parameter dependent lmis in robust analysis characterization of homogeneous polynomially parameter dependent solutions via lmi relaxations this note investigates the robust stability of uncertain linear time invariant systems in polytopic domains by means of parameter dependent linear matrix inequality pd lmi conditions exploiting some algebraic properties provided by the uncertainty representation a systematic procedure to construct a family of finite dimensional lmi relaxations is provided the robust stability is assessed by means of the existence of a lyapunov function more specifically a homogeneous polynomially parameter dependent lyapunov hppdl function of arbitrary degree for a given degree if an hppdl solution exists a sequence of relaxations based on real algebraic properties provides sufficient lmi conditions of increasing precision and constant number of decision variables for the existence of an hppdl function which tend to the necessity alternatively if an hppdl solution of degree exists a sequence of relaxations which increases the number of variables and the number of lmis will provide an hppdl solution of larger degree the method proposed can be applied to determine homogeneous parameter dependent matrix solutions to a wide variety of pd lmis by transforming the infinite dimensional lmi problem described in terms of uncertain parameters belonging to the unit simplex in a sequence of finite dimensional lmi conditions which converges to the necessary conditions for the existence of a homogeneous polynomially parameter dependent solution of arbitrary degree illustrative examples show the efficacy of the proposed conditions when compared with other methods from the literature

on the estimation of optical flow relations between different approaches and some new results abstract a common basis is suggested for the optical flow estimation approaches of nagel 1983 haralick and lee 1983 and tretiak and pastor 1984 based on a discussion of these approaches an exact solution for the system of partial differential equations proposed by horn and schunck 1981 is given at gray value corners and extrema the insight gained by this solution results in a modification of the oriented smoothness approach of nagel 1983 which thereby becomes considerably simpler in addition the optical flow estimation approach of hildreth 1983 1984 can be shown to represent a kind of special case of this modified oriented smoothness approach in a more direct manner than discussed in nagel 1984

stability and convergence of a finite element method for reactive transport in ground water an explicit finite element method is used to solve the linear convection diffusion reaction equations governing contaminant transport in ground water flowing through an adsorbing porous medium the use of discontinuous finite elements for the convective part of the equations combined with mixed finite elements for the diffusive part renders the method for the concentration solution which displays strong gradients trivially conservative and fully parallelizable we carry out a stability and convergence analysis in particular the method is proven to satisfy a maximum principle to be total variation bounded and to converge to the unique weak solution of the equations special attention is paid to the convective part of the equations numerical simulations are presented and discussed

robustness analysis of genetic regulatory networks affected by model uncertainty a fundamental problem in systems biology consists of investigating robustness properties of genetic regulatory networks grns with respect to model uncertainty this paper addresses this problem for grns where the coefficients are rationally affected by polytopic uncertainty and where the saturation functions are not exactly known first it is shown that a condition for ensuring that the grn has a globally asymptotically stable equilibrium point for all admissible uncertainties can be obtained in terms of a convex optimization problem with linear matrix inequalities lmis hence generalizing existing results that mainly consider only the case of grns where the coefficients are linearly affected by the uncertainty and the regulatory functions are in sum form second the problem of estimating the worst case convergence rate of the trajectories to the equilibrium point over all admissible uncertainties is considered and it is shown that a lower bound of this rate can be computed by solving a quasi convex optimization problem with lmis third the paper considers the problem of estimating the set of uncertainties for which the grn has a globally asymptotically stable equilibrium point this problem is addressed first by showing how one can compute estimates with fixed shape by solving a quasi convex optimization problem with lmis and second by deriving a procedure for computing estimates with variable shape numerical examples illustrate the use of the proposed techniques

solving quadratic distance problems an lmi based approach the computation of the minimum distance of a point to a surface in a finite dimensional space is a key issue in several system analysis and control problems the paper presents a general framework in which some classes of minimum distance problems are tackled via linear matrix inequality lmi techniques exploiting a suitable representation of homogeneous forms a lower bound to the solution of a canonical quadratic distance problem is obtained by solving a one parameter family of lmi optimization problems several properties of the proposed technique are discussed in particular tightness of the lower bound is investigated providing both a simple algorithmic procedure for a posteriori optimality testing and a structural condition on the related homogeneous form that ensures optimality a priori extensive numerical simulations are reported showing promising performances of the proposed method

computation of discontinuous optical flow by domain decomposition and shape optimization a well known method for the reconstruction of motion fields from noisy image data is to determine flow fields by the minimization of a quadratic functional the first approach of this class has been proposed by horn and schunck 1981 a drawback of such approaches is that an explicit representation of the discontinuities of the motion field is lacking and that in general the resulting flow fields approximate the motion fields only badly at the corresponding locations in the image plane in this article we discuss the possibility to improve the results by hypothesizing the qualitative structure of the motion field in terms of certain parameters we decompose the image plane into disjoint sets restrict the domain of definition of the functionals to these sets and use the hypotheses to deform and to move the boundaries of the sets within the image plane we discuss the range of applicability of this new technique and illustrate the algorithm by numerical examples this article is a revised and extended version of schnorr 1990

mixed finite elements for second order elliptic problems in three variables two families of mixed finite elements one based on simplices and the other on cubes are introduced as alternatives to the usual raviart thomas nedelec spaces these spaces are analogues of those introduced by brezzi douglas and marini in two space variables error estimates inl2 andh s are derived

degenerate two phase incompressible flow iii sharp error estimates this is the third paper of a series in which we analyze mathematical properties and develop numerical methods for a degenerate elliptic parabolic partial differential system which describes the flow of two incompressible immiscible fluids in porous media in this paper we consider a finite element approximation for this system the elliptic equation for the pressure and velocity is approximated by a mixed finite element method while the degenerate parabolic equation for the saturation is approximated by a galerkin finite element method a fully discrete approximation is analyzed sharp error estimates in energy norms are obtained for this approximation the error analysis does not use any regularization of the saturation equation the error estimates are derived directly from the degenerate equation also the analysis does not impose any restriction on the nature of degeneracy finally it respects the minimal regularity on the solution of the differential system

on the transport diffusion algorithm and its applications to the navier stokes equations this paper deals with an algorithm for the solution of diffusion and or convection equations where we mixed the method of characteristics and the finite element method globally it looks like one does one step of transport plus one step of diffusion or projection but the mathematics show that it is also an implicit time discretization of thepde in lagrangian form we give an error bound h t h h t in the interesting case that holds also for the navier stokes equations even when the reynolds number is infinite euler equation

determining optical flow for irregular domains by minimizing quadratic functionals of a certain class snyder 1989 has recently classified all smoothness terms which involve first order derivatives of the flowfield u x t and of the image grey value function g x t the physically plausible smoothness terms belonging to this class are known from the work of horn and schunck 1981 and nagel 1987 in this paper we discuss the possibilities of approximating the solutions to the minimization problems of horn schunk 1981 and nagel 1987 in particular it is shown that these solutions exist are unique and depend continuously on the input data these properties make it possible while taking into consideration arbitrary models of the grey value function to approximate efficiently the weak solutions of the associated boundary value problems in irregularly shaped domains with a sufficiently smooth boundary using finite elements experiments with image sequences from synthetic as well as outdoor scenes show how the orientation dependency of the smoothness term in nagel s approach influences the results

degenerate two phase incompressible flow ii regularity stability and stabilization abstract in this paper we analyze a coupled system of highly degenerate elliptic parabolic partial differential equations for two phase incompressible flow in porous media this system involves a saturation and a global pressure or a total flow velocity first we show that the saturation is holder continuous both in space and time and the total velocity is holder continuous in space uniformly in time applying this regularity result we then establish the stability of the saturation and pressure with respect to initial and boundary data from which uniqueness of the solution to the system follows finally we establish a stabilization result on the asymptotic behavior of the saturation and pressure we prove that the solution to the present system converges in appropriate norms to the solution of a stationary system as time goes to infinity an example is given to show typical regularity of the saturation

polynomially parameter dependent lyapunov functions for robust stability of polytopic systems an lmi approach in this note robust stability of state space models with respect to real parametric uncertainty is considered specifically a new class of parameter dependent quadratic lyapunov functions for establishing stability of a polytope of matrices is introduced i e the homogeneous polynomially parameter dependent quadratic lyapunov functions hpd qlfs the choice of this class which contains parameter dependent quadratic lyapunov functions whose dependence on the uncertain parameters is expressed as a polynomial homogeneous form is motivated by the property that a polytope of matrices is stable if and only there exists an hpd qlf the main result of the note is a sufficient condition for determining the sought hpd qlf which amounts to solving linear matrix inequalities lmis derived via the complete square matricial representation csmr of homogeneous matricial forms and the lyapunov matrix equation numerical examples are provided to demonstrate the effectiveness of the proposed approach

an improved lmi condition for robust d stability of uncertain polytopic systems a sufficient condition for robust d stability of linear systems with polytope type uncertainties is proposed the result is based on a linear parameter dependent lyapunov function obtained from the feasibility test of a set of linear matrix inequalities lmis defined at the vertices of the polytope this improved lmi condition encompasses previous results based on additional inequalities as well as results based on extra variables

efficient time stepping methods for miscible displacement problems in porous media efficient procedures for time stepping galerkin methods for approximating the solution of a coupled system for c c x t and p p x t with nonlinear neumann boundary conditions of the form begin gathered nabla cdot a x c nabla p y x c nabla g equiv nabla cdot u f 1 x t quad x in omega quad t in 0 t hfill nabla cdot b x c nabla p nabla c u cdot nabla c phi x frac partial c partial t f 2 x t c quad x in omega quad t in 0 t hfill u cdot v q 1 x t quad x in partial omega quad t in 0 t hfill b frac partial c partial v q x t c quad x in partial omega quad t in 0 t hfill c x 0 c 0 x quad x in omega hfill end gathered where omega subset mathbb r d 2 leqq d leqq 3 are presented and analyzed this system is a possible model system for describing the miscible displacement of one incompressible fluid by another in a porous medium when flow conditions a

timestepping along characteristics for amixed finite element approximation for compressible flow of contamination from nuclear waste in porous media a nonlinear parabolic system describing compressible nuclear waste disposal contamination in porous media is presented a finite element procedure is introduced to approximate the transport of brin

a theoretical framework for convex regularizers in pde based computation of image motion many differential methods for the recovery of the optic flow field from an image sequence can be expressed in terms of a variational problem where the optic flow minimizes some energy typically these energy functionals consist of two terms a data term which requires e g that a brightness constancy assumption holds and a regularizer that encourages global or piecewise smoothness of the flow field in this paper we present a systematic classification of rotation invariant convex regularizers by exploring their connection to diffusion filters for multichannel images this taxonomy provides a unifying framework for data driven and flow driven isotropic and anisotropic as well as spatial and spatio temporal regularizers while some of these techniques are classic methods from the literature others are derived here for the first time we prove that all these methods are well posed they posses a unique solution that depends in a continuous way on the initial data an interesting structural relation between isotropic and anisotropic flow driven regularizers is identified and a design criterion is proposed for constructing anisotropic flow driven regularizers in a simple and direct way from isotropic ones its use is illustrated by several examples

reliable estimation of dense optical flow fields with large displacements in this paper we show that a classic optical flow technique by nagel and enkelmann 1986 ieee trans pattern anal mach intell vol 8 pp 565 593 can be regarded as an early anisotropic diffusion method with a diffusion tensor we introduce three improvements into the model formulation that i avoid inconsistencies caused by centering the brightness term and the smoothness term in different images ii use a linear scale space focusing strategy from coarse to fine scales for avoiding convergence to physically irrelevant local minima and iii create an energy functional that is invariant under linear brightness changes applying a gradient descent method to the resulting energy functional leads to a system of diffusion reaction equations we prove that this system has a unique solution under realistic assumptions on the initial data and we present an efficient linear implicit numerical scheme in detail our method creates flow fields with 100 density over the entire image domain it is robust under a large range of parameter variations and it can recover displacement fields that are far beyond the typical one pixel limits which are characteristic for many differential methods for determining optical flow we show that it performs better than the optical flow methods with 100 density that are evaluated by barron et al 1994 int j comput vision vol 12 pp 43 47 our software is available from the internet

analysis of hp discontinuous galerkin methods for incompressible two phase flow in this paper we prove the convergence of a class of discontinuous galerkin methods for solving the fully coupled incompressible two phase flow problem in the non degenerate case estimates in both the mesh size and the polynomial degrees are obtained numerical convergence rates confirm the theoretical results

an effective implementation for stokes equation by the weak galerkin finite element method abstract in this paper we introduce and analyze the schur complement technique to a weak galerkin wg for short finite element method for solving stokes equation due to the special structure of the weak functions the main idea of schur decomposition method is to express the interior velocity functions defined inside partition elements in terms of the velocity functions defined on the partition boundary and the pressure functions this can largely reduce the degree of freedom of the derived discrete linear system we investigate the well posedness of the solution generated from schur complement and its coincidence with the standard wg method finally we exhibit some numerical experiments to illustrate the theoretical analysis

estimating the domain of attraction for uncertain polynomial systems estimating the domain of attraction da of equilibrium points is a problem of fundamental importance in systems engineering several approaches have been proposed for the case of known polynomial systems allowing one to find the largest estimate of the da leda for a given lyapunov function lf however the problem of estimating the robust da rda that is the da guaranteed for all possible uncertainties in an uncertain system it is still an unsolved problem in this paper lmi methods are proposed for estimating the rda in the case of systems depending polynomially in the state and in the uncertainty which is supposed to belong to a polytope specifically the issue of computing the robust leda rleda that is the intersection of all ledas is considered for common and parameter dependent lfs providing constant and parameter dependent lower bounds the computation of approximations with simple shape of the rleda in the case of parameter dependent lfs is also discussed

brief paper robust stability of time varying polytopic systems via parameter dependent homogeneous lyapunov functions this paper deals with robust stability analysis of linear state space systems affected by time varying uncertainties with bounded variation rate a new class of parameter dependent lyapunov functions is introduced whose main feature is that the dependence on the uncertain parameters and the state variables are both expressed as polynomial homogeneous forms this class of lyapunov functions generalizes those successfully employed in the special cases of unbounded variation rates and time invariant perturbations the main result of the paper is a sufficient condition to determine the sought lyapunov function which amounts to solving an lmi feasibility problem derived via a suitable parameterization of polynomial homogeneous forms moreover lower bounds on the maximum variation rate for which robust stability of the system is preserved are shown to be computable in terms of generalized eigenvalue problems numerical examples are provided to illustrate how the proposed approach compares with other techniques available in the literature

mean square exponential stability of stochastic genetic regulatory networks with time varying delays in this paper we study the mean square exponential stability of stochastic genetic regulatory networks with time varying delays two kinds of time varying delays are considered one is differentiable with bounded delay derivative the other is continuous without constraints on the delay derivative in order to investigate the mean square exponential stability in stochastic genetic regulatory networks some novel rate dependent independent mean square exponential stability criteria are derived by constructing lyapunov krasovskii functional the sufficient conditions are given in terms of linear matrix inequalities moreover illustrative examples are used to substantiate the effectiveness and less conservativeness of our results

optical flow with an intensity weighted smoothing matching algorithms which use image structure such as edges and junctions cannot perform well on unstructured images for such images global gradient based methods may be more appropriate some of the assumptions involved in applying discretized conservation equations such as the optical flow equation are discussed and an intensity weighted method of estimating dense displacement fields is presented which attempts to avoid some of the problems of the standard methods the only derivative required is the intensity gradient and the method includes procedures for automatic parameter evaluation the algorithm is expected to perform better than conventional algorithms on images without strong texture as is demonstrated on the test set of images

on the mathematical foundations of smoothness constraints for the determination of optical flow and for surface reconstruction gradient based approaches to the computation of optical flow often use a minimization technique incorporating a smoothness constraint on the optical flow field the author derives the most general form of such a smoothness constraint that is quadratic in first derivatives of the grey level image intensity function based on three simple assumptions about the smoothness constraint 1 it must be expressed in a form that is independent of the choice of cartesian coordinate system in the image 2 it must be positive definite and 3 it must not couple different component of the optical flow it is shown that there are essentially only four such constraints any smoothness constraint satisfying 1 2 or 3 must be a linear combination of these four possibly multiplied by certain quantities invariant under a change in the cartesian coordinate system beginning with the three assumptions mentioned above the author mathematically demonstrates that all best known smoothness constraints appearing in the literature are special cases of this general form and in particular that the weight matrix introduced by h h nagel is essentially modulo invariant quantities the only physically plausible such constraint

numerical methods for a model for compressible miscible displacement in porous media a nonlinear parabolic system is derived to describe compressible miscible displace ment in a porous medium the system is consistent with the usual model for incompressible miscible displacement two finite element procedures are introduced to approximate the concentration of one of the fluids and the pressure of the mixture the concentration is treated by a galerkin method in both procedures while the pressure is treated by either a lalerkin method or by a parabolic mixed finite element method optimal order estimates in l2 and essentially optimal order estimates in lx are derived for the errors in the approximate solutions for both methods introduction we shall consider the single phase miscible displacement of one compressible fluid by another in a porous medium under the assumptions that no volume change results from the mixing of the components and that a pressure den sity relation exists for each component in a form that is independent of the mixing these equations of state will imply that the fluids are in the liquid state our model will represent a direct generalization of the model 3 4 7 that has been treated extensively for incompressible miscible displacement the reservoir s will be taken to be of unit thickness and will be identified with a bounded domain in r2 we shall omit gravitational terms for simplicity of exposi tion no significant mathematical questions arise when the lower order terms are included

on functionals with greyvalue controlled smoothness terms for determining optical flow the modification by h h nagel 1987 of the approach developed by b k p horn and b g schunck 1981 for determining optical flow is generalized to the case where local motion information is given by more than one constraint equation applying this scheme to three constraint equations reported in the literature as a special case a generalization of nagel s approach is obtained an existence and uniqueness result of solutions under very general conditions that in turn ensures the applicability of standard techniques to compute an approximate solution is presented

mixed finite element methods for compressible miscible displacement in porous media a differential system describing compressible miscible displacement in a porous medium is given the concentration equation is treated by a galerkin method and the pressure equation is treated by a parabolic mixed fi nite element method optimal order estimates in l and almost optimal order estimates in l are obtained for the errors in the approximate solutions under the condition that h logh 2 0 this condition is much weaker than one given earlier by douglas and roberts for the same model furthermore we obtain the l l i2 estimates for the time derivatives of the concentration and the pressure which were not given by the above authors in addition we also consider newer mixed spaces in two or three dimensions

two families of mixed finite elements for second order elliptic problems two families of mixed finite elements one based on triangles and the other on rectangles are introduced as alternatives to the usual raviart thomas nedelec spaces error estimates inl 2 andh 5 are derived for these elements a hybrid version of the mixed method is also considered and some superconvergence phenomena are discussed

fully discrete finite element analysis of multiphase flow in groundwater hydrology this paper deals with the development and analysis of a fully discrete finite element method for a nonlinear differential system for describing an air water system in groundwater hydrology the nonlinear system is written in a fractional flow formulation i e in terms of a saturation and a global pressure the saturation equation is approximated by a finite element method while the pressure equation is treated by a mixed finite element method the analysis is carried out first for the case where the capillary diffusion coefficient is assumed to be uniformly positive and is then extended to a degenerate case where the diffusion coefficient can be zero it is shown that error estimates of optimal order in the l 2 norm and almost optimal order in the l infty norm can be obtained in the nondegenerate case in the degenerate case we consider a regularization of the saturation equation by perturbing the diffusion coefficient the norm of error estimates depends on the severity of the degeneracy in diffusivity with almost optimal order convergence for nonsevere degeneracy implementation of the fractional flow formulation with various nonhomogeneous boundary conditions is also discussed results of numerical experiments using the present approach for modeling groundwater flow in porous media are reported

convergence of a mfe fv method for two phase flow with applications to heap leaching of copper ores in this paper we describe error estimates for a finite element approximation to partial differential systems describing two phase immiscible flows in porous media with applications to heap leaching of copper ores these approximations are based on mixed finite element mfe methods for the pressure and velocity and finite volume fv for the saturation the fluids are considered incompressible numerical results for heap leaching simulation are presented

piecewise linear lyapunov functions for structural stability of biochemical networks we consider the problem of assessing structural stability of biochemical reaction networks with monotone reaction rates namely of establishing if all the networks with a certain structure are stable regardless of specific parameter values we investigate stability by absorbing the network equations in a linear differential inclusion and seeking for a polyhedral lyapunov function proper to the considered network structure a numerical recursive procedure is devised to test stability for a wide class of mono and bimolecular reaction networks which we name unitary the procedure is shown to be very efficient since due to the particular structure of the problem it requires iterations in the space of integer valued matrices we also consider a similar less conservative procedure that allows us to test even when the lyapunov function cannot be found whether the system evolution is structurally bounded in this case we absorb the equations in a positive linear differential inclusion to show the effectiveness of the proposed procedure we report the outcomes of both a stability and a boundedness test for many non trivial biochemical reaction networks and we analyze well established models in the literature

an investigation of smoothness constraints for the estimation of displacement vector fields from image sequences a mapping between one frame from an image sequence and the preceding or following frame can be represented as a displacement vector field in most situations the mere gray value variations do not provide sufficient information in order to estimate such a displacement vector field supplementary constraints are necessary for example the postulate that a displacement vector field varies smoothly as a function of the image position taken as a general requirement this creates difficulties at gray value transitions which correspond to occluding contours nagel therefore introduced the oriented smoothness requirement which restricts variations of the displacement vector field only in directions with small or no variation of gray values this contribution reports results of an investigation about how such an oriented smoothness constraint may be formulated and evaluated

error estimates for a mixed finite element discretization of a two phase porous media flow model with dynamic capillarity abstract we analyze a fully discrete numerical scheme for the model describing two phase immiscible flow in porous media with dynamic effects in the capillary pressure we employ the euler implicit method for the time discretization the spatial discretization is based on the mixed finite element method mfem specifically the lowest order raviart thomas elements are applied in this paper the error estimates for the saturation fluxes and phase pressures in l 0 t l 2 are derived for the temporal and spatial discretization to show the convergence of the scheme finally we present some numerical results to support the theoretical findings

a computational framework and an algorithm for the measurement of visual the robust measurement of visual motion from digitized image sequences has been an important but difficult problem in computer vision this paper describes a hierarchical computational framework for the determination of dense displacement fields from a pair of images and an algorithm consist ent with that framework our framework is based on the separation of the image intensity information as well as the process of measuring motion according to scale the large scale intensity information is first used to obtain rough estimates of image motion which are then refined by using intensity information at smaller scales the estimates are in the form of displacement or velocity vectors for pixels and are accompanied by a direction dependent confidence measure a smoothness constraint is employed to propagate the measurements with high confidence to their neigboring areas where the confidences are low at all levels the computations are pixel parallel uniform across the image and based on information from a small neighborhood of a pixel for our algorithm the local displacement vectors are determind by mini mizing the sum of squared differences ssd of intensities the confidence measures are derived from the shape of the ssd surface and the smoothness constraint is cast in the form of energy minimization results of applying our algorithm to pairs of real images are included in addition to our own

lucas kanade meets horn schunck combining local and global optic flow methods differential methods belong to the most widely used techniques for optic flow computation in image sequences they can be classified into local methods such as the lucas kanade technique or bigun s structure tensor method and into global methods such as the horn schunck approach and its extensions often local methods are more robust under noise while global techniques yield dense flow fields the goal of this paper is to contribute to a better understanding and the design of novel differential methods in four ways i we juxtapose the role of smoothing regularisation processes that are required in local and global differential methods for optic flow computation ii this discussion motivates us to describe and evaluate a novel method that combines important advantages of local and global approaches it yields dense flow fields that are robust against noise iii spatiotemporal and nonlinear extensions as well as multiresolution frameworks are presented for this hybrid method iv we propose a simple confidence measure for optic flow methods that minimise energy functionals it allows to sparsify a dense flow field gradually depending on the reliability required for the resulting flow comparisons with experiments from the literature demonstrate the favourable performance of the proposed methods and the confidence measure

exponential stability of a class of nonlinear systems via fixed point theory abstract in this paper the problem of globally stochastically exponential stability in the p th moment for a class of t s fuzzy stochastic impulsive genetic regulatory networks with random discrete delays distributed delays and parameter uncertainties is discussed by utilizing the theory of stochastic analysis semigroup theory and fixed point theory a novel sufficient condition to guarantee the globally stochastically exponential stability in the p th moment of the considered genetic regulatory networks is derived eventually an example is given to demonstrate that the obtained result is effective

robust stability for uncertain genetic regulatory networks with interval time varying delays this paper addresses the problem of robust stability of uncertain genetic regulatory networks grns with interval time varying delays we derive some new delay range dependent and delay derivative dependent independent stability criteria by employing some free weighting matrices and linear matrix inequalities in our analysis we carefully consider the relationship between the time varying state delays and their bounds when calculating the upper bound of the derivative of lyapunov functional we hence show that the rigorous requirement of other literatures that the time derivatives of time varying delays must be smaller than one is abandoned in the proposed scheme the new criteria are applicable to both fast and slow time varying delays finally four numerical examples are presented to illustrate the effectiveness and the less conservativeness of the developed results

brief homogeneous lyapunov functions for systems with structured uncertainties the problem addressed in this paper is the construction of homogeneous polynomial lyapunov functions hplfs for linear systems with time varying structured uncertainties a sufficient condition for the existence of an hplf of given degree is formulated in terms of a linear matrix inequalities lmi feasibility problem this condition turns out to be also necessary in some cases depending on the dimension of the system and the degree of the lyapunov function the maximum norm of the parametric uncertainty for which there exists a homogeneous polynomial lyapunov function is computed by solving a generalized eigenvalue problem the construction of such lyapunov functions is efficiently performed by means of popular convex optimization tools for the solution of problems in lmi form comparisons with other classes of lyapunov functions through numerical examples taken from the literature show that hplfs are a powerful tool for robustness analysis

lmi techniques for optimization over polynomials in control a survey numerous tasks in control systems involve optimization problems over polynomials and unfortunately these problems are in general nonconvex in order to cope with this difficulty linear matrix inequality lmi techniques have been introduced because they allow one to obtain bounds to the sought solution by solving convex optimization problems and because the conservatism of these bounds can be decreased in general by suitably increasing the size of the problems this survey aims to provide the reader with a significant overview of the lmi techniques that are used in control systems for tackling optimization problems over polynomials describing approaches such as decomposition in sum of squares positivstellensatz theory of moments polya s theorem and matrix dilation moreover it aims to provide a collection of the essential problems in control systems where these lmi techniques are used such as stability and performance investigations in nonlinear systems uncertain systems time delay systems and genetic regulatory networks it is expected that this survey may be a concise useful reference for all readers

finite difference methods for two phase incompressible flow in porous media two phase incompressible flow in porous media is governed by a system of nonlinear partial differential equations convection physically dominates diffusion and the object of this paper is to develop a finite difference procedure that reflects this dominance the pressure equation which is elliptic in appearance is discretized by a standard five point difference method the concentration equation is treated by an implicit finite difference method that applies a form of the method of characteristics to the transport terms a convergence analysis is given for the method

stability analysis of uncertain genetic sum regulatory networks this paper addresses the problem of establishing robust stability of uncertain genetic networks with sum regulatory functions specifically we first consider uncertain genetic networks where the regulation occurs at the transcriptional level and we derive a sufficient condition for robust stability by introducing a bounding set of the uncertain nonlinearity we hence show that this condition can be formulated as a convex optimization through polynomial lyapunov functions and polynomial descriptions of the bounding set by exploiting the square matricial representation smr of polynomials which allows to establish whether a polynomial is a sum of squares sos via a linear matrix inequality lmi then we propose a method for computing a family of bounding sets by means of convex optimizations it is worthwhile to remark that these results are derived in spite of the fact that the variable equilibrium point cannot be computed as being the solution of a system of parameter dependent nonlinear equations and is hence unknown lastly the proposed approach is extended to models where the regulation occurs at different levels and both mrna and protein dynamics are nonlinear

convergence of finite volume schemes for a degenerate convection diffusion equation arising in flow in porous media abstract this paper develops discretizations using the finite volume method for a nonlinear degenerate convection diffusion equation in multiple dimensions on unstructured grids we will derive three families of numerical schemes they are classified as explicit implicit and semi implicit a godunov scheme is used for the convection term it is shown that these finite volume schemes fvs satisfy a discrete maximum principle we prove the convergence of these fvs this is done by means of a priori estimates in l and weak bv estimates under appropriate cfl conditions numerical results for oil recovery simulation are presented

optic flow in harmony most variational optic flow approaches just consist of three constituents a data term a smoothness term and a smoothness weight in this paper we present an approach that harmonises these three components we start by developing an advanced data term that is robust under outliers and varying illumination conditions this is achieved by using constraint normalisation and an hsv colour representation with higher order constancy assumptions and a separate robust penalisation our novel anisotropic smoothness is designed to work complementary to the data term to this end it incorporates directional information from the data constraints to enable a filling in of information solely in the direction where the data term gives no information yielding an optimal complementary smoothing behaviour this strategy is applied in the spatial as well as in the spatio temporal domain finally we propose a simple method for automatically determining the optimal smoothness weight this method bases on a novel concept that we call optimal prediction principle opp it states that the flow field obtained with the optimal smoothness weight allows for the best prediction of the next frames in the image sequence the benefits of our optic flow in harmony ofh approach are demonstrated by an extensive experimental validation and by a competitive performance at the widely used middlebury optic flow benchmark

robust stability of time varying polytopic systems abstract this paper provides global asymptotic stability conditions for time varying continuous time polytopic systems using a parameter dependent lyapunov function the time varying parameter uncertainty as well as its time derivative are modelled as belonging to polytopic convex sets and their dependence is made explicit to get less conservative results a particular case characterized by the parameter uncertainty satisfying a linear differential equation is analyzed and a simpler version of the aforementioned stability conditions is presented the results are expressed in terms of linear matrix inequalities being thus numerically solvable with no big difficulty the theory is illustrated by the determination of the asymptotic stability region of a mathieu s type equation with an uncertain time varying parameter