robust stability of uncertain linear systems with saturating actuators we consider the robust stability of uncertain linear systems with saturating actuators and present two sufficient conditions to guarantee the stability of the closed loop system we assume that the bound of the initial state is known and that the uncertainty is unstructured the obtained results meet our intuition that the lower bound of initial state and the higher bound of saturation level make it easy to design a controller finally we show the usefulness by an example

convergence of sph method for scalar nonlinear conservation laws this paper is devoted to the study of the convergence of weighted particle approximation of nonlinear multidimensional conservation laws for euler equations the method is closely related to the smooth particle hydrodynamics sph method extension of the original algorithm is proposed we use approximate riemann solvers instead of artificial viscosity in order to stabilize the scheme the mathematical analysis is performed by connecting this new approach with the finite volume scheme convergence of the approximate solution in l loc p p infty towards the unique weak entropy solution of the cauchy problem is obtained in the scalar nonlinear case by using uniqueness of measure valued solutions

one dimensional transport equations with discontinuous coefficients we consider one dimensional linear transport equations with bounded but possibly discontinuous coefficient a the cauchy problem is studied from two different points of view in the first case we assume that a is piecewise continuous we give an existence result and a precise description of the solutions on the lines of discontinuity in the second case we assume that a satisfies a one sided lipschitz condition we give existence uniqueness and general stability results for backward lipschitz solutions and forward measure solutions by using a duality method we prove that the flux associated to these measure solutions is a product by some canonical representative of a key words linear transport equations discontinuous coefficients weak stability duality product of a measure by a discontinuous function nonnegative solutions 1991 mathematics subject classification primary 35f10 35b35 34a12 to appear in nonlinear analysis tma departement de mathematiques et applications umr cnrs 8553 ecole normale superieure et cnrs 45 rue d ulm 75230 paris cedex 05 france francois bouchut ens fr mathematiques applications et physique mathematique d orleans umr cnrs 6628 universite d orleans 45067 orleans cedex 2 france james math cnrs fr

convergence of relaxation schemes for initial boundary value problems for conservation laws abstract we consider a scalar conservation law with stiff source term in the quarter plan this equation is relaxed in a quasi linear hyperbolic system the relaxed system is approximated using an upwind scheme converging for fixed relaxation time and vanishing discretization mesh further we use chapman enskog expansion to obtain a viscous scheme for the equilibrium law and prove its convergence to the physical solution boundary information is carefully handled in an appropriate inequality linking the entropy numerical flux and the flux function an extension to general conservative schemes is also investigated

a method for registration of 3 d shapes the authors describe a general purpose representation independent method for the accurate and computationally efficient registration of 3 d shapes including free form curves and surfaces the method handles the full six degrees of freedom and is based on the iterative closest point icp algorithm which requires only a procedure to find the closest point on a geometric entity to a given point the icp algorithm always converges monotonically to the nearest local minimum of a mean square distance metric and the rate of convergence is rapid during the first few iterations therefore given an adequate set of initial rotations and translations for a particular class of objects with a certain level of shape complexity one can globally minimize the mean square distance metric over all six degrees of freedom by testing each initial registration one important application of this method is to register sensed data from unfixtured rigid objects with an ideal geometric model prior to shape inspection experimental results show the capabilities of the registration algorithm on point sets curves and surfaces

convergence of a shock capturing streamline diffusion finite element method for a scalar conservation law in two space dimensions convergence of a shock capturing streamline diffusion nite element method for a conservation law in two space dimensions

renormalized meshfree schemes i consistency stability and hybrid methods for conservation laws this paper is devoted to the study of a new kind of meshfree scheme based on a new class of meshfree derivatives the renormalized meshfree derivatives which improve the consistency of the original weighted particle methods the weak renormalized meshfree scheme built from the weak formulation of general conservation laws turns out to be l 2 stable under some geometrical conditions on the distribution of particles and some regularity conditions of the transport field a time discretization is then performed by analogy with finite volume methods and the l 1 l infty and bv stabilities of the obtained time discretized scheme are studied from the same analogy with finite volume methods a hybrid particle scheme is built using the godunov method and is numerically compared to the weak renormalized scheme

coupling of general lagrangian systems this work is devoted to the coupling of two fluid models such a s two euler systems in lagrangian coordinates at a fixed interface we define coupling conditi ons which can be expressed in terms of continuity of some well chosen variables and then solve the coupled riemann problem in the present setting where the interface is characteristic a particula r choice of dependent variables which are transmitted ensures the overall conservativity

choice of measure source terms in interface coupling for a model problem in gas dynamics this paper is devoted to the mathematical and numerical analysis of a coupling procedure for one dimensional euler systems the two systems have different closure laws and are coupled through a thin fixed interface following the work of 5 we propose to couple these systems by a bounded vector valued dirac measure concentrated at the coupling interface which in the applications may have a physical meaning we show that the proposed framework allows to control the coupling conditions and we propose an approximate riemann solver based on a relaxation approach preserving equilibrium solutions of the coupled problem numerical experiments in constrained optimization problems are then presented to assess the performances of the present method 1 introduction the study of large scale and complex problems exhibiting a wide range of physical space and time scales see for instance 62 35 14 usually requires separate solvers adapted to the resolution of specific scales this is the case of many industrial flows let us quote for example the numerical simulation of two phase flows applied to the burning liquid oxygen hydrogen gas in rocket engines 58 this kind of flow contains both separated and dispersed two phase flows due to atomization and evaporation phenomena this requires appropriate models and solvers for separated and dispersed phases that have to be appropriately coupled another example concerns turbomachine flows which can be modeled by the euler equations of gas dynamics with different closure laws between the stages of the turbine where the conditions of temperature and pressure are strongly heterogeneous the coupling of these different systems is thus necessary to give a complete description of the flow inside the whole turbine the method of interface coupling allows to represent the evolution of such flows where different models are separated by fixed interfaces first coupling conditions are specified at the interface to exchange information between the systems the definition of transmission conditions generally results from physical consideration e g the conservation or the continuity of given variables then the transmission conditions are represented at the discrete level the study of interface coupling for nonlinear hyperbolic systems has received attention for several years in 43 the authors study the scalar case from both mathematical and numerical points of view

strong traces for solutions of multidimensional scalar conservation laws in this paper we consider multidimensional scalar conservation laws without bv estimates defined in a subset d we show that with a non degeneracy hypothesis on the flux we can define a strong notion of trace at the boundary of reached by l 1 convergence

boundary layers in weak solutions of hyperbolic conservation laws this paper is concerned with the initial boundary value problem for a nonlinear hyperbolic system of conservation laws we study the boundary layers that may arise in approximations of entropy discontinuous solutions we consider both the vanishing viscosity method and finite difference schemes lax friedrichs type schemes and the godunov scheme we demonstrate that different regularization methods generate different boundary layers hence the boundary condition can be formulated only if an approximation scheme is selected first assuming solely uniform l infty bounds on the approximate solutions and so dealing with l infty solutions we derive several entropy inequalities satisfied by the boundary layer in each case under consideration a young measure is introduced to describe the boundary trace when a uniform bound on the total variation is available the boundary young measure reduces to a dirac mass from the above analysis we deduce several formulations for the boundary condition which apply whether the boundary is characteristic or not each formulation is based on a set of admissible boundary values following the terminology of dubois lefloch 15 the local structure of these sets and the well posedness of the corresponding initial boundary value problem are investigated the results are illustrated with convex and nonconvex conservation laws and examples from continuum mechanics

the numerical interface coupling of nonlinear hyperbolic systems of conservation laws i the scalar case we study the theoretical and numerical coupling of two general hyperbolic conservation laws the coupling preserves in a weak sense the continuity of the solution at the interface without imposing the overall conservativity of the coupled model in order to analyze the convergence of the coupled numerical scheme we first revisit the approximation of the boundary value problems we then prove the convergence and characterize the limit solution of the coupled schemes in a few simple but significative coupling situations the general coupling problem is analyzed for riemann initial data and illustrated by numerical simulations resume nous nous interessons a une nouvelle forme de couplage de deux systemes hyperboliques de lois de conservation ce couplage assure de facon faible la continuite de la solution a l interface sans imposer la conservativite du modele couple pour etudier la convergence du schema d approximation numerique nous commencons par reprendre les resultats concernant l approximation du probleme aux limites nous demontrons ensuite la convergence du schema couple dans un certain nombre de cas interessants le cas general du couplage est etudie et illustre numeriquement pour une donnee initiale de riemann

initial boundary value problem for conservation laws this paper concerns the initial boundary value problems for some systems of quasilinear hyperbolic conservation laws in the space of bounded measurable functions the main assumption is that the system under study admits a convex entropy extension it is proved that then any twicely differentiable entropy fluxes have traces on the boundary if the bounded solutions are generated by either godunov schemes or by suitable viscous approximations furthermore in the case that the weak interior solutions are generated by godunov schemes any lipschitz continuous entropy fluxes corresponding to convex entropies have traces on the boundary and the traces are bounded above by computable numerical boundary values this in particular gives a trace formula for the flux functions in terms of the numerical boundary data we also investigate the formulation of boundary conditions for systems of hyperbolic conservation laws it is shown that the set of expected boundary values derived from the viscous approximation contains the one derived in terms of the boundary riemann problems and the converse is not true in general the general theory is then applied to some specific examples first several new facts are obtained for convex scalar conservation laws for example we give example which show that godunov schemes produce numerical boundary layers it is shown that any continuous functions of density have traces on the boundary instead of only entropy fluxes we also obtain interior and boundary regularity of the weak solutions for bounded measurable initial and boundary data a generalized oleinik entropy condition is also obtained next we prove the existence of a weak solution to the initial boundary value problem for a family of quadratic system with a uniformly characteristic boundary condition

stability analysis for a class of nonlinear discrete time control systems subject to disturbances and to actuator saturation this paper addresses the stability characterisation problem for a class of nonlinear discrete time control systems subject to actuator saturation and energy bounded disturbance inputs the considered class of systems covers all nonlinear discrete time systems that can be modelled by rational difference equations based on quadratic and piecewise quadratic lyapunov functions conditions based on linear matrix inequalities are proposed to analyse the asymptotic stability internal stability and the l2 input to state stability external stability of the closed loop system the proposed conditions are then incorporated into convex optimisation problems to either maximise an estimate of the region of attraction or a bound on the admissible l2 disturbances and also to obtain an estimate of the system l2 gain for an admissible set of disturbances

two dimensional rigid body kinematics using image contour registration a method for calculating two dimensional rigid body kinematic parameters using shape features is presented proposed applications include the noninvasive quantification of planar joint motion in vivo by using digitized images computed tomographs radiographs etc of a bone contour at two positions the contour curvatures can be best fit to obtain a one to one mapping or registration of the bone images this produces a dense field of displacement vectors from which planar rigid body kinematic parameters can be estimated accuracy was studied using radiographic images of cadaveric femoral bone the two motions of pure rotation with a fixed center of rotation and of pure translation were simulated for pure rotation error in rotation was independent of the rotation magnitude with an average n 10 error of 0 3 0 8 degrees the translation error averaged 0 9 0 5 mm for pure translation the error in rotation was 0 01 0 69 degrees and the error in translation was 0 62 0 98 mm n 10 this novel method has broad applications in the field of planar kinematics especially in cases for which marker fixation is neither possible nor practical

sharp cfl discrete kinetic formulation and entropic schemes for scalar conservation laws we consider semidiscrete and fully discrete conservative finite volume schemes approximating the solution to one dimensional scalar conservation law we show that all e schemes are associated with a discrete kinetic formulation with a nonnegative kinetic defect measure this construction provides an alternative proof of the discrete local entropy inequalities with simple expressions of the discrete entropy fluxes in contrast to the known results which are restricted to cfl of the form lambda q leq 1 2 our proof holds under sharp cfl conditions

renormalized meshfree schemes ii convergence for scalar conservation laws we establish a convergence rate of the renormalized meshfree numerical scheme applied to scalar conservation laws renormalization is a tool introduced in order to eliminate the smoothed particle hydrodynamics sph lack of consistency a conservative scheme the weak renormalized scheme is derived from the general conservation laws weak formulation and is time discretized by using finite volume techniques because of the new form of the derivative approximation the convergence proof of the classical sph method cannot be applied thus we use a kruskov technique to obtain an l 1 norm comparison between the approximate solution and the solution of a regularized conservation law the pseudoviscous problem

technical communique lmi relaxations for robust stability of linear systems with saturating controls a method is proposed for studying robust stability of uncertain linear systems subject to actuator saturation it hinges upon successive lmi relaxations and therefore can readily be implemented using widely available numerical tools the technique is illustrated on two examples and is shown to significantly improve previously published results

augmented lyapunov function approach to l2 gain analysis for discrete time systems with saturation nonlinearities abstract this paper presents a method for l 2 gain analysis of discrete time systems with saturation nonlinearity by using an augmented lyapunov functional by using sector and slope properties of the saturation nonlinearity the l 2 gain performance criterion is obtained via lmi formulation the proposed lyapunov function have augmented quadratic form with states as well as the sector bounded nonlinear function numerical examples show that the proposed method is less conservative than the existing ones

anti windup based dynamic controller synthesis for nonlinear systems under input saturation this paper describes the design of dynamic controller and static anti windup compensator awc for lipschitz nonlinear systems under input saturation global and local awc based control schemes for stabilization of the nonlinear systems are proposed and necessary conditions for feasibility of the control approaches are investigated a one step approach for simultaneous design of h controller and awc by means of linear matrix inequalities lmis is presented herein which supports multi objective synthesis to attain stabilization or tracking robustness against disturbance and noise and penalization of large and high frequency control signals this multi objective synthesis can be accomplished by incorporating design weights as commonly used in the standard h control theory to design a performance oriented anti windup based control scheme lmis for the global control of the nonlinear systems subject to input saturation are derived by application of a quadratic lyapunov function the lipschitz condition the global sector condition l 2 gain reduction substantial matrix algebra and variable transformation in order to cope with unstable and oscillatory nonlinear systems lmi based local results are established using a local sector condition additional conditions are derived by incorporating properties of the saturation function to ensure well posedness of the controller two simulation examples are provided to show the effectiveness of the proposed control schemes for control of stable and chaotic nonlinear systems under input saturation

finite centroid and helical axis estimation from noisy landmark measurements in the study of human joint kinematics abstract recent work on joint kinematics indicates that the finite centroid centre of rotation and the finite helical axis axis of rotation screw axis twist axis are highly susceptible to measurement errors when they are experimentally determined from landmark position data this paper presents an analytical model to describe these effects under isotropic conditions for the measurement errors and for the spatial landmark distribution it appears that the position and direction errors are inversely proportional to the rotation magnitude and that they are much more error prone than the relatively well determined rotation and translation magnitudes furthermore the direction and rotation magnitude errors are inversely proportional to the landmark distribution radius and the position and translation magnitude errors are minimal if the mean position of the landmarks coincides with the centroid or helical axis for the planar centroid the use of rigid body constraints results in considerable precision improvement relative to the classical finite reuleaux method for centroid reconstruction these analytical results can be used to define suitable measurement configurations and they are used in this paper to explain experimental results on rontgenphotogrammetrically acquired in vitro wrist joint movement

calculating the 2d motion of lumbar vertebrae using splines in this study we investigate the use of splines and the icp method besl p mckay n 1992 a method for registration of 3d shapes ieee transactions on pattern analysis and machine intelligence 14 239 256 for calculating the transformation parameters for a rigid body undergoing planar motion parallel to the image plane we demonstrate the efficacy of the method by estimating the finite centre of rotation and angle of rotation from lateral flexion extension radiographs of the lumbar spine in an in vitro error study the method displayed an average error of rotation of 0 44 0 45 degrees and an average error in fcr calculation of 7 6 8 5 mm the method was shown to be superior to that of crisco et al two dimensional rigid body kinematics using image contour registration journal of biomechanics 28 1 119 124 and brinckmann et al quantification of overload injuries of the thoracolumbar spine in persons exposed to heavy physical exertions or vibration at the workplace part i the shape of vertebrae and intervertebral discs study of a yound healthy population and a middle aged control group clinical biomechanics supplement 1 s5 s83 for the tests performed here in general we believe the use of splines to represent planar shapes to be superior to using digitised curves or landmarks for several reasons first with appropriate software splines require less effort to define and are a compact representation with most vertebra outlines using less than 30 control points second splines are inherently sub pixel representations of curves even if the control points are limited to pixel resolutions third there is a well defined method the icp algorithm for registering shapes represented as splines finally like digitised curves splines are able to represent a large class of shapes with little effort but reduce potential segmentation errors from two dimensions parallel and perpendicular to the image gradient to just one parallel to the image gradient we have developed an application for performing all the necessary computations which can be downloaded from http www claritysmart com

convergence of an explicit finite volume scheme for first order symmetric systems this paper is devoted to the derivation of a o h1 2 error estimate for the classical upwind explicit in time finite volume scheme for linear first order symmetric systems such a result already existed for the corresponding implicit in time finite volume scheme since it can be interpreted as a particular case of the space time discontinuous galerkin method but the technique of proof used in that case does not extend to explicit schemes the general framework recently developed to analyse the convergence rate of finite volume schemes for non linear scalar conservation laws can not be used either because it is not adapted for systems even linear in this article we propose a new technique which takes advantage of the linearity of the problem the first step consists in controlling the approximation error u u h l2 by an expression of the form 2 where u is the exact solution g is a particular smooth function and h h are some linear forms depending on the approximate solution u h the second step consists in carefully estimating the error terms and by using uniform stability results for the discrete problem and regularity properties of the continuous solution

coupling techniques for nonlinear hyperbolic equations iv well balanced schemes for scalar multi dimensional and multi component laws this series of papers is devoted to the formulation and the approximation of coupling problems for nonlinear hyperbolic equations the coupling across an interface in the physical space is formulated in term of an augmented system of partial differential equations in an earlier work this strategy allowed us to develop a regularization method based on a thick interface model in one space variable for coupling scalar equations in the present paper we significantly extend this framework and in addition encompass equations in several space variables this new formulation includes the coupling of several distinct scalar conservation laws and allows for a possible covering in space our main contributions are on one hand the design and analysis of a well balanced finite volume method on general triangulations and on the other hand a proof of convergence of this method toward entropy solutions extending coquel cockburn and lefloch s theory restricted to a single conservation law without coupling the core of our analysis is first the derivation of entropy inequalities as well as a discrete entropy dissipation estimate and second a proof of convergence toward the entropy solution of the coupling problem

on nonconservative algorithms for grid interfaces in computations of fluid flows by domain decomposition methods the necessity of conservation at grid interfaces is now widely claimed in this paper we consider nonconservative algorithms for the interfaces our investigation begins with discussions about typical nonconservative interface treatments for one dimensional calculations the analysis shows that the conservation error of a numerical solution caused by a nonconservative interface matching has an upper bound when the solution itself is bounded furthermore if the numerical solution converges as the mesh size goes to zero it converges to a weak solution of the problem under certain conditions that may be detected numerically also we acquire similar results for two dimensional calculations on grids intersecting with each other in an arbitrary way in order to illustrate the theoretical results we present numerical examples and demonstrate that under those conditions conservation error reduces and accuracy for jumps as well as locations of discontinuities improves as the mesh size decreases

spinal shape changes resulting from scoliotic spine surgical instrumentation expressed as intervertebral rotations and centers of rotation this paper reports the changes in spinal shape resulting from scoliotic spine surgical instrumentation expressed as intervertebral rotations and centers of rotation the objective is to test the hypothesis that the type of spinal instrumentation system cotrel dubousset versus colorado does not influence these motion parameters intervertebral rotations and centers of rotation of the scoliotic spines were computed from the pre and post operative radiographs of 82 patients undergoing spinal correction the three dimensional 3d reconstruction of six anatomical landmarks was achieved for each of the thoracic and lumbar vertebrae a least squares approach based on singular value decomposition was used to calculate the rigid body transformation parameters average centers of rotation for all intervertebral levels are located in the neural canal at the mid sagittal plane and approximately at the superior endplate level of the inferior vertebra intervertebral rotations have components in all planes 6 7 degrees frontal 5 5 degrees sagittal and 4 5 degrees transverse rms for all intervertebral levels nearly all intervertebral rotations and centers of rotation are not significantly different for the two instrumentation systems various intervertebral rotations and 3d reconstruction errors were simulated on a theoretical model of a lumbar functional unit to assess the proposed method intervertebral rotation errors were 1 7 degrees when simulating 3d errors of 3mm on the position of the landmarks maximum errors for the position of centers of rotation were below 1cm in the case of intervertebral rotations larger than 2 5 degrees most cases but were larger 38 mm for small intervertebral rotations 1 degrees the type of instrumentation system did not influence intervertebral rotations and centers of rotation these results provide valuable data for the development and validation of simulation models for surgical instrumentation of idiopathic scoliosis

simultaneous quadratic stabilization for a class of non linear systems with input saturation using dynamic surface control in this paper a new method to estimate the initial condition set which guarantees the quadratic stability for a class of non linear systems via dynamic surface control dsc in the presence of input saturation has been proposed the estimated set is enlarged to allow some degree of input saturation while achieving the simultaneous quadratic stability of the system in the domain a convex optimization problem to obtain ellipsoidal initial condition sets via a linear matrix inequality lmi approach as well as an illustrative example will be presented

saturated linear quadratic regulation of uncertain linear systems stability region estimation and controller design this paper considers the problems of estimating the stability region domain of attraction and controller design for uncertain linear continuous time systems with input saturation when linear quadratic lq optimal controller is used by exploiting the structure of the lq controller and the property of saturation functions it is established that the estimation of stability region can be obtained by solving linear matrix inequality lmi problems moreover an iterative lmi ilmi algorithm is presented to design an lq controller such that the largest estimated stability region can be obtained two examples are given to compare our results with existing ones

convergence of finite volume monotone schemes for scalar conservation laws on bounded domains this paper is devoted to the study of the finite volume methods used in the discretization of conservation laws defined on bounded domains general assumptions are made on the data the initial condition and the boundary condition are supposed to be measurable bounded functions using a generalized notion of solution to the continuous problem namely the notion of entropy process solution see 9 and a uniqueness result on this solution we prove that the numerical solution converges to the entropy weak solution of the continuous problem in l p loc for every p in 1 infty this also yields a new proof of the existence of an entropy weak solution

a least squares algorithm for the equiform transformation from spatial marker co ordinates the present paper describes an algorithm for estimating the translation vector and the rotation matrix of a moving body from noisy measurements on the spatial co ordinates of at least three non collinear markers a sensitivity analysis of the estimated parameters and of the helical axis is presented in terms of characteristics of the marker distribution the implementation of the proposed algorithm in a fortran subroutine is appended

optimal marker placement for calculating the instantaneous center of rotation abstract a computer simulation with error propagation was performed to determine the optimal placement of marker points for calculating the instantaneous center of rotation cri the authors assume that planar rigid body motion occurs between two positions each defined by marker points noisy marker points were generated by perturbing their coordinates with random values from a normal population of errors the effects of these errors on the range of errors in calculating cri location were investigated parametric analysis determined that marker point placement had important effects on cri error marker placement was optimal when the estimated cri was located at the midpoint between the marker points while increasing the distance between marker points increased accuracy there is a critical distance above which no additional increase in accuracy was noted when using this placement the farther the marker midpoint was from the cri the greater was the error at these placements increasing the distance between the marker points continually decreased cri error the methodologies presented here help to improve the accuracy with which the location of the cri can be calculated however it is emphasized that the cri remains sensitive to noise and investigators should apply this kinematic parameter knowingly

a numerical method for transport equations with discontinuous flux functions application to mathematical modeling of cell dynamics in this work we propose a numerical method to handle discontinuous fluxes arising in transport like equations more precisely we study hyperbolic pdes with flux transmission conditions at interfaces between subdomains where coefficients are discontinuous a dedicated finite volume scheme with a limited high order enhancement is adapted to treat the discontinuities arising at interfaces the validation of the method is done on one and two dimensional toy problems for which exact solutions are available allowing us to do a thorough convergence study we then apply the method to a biological model focusing on complex cell dynamics that initially motivated this study and illustrates the full potentialities of the scheme

kinetic approximation of a boundary value problem for conservation laws we design numerical schemes for systems of conservation laws with boundary conditions these schemes are based on relaxation approximations taking the form of discrete bgk models with kinetic boundary conditions the resulting schemes are riemann solver free and easily extendable to higher order in time or in space for scalar equations convergence is proved we show numerical examples including solutions of euler equations

numerical viscosity and convergence of finite volume methods for conservation laws with boundary conditions the authors study the convergence of finite volume schemes for general multidimensional conservation laws with boundary conditions a unique result for a measure valued solution which generalizes those of diperna for unbounded domains and szepessy for bounded domains is proved it gives us sufficient conditions to get convergence by studying carefully the entropy production for one dimensional e schemes we are able to prove convergence of finite volume e schemes under general assumption

boundary conditions for nonlinear hyperbolic systems of conservation laws we propose two formulations of the boundary conditions for nonlinear hyperbolic systems of conservation laws a first approach is based on the vanishing viscosity method and a second one is related to the riemann problem the equivalence between these two conditions is studied the latter formulation is extended to treat numerically physically relevant boundary conditions monodimensional experiments are presented

commuting matrices equilibrium points for control systems with single saturated input in this paper commutative matrices of multiple input multiple output mimo linear systems are considered the existence of the feedback matrices of a commutative state matrix set in the mimo closed loops is reduced to the existence of an invariant subspace of a matrix a the existence of feedback matrices in systems in open loop is equivalent to the existence of the solution of matrix equations denoted by kronecker products by defining new equilibrium points the relationship between equilibrium points are discussed for a linear system with a single saturated input four criteria for equilibrium points are outlined for such linear systems finally four interesting examples including their corresponding simulink plots are shown to illustrate the above results