less conservative filter designs it is established that the results in the quadratic framework that entail fixed matrices for the entire uncertainty domain and the linearly parameter dependent framework that use linear convex combinations of matrices are special cases of the proposed conditions for the zeroth degree and the first degree respectively moreover in addition to parameter dependence the obtained conditions are also dependent on both

notes on the eigensystem of magnetohydrodynamics the eigenstructure of the equations governing one dimensional ideal magnetohy drodynamics is examined motivated by the wish to exploit it for construction of high resolution computational algorithms the results are given in simple forms that avoid indeterminacy or degeneracy whenever possible the unavoidable indeterminacy near the magnetosonic or triple umbilic state is analysed and shown to cause no difficulty in evaluating a numerical flux function the structure of wave paths close to this singularity is obtained and simple expressions are presented for the structure coefficients that govern wave steepening

delay dependent robust h control of uncertain linear systems with time varying delays abstract this paper proposes an optimization based approach to the robust h control problem of uncertain continuous or discrete time linear time invariant systems with different time varying delays in the state vector and control input of the dynamic equation and controlled output sufficient delay dependent conditions are derived for the control stabilization problem where both the size of the time varying delay and the size of its time derivative in the continuous time case play a crucial role for the closed loop stability with a guaranteed h performance index the solutions that are proposed for the h control problem are similar or less conservative when compared to other recent approaches

asymptotic stability of monotone increasing traveling wave solutions for viscous compressible fluid equations with capillarity term abstract asymptotic stability of monotone increasing traveling wave solutions is investigated for a class of viscous compressible fluid equations with capillarity term by using the theory of planar dynamical systems the existence has been proved for the monotone increasing traveling wave solution moreover through building uniformly a priori energy estimate for the perturbation of the traveling wave solution we prove that the monotone increasing traveling wave solution is asymptotically stable in h 2 h 1

state observability and observers of linear time invariant systems under irregular sampling and sensor limitations state observability and observer designs are investigated for linear time invariant systems in continuous time when the outputs are measured only at a set of irregular sampling time sequences the problem is primarily motivated by systems with limited sensor information in which sensor switching generates irregular sampling sequences state observability may be lost and the traditional observers may fail in general even if the system has a full rank observability matrix it demonstrates that if the original system is observable the irregularly sampled system will be observable if the sampling density is higher than some critical frequency independent of the actual time sequences this result extends shannon s sampling theorem for signal reconstruction under periodic sampling to system observability under arbitrary sampling sequences state observers and recursive algorithms are developed whose convergence properties are derived under potentially dependent measurement noises persistent excitation conditions are validated by designing sampling time sequences by generating suitable switching time sequences the designed state observers are shown to be convergent in mean square with probability one and with exponential convergence rates schemes for generating desired sampling sequences are summarized

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 energy to peak filter design for stochastic time delay systems abstract this paper considers the robust energy to peak filtering problem for uncertain stochastic time delay systems the stochastic uncertainties appear in both the dynamic and the measurement equations and the state delay is assumed to be time varying attention is focused on the design of full order and reduced order filters guaranteeing a prescribed energy to peak performance for the filtering error system sufficient conditions are formulated in terms of linear matrix inequalities lmis and the corresponding filter design is cast into a convex optimization problem which can be efficiently handled by using standard numerical algorithms in addition the results obtained are further extended to more general cases where the system matrices also contain uncertain parameters the most frequently used ways of dealing with parameter uncertainties including polytopic and norm bounded characterizations have been taken into consideration with convex optimization problems obtained for the design of desired robust energy to peak filters

option pricing in markov modulated exponential levy models with stochastic interest rates abstract in this paper we consider the problem of pricing european options namely vanilla options binary options and exchange options whose underlying assets prices dynamics follow markovian regime switching exponential levy models with stochastic interest rates where the stochastic interest rates are driven by markovian regime switching hull white process we obtain the integral representations of the option prices by fourier transform ft technique and some numerical results of 3 state case for merton jump diffusion model by the fast fourier transform fft approach the numerical results show that the pricing formulas are considerably accurate and easy to be implemented

filtering continuous time linear systems with time varying measurement delay we consider the filtering problem of lti continuous time systems with known and bounded measurement delays the aim of the technical note is the design of a finite dimensional sub optimal filter whose performance in terms of the estimation error is comparable to optimal infinite dimensional approaches we show that the proposed approach allows for a precise characterization of the relationship between measurement delay and the covariance of the estimation error in the time varying case no restrictive hypotheses on the delay function are needed the proposed filter can therefore be applied to delay functions for which traditional infinite dimensional approaches cannot be straightforwardly applied

non classical riemann solvers with nucleation we introduce a new nonclassical riemann solver for scalar conservation laws with concave convex flux function this solver is based on both a kinetic relation which determines the propagation speed of undercompressive nonclassical shock waves and a nucleation crite rion which makes a choice between a classical riemann solution and a nonclassical one we establish the existence of nonclassical entropy solutions of the cauchy problem and discuss several examples of wave interactions we also show the existence of a class of solutions called splitting merging solutions which are made of two large shocks and small bv bounded variation perturbations the nucleation solvers as we call them are applied to and actually motivated by the theory of thin film flows they help explain numerical results observed for such flows

event based h_ infty filter design for a class of nonlinear time varying systems with fading channels and multiplicative noises in this paper a general event triggered framework is developed to deal with the finite horizon h infty filtering problem for discrete time varying systems with fading channels randomly occurring nonlinearities and multiplicative noises an event indicator variable is constructed and the corresponding event triggered scheme is proposed such a scheme is based on the relative error with respect to the measurement signal in order to determine whether the measurement output should be transmitted to the filter or not the fading channels are described by modified stochastic rice fading models some uncorrelated random variables are introduced respectively to govern the phenomena of state multiplicative noises randomly occurring nonlinearities as well as fading measurements the purpose of the addressed problem is to design a set of time varying filter such that the influence from the exogenous disturbances onto the filtering errors is attenuated at the given level quantified by a h infty norm in the mean square sense by utilizing stochastic analysis techniques sufficient conditions are established to ensure that the dynamic system under consideration satisfies the h infty filtering performance constraint and then a recursive linear matrix inequality rlmi approach is employed to design the desired filter gains simulation results demonstrate the effectiveness of the developed filter design scheme

robust h spl infin filter design for uncertain linear systems with multiple time varying state delays the problem of robust h spl infin filtering for continuous time uncertain linear systems with multiple time varying delays in the state variables is investigated the uncertain parameters are supposed to belong to a given convex bounded polyhedral domain the aim is to design a stable linear filter assuring asymptotic stability and a prescribed h spl infin performance level for the filtering error system irrespective of the uncertainties and the time delays sufficient conditions for the existence of such a filter are established in terms of linear matrix inequalities which can be efficiently solved by means of powerful convex programming tools with global convergence assured an example illustrates the proposed methodology

ito volterra optimal state estimation with continuous multirate randomly sampled and delayed measurements the optimal filter for continuous linear stochastic time varying systems described by the itocirc volterra equations with discontinuous measure is derived with an appropriately selected measure the result is applicable to a wide range of observation processes including the hybrid case of observations formed by an arbitrary combination of continuous and discrete measurements which may be sampled with a priori unknown changing and possibly random rates and delays the simultaneous presence of continuous and sampled measurements causes impulsive discontinuity in the inputs of the optimal filter equations which leads to a discontinuous change in state estimates every time a sampled measurement becomes available using the theory of vibrosolutions the explicit and unique expressions for the jumps in state estimates and estimation error covariance are derived several examples illustrate the procedure of modeling hybrid measurement systems by selecting an appropriate discontinuous measure we further show that the itocirc volterra model and the main result of the paper can be specialized to several important cases including state space systems for which we recover several known state estimation results and derive a novel optimal filter for continuous ltv systems with an arbitrary combination of continuous and delayed sampled measurements this optimal filter updates the state estimates for incoming measurements as soon as they become available and does not require prior knowledge of sampling instants and delays which makes it applicable when deterministic and random changes in sampling and delays are present several computational examples demonstrate the implementation of the developed filter and compare its performance to the traditional alternatives using monte carlo simulations

the riemann problem for 2 2 systems of hyperbolic conservation laws with case i quadratic nonlinearities on etudie les problemes de riemann pour des systemes 2 2 de lois de conservation non strictement hyperboliques avec des non linearites quadratiques

reduced order h filtering for singular systems abstract this paper solves the problem of reduced order h filtering for singular systems the purpose is to design linear filters with a specified order lower than the given system such that the filtering error dynamic system is regular impulse free or causal stable and satisfies a prescribed h performance level one major contribution of the present work is that necessary and sufficient conditions for the solvability of this problem are obtained for both continuous and discrete singular systems these conditions are characterized in terms of linear matrix inequalities lmis and a coupling non convex rank constraint moreover an explicit parametrization of all desired reduced order filters is presented when these inequalities are feasible in particular when a static or zeroth order h filter is desired it is shown that the h filtering problem reduces to a convex lmi problem all these results are expressed in terms of the original system matrices without decomposition which makes the design procedure simple and directly last but not least the results have generalized previous works on h filtering for state space systems an illustrative example is given to demonstrate the effectiveness of the proposed approach

a novel approach to filter design for t s fuzzy discrete time systems with time varying delay in this paper the problem of l2 l filtering for a class of discrete time takagi sugeno t s fuzzy time varying delay systems is studied our attention is focused on the design of full and reduced order filters that guarantee the filtering error system to be asymptotically stable with a prescribed h performance sufficient conditions for the obtained filtering error system are proposed by applying an input output approach and a two term approximation method which is employed to approximate the time varying delay the corresponding full and reduced order filter design is cast into a convex optimization problem which can be efficiently solved by standard numerical algorithms finally simulation examples are provided to illustrate the effectiveness of the proposed approaches

delay dependent robust h sub spl infin and l sub 2 l sub spl infin filtering for a class of uncertain nonlinear time delay systems this note presents delay dependent robust h sub spl infin and l sub 2 l sub spl infin filter designs for a class of nonlinear systems with multiple time varying delays in the state and parameter uncertainties residing in a polytope the nonlinearities are assumed to satisfy global lipschitz conditions attention is focused on the design of robust full order and reduced order filters guaranteeing a prescribed noise attenuation level in an h sub spl infin or l sub 2 l sub spl infin sense the admissible filters can be obtained from the solution of convex optimization problems in terms of linear matrix inequalities which can be solved via efficient interior point algorithms

riemann problems for nonstrictly hyperbolic 2 2 systems of conservation laws on resout le probleme de riemann pour des systemes 2 2 de lois de conservation hyperboliques ayant des fonctions flux quadratiques

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

hyperbolic conservation laws with umbilic degeneracy i in this paper a compactness framework for approximate solutions to nonlinear hyperbolic systems with umbilic degeneracy is established by combining techniques of compensated compactness with some classical methods and by a detailed analysis of a highly singular equation of euler poisson darboux type then this framework is successfully applied to prove the convergence of the viscosity method and to prove the existence of global entropy solutions for the cauchy problem with large initial data for a canonical class of the systems with quadratic flux form

reduced order h sub spl infin filtering for stochastic systems this paper deals with the reduced order h sub spl infin filtering problem for stochastic systems necessary and sufficient conditions are obtained for the existence of solutions to the continuous time and discrete time problems in terms of certain linear matrix inequalities lmis and a coupling nonconvex rank constraint condition furthermore when these conditions are feasible an explicit parametrization of all desired reduced order filters corresponding to a feasible solution is given in particular when the reduced order filter is restricted to be a static one then simple conditions expressed by lmis only without any rank constraints are derived and a parametrization of all solutions is also given finally an illustrative example is provided to show the effectiveness of the proposed approach

observation and stabilization of ltv systems with time varying measurement delay abstract this work deals with observer based output feedback stabilization of linear time varying ltv systems with time varying measurement delay the delay is modeled by a first order hyperbolic partial differential equation pde whose boundary condition evolves according to an ordinary differential equation ode namely the plant the overall system is thus represented by an ode pde cascade which is also the structure of the proposed observer the exponential stability of the estimation error is established for arbitrarily large time varying delays an observer based controller is also introduced and the closed loop stability is proved the separation principle holds and the design of both the observer and controller gains can be done as if there was no delay some simulations illustrate the feasibility of this approach

a simple necessary and sufficient lmi condition for the strong delay independent stability of lti systems with single delay abstract this paper is concerned with strong delay independent stability of linear time invariant lti systems with a single time delay stability analysis of linear delay systems is complicated by the need to locate the roots of a transcendental characteristic equation in this paper we propose a convex necessary and sufficient condition for strong delay independent stability this result mainly follows from the kronecker sum properties and the kalman yakubovich popov lemma which allows us to present the main result in terms of a single linear matrix inequality lmi feasibility test the result is illustrated by simple numerical examples

robust h filter design for uncertain fuzzy neutral systems this paper investigates the problem of robust h filtering for a class of uncertain takagi sugeno t s fuzzy neutral systems with time varying delay and linear fractional parametric uncertainties the aim is to design an asymptotically stable fuzzy filter ensuring asymptotical stability and prescribed h performance of the filtering error system for all admissible uncertainties based on the lyapunov krasovskii functional the barbalat lemma and the lmi approach delay dependent sufficient conditions for the solvability of this problem are proposed in terms of lmis and an explicit expression of the desired h fuzzy filter is readily given when these lmis are feasible finally the h filter design problem for a neutral type nonlinear distributed network long line with tunnel diode is considered in the simulation example to demonstrate the effectiveness and applicability of the proposed method

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

delay dependent l2 l filter design for stochastic time delay systems abstract this paper is concerned with the problem of l 2 l filter design for a class of stochastic time delay systems a delay dependent sufficient condition is presented which guarantees the existence of a linear filter ensuring that the filtering error system is stochastically asymptotically stable and its l 2 l performance satisfies a prescribed level a desired filter can be constructed by solving certain linear matrix inequalities a numerical example is given to demonstrate the effectiveness of the proposed method

new filter design for linear time delay systems abstract this paper develops new robust delay dependent filter design for a class of linear systems with time varying delays and convex bounded parameter uncertainties the design procedure hinges upon the constructive use of an appropriate lyapunov functional plus a free weighting matrices in order to exhibit the delay dependent dynamics the developed approach utilizes smaller number of lmi decision variables thereby leading to less conservative solutions to the delay dependent stability and filtering problems subsequently linear matrix inequalities lmis based conditions are characterized such that the linear delay system is robustly asymptotically stable with an level l 2 gain all the developed results are tested on representative examples

nonclassical multidimensional viscous and inviscid shocks extending our earlier work on lax type shocks of systems of conservation laws we establish existence and stability of curved multidimensional shock fronts in the vanishing viscosity limit for general lax or undercompressive type shock waves of nonconservative hyperbolic systems with parabolic regularization the hyperbolic equations may be of variable multiplicity and the parabolic regularization may be of real or partially parabolic type we prove an existence result for inviscid nonconservative shocks that extends to multidimensional shocks a one dimensional result of x lin proved by quite different methods in addition we construct families of smooth viscous shocks converging to a given inviscid shock as viscosity goes to zero thereby justifying the small viscosity limit for multidimensional nonconservative shocks in our previous work on shocks we made use of conservative form especially in parts of the low frequency analysis thus most of the new analysis of this paper is concentrated in this area by adopting the more general nonconservative viewpoint we are able to shed new light on both the viscous and inviscid theory for example we can now provide a clearer geometric motivation for the low frequency analysis in the viscous case also we show that one may in the treatment of inviscid stability of nonclassical and or nonconservative shocks remove an apparently restrictive technical assumption made by mokrane and coulombel in their work on respectively shocktype nonconservative boundary problems and conservative undercompressive shocks another advantage of the nonconservative perspective is that lax and undercompressive shocks can be treated by exactly the same analysis

spl hscr sub spl infin filtering for continuous time linear systems with delay the problem of spl hscr sub spl infin filtering for continuous time linear systems with time delayed measurement is investigated the authors develop a methodology for designing linear filters which ensure a prescribed bound on the spl lscr sub 2 induced gain from the noise signals to the estimation error filtering problems for time varying systems over a finite horizon as well as stationary infinite horizon filtering for time invariant systems are tackled in the finite horizon case our estimation procedure entails an overdesign that stems from the last d seconds of the time interval 0 t where d is the delay length this overdesign becomes smaller as t increases and it vanishes in the infinite horizon case

a delay dependent approach to robust h sub spl infin filtering for uncertain discrete time state delayed systems a delay dependent approach to robust h sub spl infin filtering is proposed for linear discrete time uncertain systems with multiple delays in the state the uncertain parameters are supposed to reside in a polytope and the attention is focused on the design of robust filters guaranteeing a prescribed h sub spl infin noise attenuation level the proposed filter design methodology incorporates some recently appeared results such as moon s new version of the upper bound for the inner product of two vectors and de oliveira s idea of parameter dependent stability which greatly reduce the overdesign introduced in the derivation process in addition to the full order filtering problem the challenging reduced order case is also addressed by using different linearization procedures both full and reduced order filters can be obtained from the solution of convex optimization problems in terms of linear matrix inequalities which can be solved via efficient interior point algorithms numerical examples have been presented to illustrate the feasibility and advantages of the proposed methodologies

weak stability in the global norm for systems of hyperbolic conservation laws we prove that solutions for systems of two conservation laws which are generated by glimm s method are weakly stable in the global l norm the method relies on a previous decay result of the author together with a new estimate for the l1 lipschitz constant that relates solutions at different times the estimate shows that this constant can be bounded by the supnorm of the solution and is proved for any number of equations the techniques do not rely on the existence of a family of entropies and moreover the results would generalize immediately to more than two equations if one were to establish the stability of solutions in the supnorm for more than two equations

robust h filter design for neutral stochastic uncertain systems with time varying delay abstract in this paper the robust h filtering problem for a class of neutral stochastic systems is discussed the system under consideration contains parameter uncertainties ito type stochastic disturbances time varying delay the parameter uncertainties are assumed to be time varying norm bounded using the stochastic lyapunov stability theory and ito s differential rule a full order filter is designed for all admissible uncertainties and time varying delay which is expressed in the form of linear matrix inequality lmi the dynamics of the filtering error systems are guaranteed to be robust stochastically mean square asymptotically stable while achieving a prescribed stochastic robust h performance level at the end of this paper a numerical example is given to demonstrate the usefulness of the proposed method

bond pricing under a markovian regime switching jump augmented vasicek model via stochastic flows in this article we shall explore the state of art of stochastic flows to derive an exponential affine form of the bond price when the short rate process is governed by a markovian regime switching jump diffusion version of the vasicek model we provide the flexibility that the market parameters including the mean reversion level the volatility rate and the intensity of the jump component switch over time according to a continuous time finite state markov chain the states of the chain may be interpreted as different states of an economy or different stages of a business cycle we shall provide a representation for the exponential affine form of the bond price in terms of fundamental matrix solutions of linear matrix differential equations

a numerical study of riemann problem solutions and stability for a system of viscous conservation laws of mixed type a numerical study of the isothermal fluid equations with a nonmonotone equation of state like that of van der waals and with viscosity and capillarity terms is presented this system is ill posed i e elliptic in x vs t in some regions of state space and well posed i e hyperbolic in other regions thus it may serve as a model for describing dynamic phase transitions numerical computations of phase jumps shock waves and rarefaction waves for this system are presented although the solution of the riemann problem is not unique all of these waves are found to be stable to infinitesimal initial perturbations criteria are found for instability after o 1 initial perturbations an analytic argument is made for stability of phase transitions

viscous solutions of quadratic conservation laws with umbilic points viscous solutions of quadratic conservation laws with umbilic points ltj yunguang zhu changjiang and zhao huijiang wuhan institute of mathematical sciences academia sinica wuhan 430071 people s republic of china received 10 january 1991 received in revised form 4 august 1992 received for publication 1 march 1993

decay of entropy solutions of nonlinear conservation laws we are concerned with the asymptotic behavior of entropy solutions of nonlinear conservation laws the main objective of this paper is to present an analytical approach and to explore its applications to studying the large time behavior of periodic entropy solutions of hyperbolic conservation laws the asymptotic decay of periodic solutions of nonlinear hyperbolic conservation laws is an important nonlinear phenomenon it is observed that the genuine nonlinearity of equations forces the waves of each characteristic family to interact vigorously and to cancel each other the insightful analysis of glimm lax gl for scalar equations and 2 2 systems has indicated that the resultant mutual cancellation of interacting shock and rarefaction waves of the same family induces the decay of periodic solutions such a result was first shown by lax l1 in 1957 for one dimensional convex scalar conservation laws dafermos d1 applying his uniform processes proved the decay result for the case that the set of inflection points of the flux does not have an accumulation point the glimm lax theory gl indicates that for 2 2 strictly hyperbolic and genuinely nonlinear systems any periodic glimm solution decays like o 1 t this result was proved by using the approximate characteristic method in the glimm difference solutions provided that the oscillation of the corresponding initial data is small recently using the method of generalized characteristics dafermos d3 showed that any periodic solution with local bounded variation and small oscillation for 2 2 systems decays asymptotically with the same detailed structure pas found by lax l1 for the

conservation laws of mixed type describing three phase flow in porous media in this paper we examine the mathematical structure of a model for three phase incompressible flow in a porous medium we show that in the absence of diffusive forces the system of conservation laws describing the flow is not necessarily hyperbolic we present an example in which there is an elliptic region in saturation space for reasonable relative permeability data a linearized analysis shows that in nonhyperbolic regions solutions grow exponentially however the nonhyperbolic region if present will be of limited extent which inherently limits the exponential growth to examine these nonlinear effects we resort to fine grid numerical experiments with a suitably dissipative numerical method these experiments indicate that the solutions of riemann problems remain well behaved in spite of the presence of a linearly unstable elliptic region in saturation space in particular when initial states are outside the elliptic region the riemann problem solution appears to stay outside the region further

robust h filtering for uncertain discrete piecewise time delay systems this paper investigates the problem of robust h filter design for uncertain discrete piecewise time delay systems based on a piecewise lyapunov functional the parametric uncertainties are assumed to be time varying but norm bounded the purpose is the design of a piecewise filter such that for all admissible uncertainties the resulting filtering error system is asymptotically stable and satisfies a prescribed h performance level by introducing some different extra matrix variables a sufficient condition for the solvability of this problem is obtained in terms of linear matrix inequalities lmis when these lmis are feasible the explicit expression of a desired piecewise filter is given two numerical examples are provided to demonstrate the effectiveness of the proposed design method

multivariate european option pricing in a markov modulated lvy framework this paper studies the pricing of some multivariate european options namely exchange options and quanto options when the risky assets involved are modelled by markov modulated lvy processes mmlps pricing formulae are based upon the characteristic exponents by using the well known fft methodology we study these pricing issues both under a risk neutral martingale measure and the historical measure the dependence between the assets components is incorporated in the joint characteristic function of the mmlps as an example we concentrate upon a regime switching version of the model of ballotta etal 2015 in which the dependence structure is introduced in a flexible way several numerical examples are provided to illustrate our results

an exact riemann solver for compressible two phase flow models containing non conservative products in this article we present a new numerical procedure for solving exactly the riemann problem of compressible two phase flow models containing non conservative products these products appear in the expressions for the interactions between the two phases thus in the compressible limit the governing equations are hyperbolic but can not be written as conservation laws i e in divergence form in general the solution to the riemann problem of these models contains six distinct centered waves according to the relative position of these waves in the x t plane the possible solutions can be classified into four principal configurations the riemann solver we propose herein investigates sequentially each of these configurations until an admissible solution is calculated special configurations corresponding to coalescence of waves are also analyzed and included in the solver further we examine the accuracy and robustness of three known methods for the integration of the non conservative products via a series of numerical tests finally the issue of existence and uniqueness of solutions to the riemann problem is discussed

robust h infinity filtering for a class of non linear systems with state delay and parameter uncertainty this paper deals with the problem of robust h infinity filtering for a class of state delayed non linear systems with normbounded parameter uncertainty appearing in all the matrices of the linear part of the system model the non linearities are assumed to satisfy the global lipschitz conditions and appear in both the state and measured output equations attention is focused on the design of a non linear filter which ensures both the robust stability and a prescribed h infinity performance of the filtering error dynamics for all admissible uncertainties a sufficient condition for the existence of such a filter is given in terms of a linear matrix inequality lmi when this lmi is feasible the expression of a desired h infinity filter is also presented a numerical example is provided to demonstrate the applicability of the proposed approach

robust switching type h filter design for linear uncertain systems with time varying delay this paper is concerned with the problem of robust h filter design for a class of linear uncertain systems with time varying delay the uncertainty parameters are supposed to be time varying unknown but bounded which appear affinely in the matrices of the considered system model based on linear matrix inequality lmi method and switching laws a new switching type filter is designed to guarantee the asymptotic stability and h performance level of the filtering error systems the key feature is that the new proposed filter parameters are switching between certain fixed gains automatically via the designed switching law it is shown that the new filter design method is less conservative than the traditional fixed gain filter design method an example is given to illustrate the validity of the proposed design