robust stability and robust stabilizability for periodically switched linear systems abstract in this paper the problem of robust stability and robust stabilizability for periodically switched linear systems is studied the stability radius involving structured perturbations acting on both coefficient matrices and switching moments is introduced and investigated some lower bounds for stability radii of periodically switched linear systems are provided after that we derive the notion of fast and slow stabilizability for these systems some characterizations for robust stabilizability under structured perturbations are established several examples are given to illustrate the obtained results

stochastic stability and l1 gain analysis for positive nonlinear semi markov jump systems with time varying delay via t s fuzzy model approach abstract this paper treats the issues of stochastic stability and l 1 gain analysis for continuous time positive fuzzy semi markov jump systems pfsmjss with time varying delay the system under consideration involves semi markov stochastic process related to weibull distribution the practical systems such as lotka volterra population model described by pfsmjss always need to consider the sudden change in the operating process to deal with these problems a sufficient condition for stochastic stability of pfsmjss is established which is dependent of the bound of time varying delay then based on the obtained results l 1 gain performance is analyzed in standard linear programming lp finally lotka volterra population model shows the validity of the conclusions

disturbance observer based control for semi markovian jump systems with generally uncertain transition rate and saturation nonlinearity abstract this paper deals with the problem of disturbance observer based control dobc for semi markovian jump systems s mjss with generally uncertain transition rate tr and saturation nonlinearity unlike the existing theories the proposed method considers the external disturbance and saturation nonlinearity in s mjss with more general tr first of all to study this dobc problem the sufficient condition for stochastic stability of the system is derived by the use of lyapunov krasovskii functional then the design methods of the anti disturbance controller and the disturbance observer are proposed based on the given stability condition of the closed loop system furthermore the maximum domain of attraction is estimated by solving an optimization iterative algorithm finally two numerical examples are given to prove the correctness of the proposed results

application of a fractional step method to incompressible navier stokes equations a numerical method for computing three dimensional time dependent incompressible flows is presented the method is based on a fractional step or time splitting scheme in conjunction with the approximate factorization technique it is shown that the use of velocity boundary conditions for the intermediate velocity field can lead to inconsistent numerical solutions appropriate boundary conditions for the intermediate velocity field are derived and tested numerical solutions for flows inside a driven cavity and over a backward facing step are presented and compared with experimental data and other numerical results

absolute exponential l1 gain analysis and synthesis of switched nonlinear positive systems with time varying delay this paper investigates absolute exponential stability and stabilization with l1 gain performance of switched nonlinear positive systems with time varying delay nonlinear functions considered in the paper are located in a sector field and the time varying delay is unknown but bounded the notion of absolute exponential l1 stability of switched nonlinear positive systems is first introduced a nonlinear lyapunov krasovskii functional is constructed for the underlying systems by using the lyapunov krasovskii functional a sufficient condition for absolute exponential l1 stability of the systems is established in terms of linear programming then absolute exponential l1 control synthesis of the systems is addressed a feedback control law containing nonlinear functions and a state feedback control law are designed respectively by comparing with existing results it is shown that the present design is less conservative finally an illustrative example is provided to illustrate the effectiveness of the results

robust stability for switched positive systems with d perturbation and time varying delay this paper is focused on studying the robust stability of switched positive systems with d perturbation and time varying delay all subsystems are considered to be unstable based on the partition of state space on the nonnegative orthant sufficient conditions in terms of linear programming are obtained to guarantee such system to be asymptotically stable the hysteresis switching laws are designed to prevent chattering behavior via the single copositive lyapunov function and multiple copositive lyapunov functions approaches respectively two illustrative examples concerned with price model of goods are provided to display the effectiveness of the obtained results

linear stability analysis in fluid structure interaction with transpiration part ii numerical analysis and applications this paper constitutes the numerical counterpart of the mathematical framework introduced in part i we address the problem of flutter analysis of a coupled fluid structure system involving an incompressible newtonian fluid and a reduced structure we use the linearization principle approach developed in part i particularly suited for fluid structure problems involving moving boundaries thus the stability analysis is reduced to the computation of the leftmost eigenvalues of a coupled eigenproblem of minimal complexity this eigenproblem involves the linearized incompressible navier stokes equations and those of a reduced linear structure the coupling is realized through specific transpiration interface conditions the eigenproblem is discretized using a finite element approximation and its smallest real part eigenvalues are computed by combining a generalized cayley transform and an implicit restarted arnoldi method finally we report three numerical experiments a structure immersed in a fluid at rest a cantilever pipe conveying a fluid flow and a rectangular bridge deck profile under wind effects the numerical results are compared to former approaches and experimental data the quality of these numerical results is very satisfactory and promising

on delay independent stability of a class of nonlinear positive time delay systems we present a condition for delay independent stability of a class of nonlinear positive systems this result applies to systems that are not necessarily monotone and extends recent work on cooperative nonlinear systems

the brunn minkowski inequality minkowski s first inequality and their duals abstract quantitative versions are given of the equivalence of the brunn minkowski inequality and minkowski s first inequality from the brunn minkowski theory similar quantitative versions are obtained of the equivalence of the corresponding inequalities from lutwak s dual brunn minkowski theory the main results are shown to be the best possible up to constant factors

l1 induced norm and controller synthesis of positive systems in this paper the problem of 1 1 induced controller design for discrete time positive systems is investigated with the use of linear lyapunov function an analytical method to compute the exact value of 1 1 induced norm is first presented then a novel characterization for stability and 1 1 induced performance is proposed based on the characterization a necessary and sufficient condition for the existence of desired controllers is derived and an iterative convex optimization approach is developed to solve the condition in addition the synthesis of the state feedback controller for single input multiple output simo positive systems is investigated for this special case an analytic solution is established to show how the optimal 1 1 induced controller can be designed and some links to the spectral radius of the closed loop systems are provided finally the theoretical results are illustrated through a numerical example

finite time h filtering for a class of discrete time markovian jump systems with switching transition probabilities subject to average dwell time switching an extension of fixed transition probability markovian switching model to combine time varying transition probabilities has offered another set of useful regime switching models this paper investigated the problem of finite time h filtering for a class of discrete time markovian jump systems with switching transition probabilities subject to average dwell time switching based on the results of finite time boundness and average dwell time a novel sufficient condition for finite time bounded of h filtering is derived and the system trajectory stays within a prescribed bound finally an example is provided to illustrate the usefulness and effectiveness of the proposed method

finite element methods for viscous incompressible biglobal instability analysis on unstructured meshes viscous linear 3 d biglobal instability analyses of incompressible flows have been performed using finite element numerical methods with a view to extend the scope of application of this analysis methodology to flows over complex geometries the initial value problem ivp based on the linearized navier stokes equations lnse as well as the real and the complex partial differential equation based generalized eigenvalue problems evp have been solved a mixed p 2 p 1 finite element spatial discretization on unstructured meshes for both the lnse and the evp approaches has been used for the time discretization of the lnse a characteristics method has been used for the first time in the context of flow stability analysis the complex biglobal evp has also been solved for the first time in the context of a finite element numerical discretization in either its real or its complex form the evp has been solved without the need to introduce pseudocompressibility into the incompressible equations which has simplified the systems to be solved without sacrificing accuracy an arnoldi approach has been used to recover the most significant eigenvalues in this context the associated solutions to the resulting linear systems were obtained by iterative methods generalized minimal residual with incomplete lower upper preconditioning or conjugate gradient with i cholesky preconditioning depending on whether the coefficient matrix was symmetric or not the 3 d instability of the classic 2 d lid driven cavity flow and that of the rectangular duct flow were used as validation cases for the real and complex evp respectively new results have been obtained for the 3 d biglobal instability of two closed and one open flow namely the regularized lid driven cavity of rectangular and triangular shape and flow in the wake of a model bluff body

dual orlicz brunn minkowski theory dual orlicz lϕ affine and geominimal surface areas abstract this paper aims to develop the basic theory for the dual orlicz l affine and geominimal surface areas of star bodies basic properties of these new affine invariants are established moreover related orlicz affine isoperimetric cyclic santalo type and alexandrov fenchel type inequalities are obtained

bifurcation analysis of brown tide by reaction diffusion equation using finite element method in this paper we analyze the bifurcation of a biodynamics system in a two dimensional domain by virtue of reaction diffusion equations the discretization method in space is the finite element method the computational algorithm for an eigenspectrum is described in detail on the basis of an analysis of eigenspectra according to helmholtz s equation the discrete spectra in regards to the physical variables are numerically obtained in two dimensional space in order to investigate this mathematical model in regards to its practical use we analysed the stability of two cases i e hydranth regeneration in the marine hydroidtubulariaand a brown tide in a harbor in japan by evaluating the stability according to the linearized stability definition the critical parameters for outbreaks of brown tide can be theoretically determined in addition results for the linear combination of eigenspectrum coincide with the distribution of the observed brown tide its periodic characteristic was also verified

valuations and busemann petty type problems projection and intersection bodies define continuous and gl n contravariant valuations they played a critical role in the solution of the shephard problem for projections of convex bodies and its dual version for sections the busemann petty problem we consider the question whether fkfl implies v k v l where f is a homogeneous continuous operator on convex or star bodies which is an so n equivariant valuation important previous results for projection and intersection bodies are extended to a large class of valuations

time dependent algorithms for the simulation of viscoelastic flows with spectral element methods applications and stability this paper presents the development of spectral element methods to simulate unsteady flows of viscoelastic fluids using a closed form differential constitutive equation the generation and decay poiseuille planar flows are considered as benchmark problems to test the abilities of our computational method to deal with truly time dependent flows satisfactory results converging toward steady state regimes have been obtained for the flow through a four to one planar abrupt contraction with unsteady algorithms time dependent simulations of viscoelastic flows are prone to numerical instabilities even for simple geometrical configurations possible methods to improve the numerical stability of the computational algorithms are discussed in view of the results carried out with numerical simulations for the flows through a straight channel and the four to one contraction

one dimensional finite element method in hydrodynamic stability the stability of plane poiseuille flow and circular couette flow are examined with respect to linear azimuthally periodic disturbances by the finite element method in the case of couette motion solutions are obtained for a narrow gap a wide gap and a dilute polymer solution with an elongational viscosity in the narrow gap limit when both cylinders rotate at almost equal speed in the same direction results are in good agreement with previous calculations by other numerical methods

l gain analysis for positive systems with distributed delays this paper addresses the l gain analysis problem of positive linear systems with distributed delays by virtue of the positivity and linearity of the system we first study the monotonic and asymptotic property of the system with distributed delays then by resorting to an auxiliary system without time delay an explicit expression of the l gain of positive systems with distributed delays is given in terms of system matrices moreover the results are extended to positive systems with distributed delays over a bounded time varying interval finally a necessary and sufficient condition on the l gain of an asymptotically stable positive system with distributed delays is presented via linear programming

numerical methods for hypersonic boundary layer stability various numerical methods for the solution of linear stability equations for compressible boundary layers are compared both the global and local eigenvalue methods for temporal stability analysis are discussed global methods are used to compute all the eigenvalues of the discretized system when a guess for the desired eigenvalue is available local methods may be used both to purify the eigenvalue and compute the associated eigenfunctions the extension to spatial stability analysis is also considered the discretizations studied include a second order finite difference method a fourth order accurate two point compact difference scheme and a chebyshev spectral collocation method eigenvalue results are presented for mach numbers up to 10 as the mach number increases the performance of the spectral method deteriorates due to the outward movement of the critical layer to alleviate this problem a multi domain spectral collocation method is developed which exhibits better convergence the overall performance of the fourth order compact scheme is excellent our results also indicate that in the limit of vanishing mach number there exist stable discrete modes in addition to the discrete modes of the orr sommerfeld equation

eigenmodes of a counter rotating vortex dipole highly resolved solutions of the two dimensional incompressible navier stokes and continuity equations describing the evolution of a counter rotating pair of vortices have been obtained accurately and efficiently by spectral collocation methods and an eigenvalue decomposition algorithm such solutions have formed the basic state for subsequent three dimensional biglobal eigenvalue problem linear instability analyses which monitor the modal response of these vortical systems to small amplitude perturbations periodic along the homogeneous axial spatial direction without the need to invoke an assumption of azimuthal spatial homogeneity a finite element methodology gonzalez l m theofilis v and gomez blanco r finite element numerical methods for viscous incompressible biglobal linear instability analysis on unstructured meshes aiaa journal vol 45 no 4 2007 pp 840 855 has been adapted to study the instability of vortical flows and has been validated on the batchelor vortex mayer e w and powell k g viscous and inviscid instabilities of a trailing vortex journal of fluid mechanics vol 245 1992 pp 91 114 subsequently the instability of the counter rotating dipole has been analyzed aspects monitored have been the dependence of the results on the reynolds number the value of the nonzero axial velocity considered and the time at which the quasi steady basic flow has been monitored essential to the success of the analysis has been the appropriate design of a calculation mesh as well as exploitation of the symmetries of the basic state the spatial structure of the amplitude functions of all unstable eigenmodes reflects the inhomogeneity of the basic state in the azimuthal spatial direction thus providing a posteriori justification for the use of the biglobal eigenvalue problem concept

high re solutions for incompressible flow using the navier stokes equations and a multigrid method the vorticity stream function formulation of the two dimensional incompressible navierstokes equations is used to study the effectiveness of the coupled strongly implicit multigrid csi mg method in the determination of high re fine mesh flow solutions the driven flow in a square cavity is used as the model problem solutions are obtained for configurations with reynolds number as high as 10 000 and meshes consisting of as many as 257 x 257 points for re 1000 the 129 x 129 grid solution required 1 5 minutes of cpu time on the amdahl 470 v 6 computer because of the appearance of one or more secondary vortices in the flow field uniform mesh refinement was preferred to the use of one dimensional gridclustering coordinate transformations the past decade has witnessed a great deal of progress in the area of computational fluid dynamics developments in computer technology hardware as well as in advanced numerical algorithms have enabled attempts to be made towards analysis and numerical solution of highly complex flow problems for some of these applications the use of simple iterative techniques to solve the navier stokes equations leads to a rather slow convergence rate for the solutions the solution convergence rate can be seriously affected if the coupling among the various governing differential equations is not properly honored either in the interior of the solution domain or at its boundaries the rate of convergence is also generally strongly dependent on such problem parameters as the reynolds number the mesh size and the total number of computational points this has led several researchers to examine carefully the recently emerging multigrid mg technique as a useful means for enhancing the convergence rate of iterative numerical methods for solving discretized equations at a number of computational grid points so large as to be considered impractical previously

effect of curvature on three dimensional boundary layer stability the problem of the stability of a three dimensional laminar boundary layer formed on a curved surface is considered a calculation scheme which takes account of the curvature of the flow streamlines and of the surface is proposed for the prediction of the development of small amplitude temporal disturbances computations have been performed for the flow over the windward face of an infinitely long yawed cylinder and comparisons have been made with experimental data these indicate that the theory correctly predicts many of the features of the unstable laminar flow the theory also suggests that transition in this particular situation is dominated by traveling disturbance waves and that at the experimentally observed transition location the wave which has undergone greatest total amplification has an amplitude ratio of approximately e to the 11th when the effects of curvature are omitted the maximum amplitude ratio at transition is about e to the 17th

a direct method for computation of simple bifurcations in the present study we focus on the computational analysis of partial differential equations with emphasis on the stability of the equilibrium states and on their bifurcations in practical applications it is not sufficient to obtain an equilibrium solution at a point in the parameter space the equilibrium solution branches their stability characteristics and particularly the critical points of transition from one state to another e g bifurcation points are required for understanding the physics of the problem in principle the linear stability of an equilibrium state can be investigated by solving an eigenvalue problem and consequently the points of bifurcations can be detected we review alternative techniques for detecting bifurcation points which are direct and numerically efficient and therefore more practical starting with a large dimension dynamical system which represents a projection of a set of coupled partial differential equations onto a basis function we discuss the relative effectiveness of the time evolution approach the test function approach and the direct method we will then extend the direct method for a more practical and efficient implementation with this technique we compute the sequence of transitions from steady state to chaotic flow in a two dimensional lid driven cavity of aspect ratio 0 8 1 0 and 1 5 we demonstrate the effectiveness of this technique by computing interesting new dynamics in this relatively simple hydrodynamic system in particular we show that depending on the aspect ratio the first transition from steady state could be through a supercritical or a subcritical hopf bifurcation leading the system to a time periodic state we construct the destabilizing disturbance structure and conclude that the first bifurcation of the primary steady state is due to the centrifugal instability of the primary eddy the mechanism of transition to chaos is low dimensional the transition to chaos occurs after a secondary hopf bifurcation

stability and stabilization of discrete time semi markov jump linear systems via semi markov kernel approach this technical note is concerned with the problems of stability and stabilization for a class of discrete time semi markov jump linear systems s mjlss the discrete time semi markov kernel smk is introduced where the probability density function of sojourn time is dependent on both current and next system mode as a consequence different types of distributions and or different parameters in a same type of distribution of sojourn time depending on the target mode towards which the system jumps can coexist in each mode of a smk the underlying s mjlss are therefore more general than those considered in existing studies a new stability concept generalizing the traditional mean square stability is proposed such that numerically testable criteria on the basis of smk are obtained numerical examples are presented to illustrate the validity and advantage of the developed theoretical results

three dimensional solutions of trailing vortex flows using parabolized equations flows of practical significance exist like systems of trailing vortices which are inhomogeneous in two directions and weakly dependent along the third spatial direction exploiting these characteristics an integration of the navier stokes equations using the parabolic navier stokes concept is proposed for the recovery of steady solutions that might be used subsequently in the scope of primary instability analyses the parabolic navier stokes equations are first formulated in a cylindrical coordinate frame and used to calculate the solution of an isolated axisymmetric nonparallel axially developing vortex then the fully three dimensional flow corresponding to a counter rotating pair of nonparallel vortices is obtained by parabolic navier stokes formulated in cartesian coordinates stable high order finite difference based numerical schemes are used for the spatial discretization to exploit the benefits of using a sparse direct solver for the inversion of the large matrices resulting from the discre

application of spectral collocation techniques to the stability of swirling flows abstract a chebyshev spectral collocation method for the temporal and spatial stability of swirling flows is presented the linearized stability equations in cylindrical coordinates are solved using the method and eigenvalues obtained by employing the qz routine the developed algorithm is found to be robust and easily adaptable to various flow configurations including internal and external flows with only minor changes in the application of the boundary conditions the accuracy and efficiency of the spectral method is tested for plane poiseuille flow annular flow rotating pipe flow and a trailing line vortex

tomography of convex and star bodies new definitions of a star body and its radial function are given these are used in studying sections of convex and star bodies in conjunction with the dual mixed volumes of lutwak the spherical radon transform and the i chord functions when the body contains the origin in its interior and i 0 the latter equals the sum of the values of the ith power of the radial function at antipodal points in the unit sphere special cases of results obtained include the following a simple construction is given of non spherical convex bodies of constant i section i e such that each i dimensional section through an interior point has the same i dimensional volume it is shown that two star bodies containing the origin in their interiors and with analytic boundaries must be equal up to reflection in the origin if the volumes of their sections by i dimensional subspaces for two different values of i are equal examples are given to show that the last statement is no longer necessarily true if the boundaries are only infinitely differentiable or if the bodies are convex polytopes it is also proved that a star body which has constant i section for two different values of i with respect to the same interior point must be a ball centered at that point this answers the dual of the old question as to whether there exist non spherical convex bodies of constant width and constant brightness new results are also obtained concerning the determination of convex polytopes by the volumes of their sections through one or more points

a positive answer to the busemann petty problem in three dimensions we prove that in e3 the busemann petty problem concerning cen tral sections of centrally symmetric convex bodies has a positive answer together with other results this settles the problem in each dimension

finite time stabilization for a class of switched time delay systems under asynchronous switching switched control systems can be used to describe many practical processes with switching phenomena such as power electronics mechanical systems etc in this paper the problem of finite time stabilization under asynchronous switching is dealt with for a class of switched time delay systems with nonlinear disturbances firstly the nonlinear uncertainties are transformed into the linear time varying forms via the differential mean value theorem under some assumptions secondly by applying the average dwell time method and convexity principle a finite time stability condition for the unforced switched time delay system is established finally an asynchronous switching state feedback controller is designed which renders the considered system finite time stable a numerical example is provided to show the effectiveness of the developed results

stochastic stability of positive markov jump linear systems abstract this paper investigates on the stability properties of positive markov jump linear systems pmjls s i e markov jump linear systems with nonnegative state variables specific features of these systems are highlighted in particular a new notion of stability exponential mean stability is introduced and is shown to be equivalent to the standard notion of 1 moment stability moreover various sufficient conditions for exponential almost sure stability are worked out with different levels of conservatism the implications among the different stability notions are discussed it is remarkable that thanks to the positivity assumption some conditions can be checked by solving linear programming feasibility problems

l1 gain performance analysis and positive filter design for positive discrete time markov jump linear systems a linear programming approach abstract this paper is concerned with the l 1 gain performance analysis and positive filter design for a positive discrete time markov jump linear system mjls by using a linear programming lp approach first by constructing a linear stochastic lyapunov function and introducing an equivalent deterministic positive discrete time linear system necessary and sufficient conditions in the form of lp are derived for stochastic stability and l 1 gain performance of the positive discrete time mjls then a sufficient condition on the existence of the desired positive l 1 gain filter is provided the desired positive l 1 gain filter can be designed by solving a standard lp problem the pest s structured population dynamic model is employed to illustrate the effectiveness of the proposed method

stability analysis and control synthesis for positive semi markov jump systems with time varying delay abstract this paper deals with stability analysis and control synthesis for positive semi markov jump systems s mjss with time varying delay in which the stochastic semi markov process related to nonexponential distribution is considered the main motivation for this paper is that the positive condition sometimes needs to be considered in s mjss and the controller design methods in the existing have some conservation to deal with these problems the weak infinitesimal operator is firstly derived from the point of view of probability distribution under the constraint of positive condition then some sufficient conditions for stochastic stability of positive s mjss are established by implying the linear lyapunov krasovskii functional depending on the bound of time varying delay furthermore an improved stabilizing controller is designed via decomposing the controller gain matrix such that the resulting closed loop system is positive and stochastically stable in standard linear programming the advantages of the new framework lie in the following facts 1 the weak infinitesimal operator is derived for s mjss with time varying delay under the constraint of positive condition and 2 the less conservative stabilizing controller is designed to achieve the desired control performance finally three examples one of which is the virus mutation treatment model are given to demonstrate the validity of the main results

linear stability of incompressible flow using a mixed finite element method we analyzed the linear stability for incompressible flow using the mixed finite element method first by means of the fractional step finite element method the two dimensional base flows were numerically computed over a range of reynolds numbers and then they were perturbed with three dimensional disturbances by using linear stability and normal mode analysis we obtained the partial differential equations governing the evolution of perturbation from linearized navier stokes equations with slight compressibility in terms of the mixed finite element discretization in which six node quadratic lagrange triangular elements with quadratic interpolation for velocities p2 and three node linear lagrange triangular elements for pressure p1 were used a nonsingular generalized eigenproblem was formulated from these equations whose solution gives the dispersion relationship between the complex growth rate and the wave number we examined the stability of lid driven cavity flow in this study the stability results obtained from thep2p1elements were compared with those fromp1p1elements the spatial distribution of the pressure disturbance can be smoothed by using ap2p1element such as that in the simulation of incompressible flows by the mixed finite element method however the choice of elemental type has little influence on the stability results this study presents stability curves to identify the critical reynolds number and the critical wavelength of the neutral mode and discusses the instability mechanism the taylor goertler like vortices in the cavity were obtained by means of the reconstruction of three dimensional flows the stability results and the reconstructed three dimensional flows were in agreement with the observed ones and the other numerical stability results respectively

stability of inequalities in the dual brunn minkowski theory abstract stability versions are given of several inequalities from e lutwak s dual brunn minkowski theory these include the dual aleksandrov fenchel inequality the dual brunn minkowski inequality and the dual isoperimetric inequality two methods are used one involves the application of strong forms of clarkson s inequality forlpnorms that hold for nonnegative functions and the other utilizes a refinement of the arithmetic geometric mean inequality a new and more informative proof of the equivalence of the dual brunn minkowski inequality and the dual minkowski inequality is given the main results are shown to be the best possible up to constant factors

chain recurrence in dynamical systems without uniqueness on presente la theorie des systemes dynamiques disperses on considere les attracteurs et leurs repulseurs complementaires on introduit la notion de point recurrent en chaine pour un systeme dynamique disperse

order 104 speedup in global linear instability analysis using matrix formation abstract a unified solution framework is presented for one two or three dimensional complex non symmetric eigenvalue problems respectively governing linear modal instability of incompressible fluid flows in rectangular domains having two one or no homogeneous spatial directions the solution algorithm is based on subspace iteration in which the spatial discretization matrix is formed stored and inverted serially results delivered by spectral collocation based on the chebyshev gauss lobatto cgl points and a suite of high order finite difference methods comprising the previously employed for this type of work dispersion relation preserving drp and pade finite difference schemes as well as the summation by parts sbp and the new high order finite difference scheme of order q fd q have been compared from the point of view of accuracy and efficiency in standard validation cases of temporal local and biglobal linear instability the fd q method has been found to significantly outperform all other finite difference schemes in solving classic linear local biglobal and triglobal eigenvalue problems as regards both memory and cpu time requirements results shown in the present study disprove the paradigm that spectral methods are superior to finite difference methods in terms of computational cost at equal accuracy fd q spatial discretization delivering a speedup of o 10 4 consequently accurate solutions of the three dimensional triglobal eigenvalue problems may be solved on typical desktop computers with modest computational effort

intersection bodies and dual mixed volumes the setting for this article is euclidean n space ky n 2 let x denote the set of convex bodies compact convex subsets with nonempty interiors in r and let x denote the subset of x that contains the centered centrally symmetric with respect to the origin bodies for ue s let e denote the hyperplane through the origin that is orthogonal to u and let ki e denote the image of the orthogonal projection of the body ke x onto e we shall use v to denote i dimensional lebesgue measure for v and v we shall usually write v and u shephard 38 poses the question if k l e xe and

state estimation and sliding mode control for semi markovian jump systems with mismatched uncertainties this paper is concerned with the state estimation and sliding mode control problems for phase type semi markovian jump systems using a supplementary variable technique and a plant transformation a finite phase type semi markov process has been transformed into a finite markov chain which is called its associated markov chain as a result phase type semi markovian jump systems can be equivalently expressed as its associated markovian jump systems a sliding surface is then constructed and a sliding mode controller is synthesized to ensure that the associated markovian jump systems satisfy the reaching condition moreover an observer based sliding mode control problem is investigated sufficient conditions are established for the solvability of the desired observer two numerical examples are presented to show the effectiveness of the proposed design techniques

steady viscous flow in a triangular cavity by efficient numerical techniques abstract accurate and efficient calculations of the flow inside a triangular cavity are presented for high reynolds numbers the navier stokes equations expressed in a stream function and vorticity formulation are solved numerically using finite differences on a transformed geometry second order numerical boundary conditions are derived and newton s iteration is employed to solve the nonlinear system resulting from the finite difference discretization aside from solving the equilateral triangular cavity problem we have also been able to compute numerical solutions for scalene triangular cavity problems our coarse mesh results for the equilateral triangular cavity problem are compared with finer mesh results in the literature and the agreement is good

different modes of rayleigh benard instability in two and three dimensional rectangular enclosures the article describes a complete numerical solution of a recently formulated benchmark problem devoted to the parametric study of rayleigh benard instability in rectangular two and three dimensional boxes the solution is carried out by the spectral galerkin method with globally defined three dimensional divergent free basis functions which satisfy all boundary conditions the general description of these three dimensional basis functions which can be used for a rather wide spectrum of problems is presented the results of the parametric calculations are presented as neutral curves showing the dependence of the critical rayleigh number on the aspect ratio of the cavity the neutral curves consist of several continuous branches which belong to different modes of the most dangerous perturbation the patterns of different perturbations are also reported the results obtained lead to some new conclusions about the patterns of the most dangerous perturbations and about the similarities between two and three dimensional models some extensions of the considered benchmark problem are discussed

global stability analysis of a compressible turbulent flow around a high lift configuration the stability of flow over a complex high lift configuration with significant regions of separated flow is analyzed current state of the art flow solvers encounter difficulties in predicting both the onset of flow separation over similar configurations and the progression of the separated region when the angle of attack is increased the present analysis provides useful insights into the mechanisms responsible for limiting the maximum lift on multielement wing configurations by relating flow separation with the onset of flow instability a steady solution based on a finite volume discretization is used as the basic state for the linear stability analysis the resulting generalized eigenvalue problem has been solved using a krylov subspace projection technique in the form of the arnoldi iterative method this methodology is first applied to a naca0012 test case at subsonic and transonic conditions then for the first time the stability of flow over an industrial multicomponent geometry involving the a31

state estimation on positive markovian jump systems with time varying delay and uncertain transition probabilities investigate the positive discrete time mjs with disturbance input time varying delay and uncertain transition probabilities together for the first time where the transition probability matrix is described by a polytope set provide a necessary and sufficient condition of stochastic stability with regard to the resulting error dynamic system present the exact computation of l gain index for the resulting stochastically stable error dynamic systems firstly and derive a necessary and sufficient condition of the l gain performance correspondingly provide a sufficient condition on the existence of a desired observer to solve the state estimation problem such that the error dynamic system is stochastically stable with a prescribed l gain performance all the proposed conditions are expressed in linear programming forms which can be solved effectively by using some existing softwares and the observer gain matrices can be directly obtained by an effective algorithm this paper is concerned with the state estimation problem based on an l observer for a class of positive discrete time markovian jump systems mjss the system under consideration consists of time varying delay and uncertain transition probabilities where the transition probability matrix is described by a polytope set necessary and sufficient conditions are presented in linear programming lp form for the resulting error dynamic system to be stochastically stable and stochastically stable with an l gain performance respectively furthermore an l observer design scheme is presented to solve the state estimation problem such that the resulting error dynamic system is stochastically stable and achieves a prescribed l gain performance all the proposed conditions are solvable in terms of lp with additional parameters finally some examples are given to demonstrate the validity of the developed technique

stability and stabilization for positive systems with semi markov switching abstract in this article the problems of mean stability analysis and control synthesis are studied for stochastic switching systems subject to positive constraint such a switching is governed by a semi markov process subject to a special non exponential distribution considering a linear lyapunov krasovskii function lkf necessary and sufficient conditions are proposed to realize mean stability for the open loop system based on this the solvability conditions for the desired stabilizing controller can be determined under a linear programming lp framework finally the theoretical findings are illustrated by the virus mutation treatment model

exponential stability and l1 gain analysis for positive time delay markovian jump systems with switching transition rates subject to average dwell time abstract the paper deals with the problems of exponential stability and l 1 gain analysis for positive time delay markovian jump systems mjss with switching transition rates another set of useful regime switching model is given which extends fixed transition rates to time varying transition rates by resorting to the linear co positive lyapunov function and average dwell time sufficient conditions for exponential stability are proposed in terms of standard linear programming based on the obtained results l 1 gain performance is analyzed finally an example is proposed to illustrate the validity of the main results