cored hypergraphs power hypergraphs and their laplacian h eigenvalues abstract in this paper we introduce the class of cored hypergraphs and power hypergraphs and investigate the properties of their laplacian h eigenvalues from an ordinary graph one may generate a k uniform hypergraph called the kth power hypergraph of that graph power hypergraphs are cored hypergraphs but not vice versa sunflowers loose paths and loose cycles are power hypergraphs while squids generalized loose s paths and loose s cycles for 2 s k 2 are cored hypergraphs but not power graphs in general we show that the largest laplacian h eigenvalue of an even uniform cored hypergraph is equal to its largest signless laplacian h eigenvalue especially we find out these largest h eigenvalues for even uniform squids moreover we show that the largest laplacian h eigenvalue of an odd uniform squid loose path and loose cycle is equal to the maximum degree i e 2 we also compute the laplacian h spectra of the class of sunflowers when k is odd the laplacian h spectra of the loose cycle of size 3 and the loose path of length 3 are characterized as well

adjacency spectra of random and complete hypergraphs abstract we present progress on the problem of asymptotically describing the adjacency eigenvalues of random and complete uniform hypergraphs there is a natural conjecture arising from analogy with random matrix theory that connects these spectra to that of the all ones hypermatrix several of the ingredients along a possible path to this conjecture are established and may be of independent interest in spectral hypergraph hypermatrix theory in particular we provide a bound on the spectral radius of the symmetric bernoulli hyperensemble and show that the spectrum of the complete k uniform hypergraph for k 2 3 is close to that of an appropriately scaled all ones hypermatrix

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

regular uniform hypergraphs s cycles s paths and their largest laplacian h eigenvalues abstract in this paper we show that the largest signless laplacian h eigenvalue of a connected k uniform hypergraph g where k 3 reaches its upper bound 2 g where g is the largest degree of g if and only if g is regular thus the largest laplacian h eigenvalue of g reaches the same upper bound if and only if g is regular and odd bipartite we show that an s cycle g as a k uniform hypergraph where 1 s k 1 is regular if and only if there is a positive integer q such that k q k s we show that an even uniform s path and an even uniform non regular s cycle are always odd bipartite we prove that a regular s cycle g with k q k s is odd bipartite if and only if m is a multiple of 2 t 0 where m is the number of edges in g and q 2 t 0 2 l 0 1 for some integers t 0 and l 0 we identify the value of the largest signless laplacian h eigenvalue of an s cycle g in all possible cases when g is odd bipartite this is also its largest laplacian h eigenvalue we introduce supervertices for hypergraphs and show the components of a laplacian h eigenvector of an odd uniform hypergraph are equal if such components correspond vertices in the same supervertex and the corresponding laplacian h eigenvalue is not equal to the degree of the supervertex using this property we show that the largest laplacian h eigenvalue of an odd uniform generalized loose s cycle g is equal to g 2 we also show that the largest laplacian h eigenvalue of a k uniform tight s cycle g is not less than g 1 if the number of vertices is even and k 4 l 3 for some nonnegative integer l

passivity based sliding mode control of uncertain singular markovian jump systems with time varying delay and nonlinear perturbations in this paper a sliding mode control smc with passivity of uncertain singular markovian jump systems smjs with time varying delay and nonlinear perturbations is investigated firstly a new integral type switching surface is designed secondly by introducing free matrix method and lyapunov functionals a delay dependent sufficient condition in terms of strict linear matrix inequalities lmi is derived for the resulting sliding mode dynamics such that the closed loop system is stochastically admissible and robustly passive for all admissible uncertainties thirdly a smc law is synthesized to drive the system trajectories onto the predefined switching surface in a finite time finally numerical examples are provided to demonstrate the effectiveness of the proposed method

robust mixed generalized h sub 2 h sub spl infin filtering of 2 d nonlinear fractional transformation systems this study considers robust filtering problems for uncertain two dimensional 2 d discrete systems in nonlinear fractional transformation nft representations like one dimensional 1 d systems the nft in this paper serves to complement the linear fractional transformation lft linear matrix inequality lmi formulations are given to analyze as well as synthesize robust filters numerical examples show the advantage of the nft over the lft in terms of not only computational savings but also substantial performance gains and verify the efficiency of the proposed techniques

asynchronous h filtering for 2d discrete markovian jump systems with sensor failure this paper investigates the problem of the asynchronous h filtering for a class of two dimensional 2d markovian jump systems with sensor failure the asynchronous phenomenon is considered to be random mismatch between system modes and candidate filters the mismatch behavior is assumed to be stochastic with a certain probability and a new markov chain is proposed to model the jumping process of the filtering error system besides a switching method is proposed to dealing with the sensor failure sufficient conditions for the existence of a desired filter such that the filtering error system is stochastically stable with a guaranteed h performance index are obtained in the form of linear matrix inequalities lmis two examples are provided to illustrate the effectiveness and advantage of the proposed method

the largest laplacian and signless laplacian h eigenvalues of a uniform hypergraph a b s t r a c t in this paper we show that the largest laplacian h eigen value of a k uniform nontrivial hypergraph is strictly larger than the maximum degree when k is even a tight lower bound for this eigenvalue is given for a connected even uniform hypergraph this lower bound is achieved if and only if it is a hyperstar however when k is odd in certain cases the largest laplacian h eigenvalue is equal to the maximum degree which is a tight lower bound on the other hand tight upper and lower bounds for the largest signless laplacian h eigenvalue of a k uniform connected hypergraph are given for connected k uniform hypergraphs of fixed number of vertices respectively fixed maximum degree the upper respectively lower bound of their largest signless laplacian h eigenvalues is achieved exactly for the complete hypergraph respectively the hyperstar the largest laplacian h eigenvalue is always less than or equal to the

wall normal free reynolds stress closure for three dimensional compressible separated flows a near wall reynolds stress closure that is independent of the distance from the wall and of the normal to the walldirection isdevelopedandvalidated particularattention wasgiven intheapplicabilityofthemodeltocomplex three dimensional e ows with shock waves and boundary layer separation in the separated e ow region measurements andmodelcomputations indicatethatthe e atnessparameter aoftheanisotropy tensor aij approaches unity therefore controlofseparation isachieved in themodel through theparticularfunctional dependenceoftherapid pressure strain isotropization of production model coefe cienton a echo termsaretreated by replacing geometric normalsanddistancesbyfunctionsofthegradientsofturbulencelengthscaleandanisotropytensorinvariants the modelisinitiallycomparedwithmeasurementsforcompressiblee at plateboundary layere ows itisthenvalidated by comparison with experimental data in a two dimensional compression corner oblique shock wave boundarylayer interaction at mach 3 finally the model is applied to the computation of the three dimensional interaction of a mach 1 5 1 8 strong shock wave with the boundary layers of a rectangular channel e tted with a swept bump on the lower wall and results are compared with measurements one important advantage of the proposed model is its robustness in complex three dimensional e ows a detailed discussion of therange of validity of the model and possible improvements is presented

joins of hypergraphs and their spectra abstract here we represent a general hypergraph by a matrix and study its spectrum we extend the definition of equitable partition and joining operation for hypergraphs and use those to compute eigenvalues of different hypergraphs we derive the characteristics polynomial of a complete m uniform m partite hypergraph k n 1 n 2 n m m studying edge corona of hypergraphs we find the complete spectrum of s loose cycles c l s n m for m 2 s 1 and the characteristics polynomial of s loose paths p l s n m some of the eigenvalues of p l s n m are also derived moreover using vertex corona we show how to generate infinitely many pairs of non isomorphic co spectral hypergraphs

variational multiscale stabilized fem formulations for transport equations stochastic advection diffusion and incompressible stochastic navier stokes equations an extension of the deterministic variational multiscale vms approach with algebraic subgrid scale sgs modeling is considered for developing stabilized finite element formulations for the stochastic advection and the incompressible stochastic navier stokes equations the stabilized formulations are numerically implemented using the spectral stochastic formulation of the finite element method ssfem generalized polynomial chaos and karhunen loeve expansion techniques are used for representation of uncertain quantities the proposed stabilized method is then applied to various standard advection diffusion and fluid flow examples with uncertainty in essential boundary conditions comparisons are drawn between the numerical solutions and monte carlo analytical solutions wherever possible

spectra of general hypergraphs abstract here we show a method to reconstruct connectivity hypermatrices of a general hypergraph without any self loop or multiple edge using tensor we also study the different spectral properties of these hypermatrices and find that these properties are similar for graphs and uniform hypergraphs the representation of a connectivity hypermatrix that is proposed here can be very useful for the further development in spectral hypergraph theory

uncertainty quantification of limit cycle oscillations different computational methodologies have been developed to quantify the uncertain response of a relatively simple aeroelastic system in limit cycle oscillation subject to parametric variability the aeroelastic system is that of a rigid airfoil supported by pitch and plunge structural coupling with nonlinearities in the component in pitch the nonlinearities are adjusted to permit the formation of a either a subcritical or supercritical branch of limit cycle oscillations uncertainties are specified in the cubic coefficient of the torsional spring and in the initial pitch angle of the airfoil stochastic projections of the time domain and cyclic equations governing system response are carried out leading to both intrusive and non intrusive computational formulations non intrusive formulations are examined using stochastic projections derived from wiener expansions involving haar wavelet and b spline bases while wiener hermite expansions of the cyclic equations are employed intrusively and non intrusively application of the b spline stochastic projection is extended to the treatment of aerodynamic nonlinearities as modeled through the discrete euler equations the methodologies are compared in terms of computational cost convergence properties ease of implementation and potential for application to complex aeroelastic systems

high order collocation methods for differential equations with random inputs recently there has been a growing interest in designing efficient methods for the solution of ordinary partial differential equations with random inputs to this end stochastic galerkin methods appear to be superior to other nonsampling methods and in many cases to several sampling methods however when the governing equations take complicated forms numerical implementations of stochastic galerkin methods can become nontrivial and care is needed to design robust and efficient solvers for the resulting equations on the other hand the traditional sampling methods e g monte carlo methods are straightforward to implement but they do not offer convergence as fast as stochastic galerkin methods in this paper a high order stochastic collocation approach is proposed similar to stochastic galerkin methods the collocation methods take advantage of an assumption of smoothness of the solution in random space to achieve fast convergence however the numerical implementation of stochastic collocation is trivial as it requires only repetitive runs of an existing deterministic solver similar to monte carlo methods the computational cost of the collocation methods depends on the choice of the collocation points and we present several feasible constructions one particular choice based on sparse grids depends weakly on the dimensionality of the random space and is more suitable for highly accurate computations of practical applications with large dimensional random inputs numerical examples are presented to demonstrate the accuracy and efficiency of the stochastic collocation methods

sharp bounds for ordinary and signless laplacian spectral radii of uniform hypergraphs we give sharp upper bounds for the ordinary spectral radius and signless laplacian spectral radius of a uniform hypergraph in terms of the average 2 degrees or degrees of vertices respectively and we also give a lower bound for the ordinary spectral radius we also compare these bounds with known ones

probabilistic collocation for period 1 limit cycle oscillations in this paper probabilistic collocation for limit cycle oscillations pclco is proposed probabilistic collocation pc is a non intrusive approach to compute the polynomial chaos description of uncertainty numerically polynomial chaos can require impractical high orders to approximate long term time integration problems due to the fast increase of required polynomial chaos order with time pclco is a pc formulation for modeling the long term stochastic behavior of dynamical systems exhibiting a periodic response i e a limit cycle oscillation lco in the pc method deterministic time series are computed at collocation points in probability space in pclco pc is applied to a time independent parametrization of the periodic response of the deterministic solves instead of to the time dependent functions themselves due to the time independent parametrization the accuracy of pclco is independent of time the approach is applied to period 1 oscillations with one main frequency subject to a random parameter numerical results are presented for the harmonic oscillator a two dof airfoil flutter model and the fluid structure interaction of an elastically mounted cylinder

brief on robust stabilization of markovian jump systems with uncertain switching probabilities this brief paper is concerned with the robust stabilization problem for a class of markovian jump linear systems with uncertain switching probabilities the uncertain markovian jump system under consideration involves parameter uncertainties both in the system matrices and in the mode transition rate matrix first a new criterion for testing the robust stability of such systems is established in terms of linear matrix inequalities then a sufficient condition is proposed for the design of robust state feedback controllers a globally convergent algorithm involving convex optimization is also presented to help construct such controllers effectively finally a numerical simulation is used to illustrate the developed theory

continuous time analysis eigenstructure assignment and h sub 2 synthesis with enhanced linear matrix inequalities lmi characterizations this note describes a new framework for the analysis and synthesis of control systems which constitutes a genuine continuous time extension of results that are only available in discrete time in contrast to earlier results the proposed methods involve a specific transformation on the lyapunov variables and a reciprocal variant of the projection lemma in addition to the classical linearizing transformations on the controller data for a wide range of problems including robust analysis and synthesis multichannel h sub 2 stateand output feedback syntheses the approach leads to potentially less conservative linear matrix inequality lmi characterizations this comes from the fact that the technical restriction of using a single lyapunov function is to some extent ruled out in this new approach moreover the approach offers new potentials for problems that cannot be handled using earlier techniques an important instance is the eigenstructure assignment problem blended with lyapunov type constraints which is given a simple and tractable formulation

efficient and robust reynolds stress model computation of three dimensional compressible flows thepurposeofthiswork isthedevelopmentofanefe cientand robustimplicitmethodology fortheintegration of the three dimensional compressible favre reynolds averaged navier stokes equations with near wall reynoldsstressclosure thee vemean e owandseventurbulencetransportequationsarediscretizedinspace ona structured multiblock grid using an o x 3 e nitevolumeupwind biased muscl schemewithvanleere ux vectorsplitting and van albada limiters time integration is based on an implicit dual time stepping procedure with alternating direction implicit subiterations a particular treatment of the approximate jacobians used in the subiterations substantiallydiminishesthecomputing timerequirementsoftheimplicitphase sothatthecomputationaloverhead of the reynolds stress seven equation closure compared to a two equation closure is less than 30 per iteration for steady e ow computations local time steps are used for both the subiterations and the time marching with courant friedrichs lewynumbersof o 10 20 fortheo 1 20 subiterationsneededand o 100 500 forthetime marching the robustness of the method is ensured by appropriate positivity boundedness and reynolds stress realizability constraints the numerical method is illustrated by computing and conducting numerical studies for a high subsonic m 0 7 three dimensional e ow with large separation and for a transonic three dimensional shock wave boundary layer interaction

supersensitivity due to uncertain boundary conditions summary we study the viscous burgers equation subject to perturbations on the boundary conditions two kinds of perturbations are considered deterministic and random for deterministic perturbations we show that small perturbations can result in o 1 changes in the location of the transition layer for random perturbations we solve the stochastic burgers equation using different approaches first we employ the jacobi polynomial chaos which is a subset of the generalized polynomial chaos for stochastic modeling converged numerical results are reported up to seven significant digits and we observe similar stochastic supersensitivity for the mean location of the transition layer subsequently we employ up to fourth order perturbation expansions we show that even with small random inputs the resolution of the perturbation method is relatively poor due to the larger stochastic responses in the output two types of distributions are considered uniform distribution and a truncated gaussian distribution with no tails various solution statistics including the spatial evolution of probability density function at steady state are studied copyright 2004 john wiley sons ltd

reynolds stress model dual time stepping computation of unsteady three dimensional flows an efficient and robust implicit methodology for the integration of the unsteady three dimensional compressible favre reynolds averaged navier stokes equations with near wall reynolds stress closure is developed the five mean flow and seven turbulence transport equations are discretized on a structured deforming grid using an o x 3 finite volume upwind biased muscl scheme time integration uses an implicit o t 2 dual time stepping procedure with alternating direction implict subiterations with approximate jacobians designed to minimize the computing time requirements of the implicit phase for the reynolds stresses so that the computational overhead of the reynolds stress seven equation closure compared to a two equation closure is less than 30 per iteration based on a dynamic criterion of subiterative convergence grid deformation velocities associated with solid wall displacement are computed using a laplacian operator the method is validated by comparison with experimental data for 1 two dimensional pitching oscillations of a naca 0012 airfoil and 2 three dimensional shock wave oscillation in a transonic channel the influence of the various parameters of the method is analyzed in detail

state estimation and sliding mode control of markovian jump singular systems this paper is concerned with the state estimation and sliding mode control problems for continuous time markovian jump singular systems with unmeasured states firstly a new necessary and sufficient condition is proposed in terms of strict linear matrix inequality lmi which guarantees the stochastic admissibility of the unforced markovian jump singular system then the sliding mode control problem is considered by designing an integral sliding surface function an observer is designed to estimate the system states and a sliding mode control scheme is synthesized for the reaching motion based on the state estimates it is shown that the sliding mode in the estimation space can be attained in a finite time some conditions for the stochastic admissibility of the overall closed loop system are derived finally a numerical example is provided to illustrate the effectiveness of the proposed theory

mb tensors and mb0 tensors abstract the class of mb mb 0 tensors which is a generation of b b 0 tensors and quasi double b b 0 tensors is proposed and we prove that an even order symmetric mb mb 0 tensor is positive semi definite by giving some conditions to determine mb mb 0 tensors some checkable sufficient conditions for the positive semi definiteness of tensors are given

an even order symmetric b tensor is positive definite it is easily checkable if a given tensor is a b tensor or a b0 tensor or not in this paper we show that a symmetric b tensor can always be decomposed to the sum of a strictly diagonally dominated symmetric m tensor and several positive multiples of partially all one tensors and a symmetric b0 tensor can always be decomposed to the sum of a diagonally dominated symmetric m tensor and several positive multiples of partially all one tensors when the order is even this implies that the corresponding b tensor is positive definite and the corresponding b0 tensor is positive semi definite this gives a checkable sufficient condition for positive definite and semi definite tensors this approach is different from the approach in the literature for proving a symmetric b matrix is positive definite as that matrix approach cannot be extended to the tensor case

uncertainty quantification for systems of conservation laws uncertainty quantification through stochastic spectral methods has been recently applied to several kinds of non linear stochastic pdes in this paper we introduce a formalism based on kinetic theory to tackle uncertain hyperbolic systems of conservation laws with polynomial chaos pc methods the idea is to introduce a new variable the entropic variable in bijection with our vector of unknowns which we develop on the polynomial basis by performing a galerkin projection we obtain a deterministic system of conservation laws we state several properties of this deterministic system in the case of a general uncertain system of conservation laws we then apply the method to the case of the inviscid burgers equation with random initial conditions and we present some preliminary results for the euler system we systematically compare results from our new approach to results from the stochastic galerkin method in the vicinity of discontinuities the new method bounds the oscillations due to gibbs phenomenon to a certain range through the entropy of the system without the use of any adaptative random space discretizations it is found to be more precise than the stochastic galerkin method for smooth cases but above all for discontinuous cases

finite region dissipative dynamic output feedback control for 2 d fm systems with missing measurements abstract this paper focuses on the finite region dissipative dynamic output feedback control problem for a class of discrete time two dimensional 2 d fornasini marchesini fm systems with missing measurements firstly the definitions of finite region boundedness frb and finite region t s r dissipativity are introduced for 2 d fm systems secondly sufficient conditions on the frb and finite region t s r dissipativity of the resultant closed loop 2 d systems are obtained by the construction of the lyapunov function and the special recursive formulas thirdly based on the decoupling technique the desired dynamic output feedback controller design method for the considered 2 d systems is further provided in the end an example of the metal rolling process is given to show the effectiveness of the proposed design results

stochastic nonlinear aeroelastic analysis of a supersonic lifting surface using an adaptive spectral method an adaptive stochastic spectral projection method is deployed for the uncertainty quantification in limit cycle oscillations of an elastically mounted two dimensional lifting surface in a supersonic flow field variabilities in the structural parameters are propagated in the aeroelastic system which accounts for nonlinear restoring force and moment by means of hardening cubic springs the physical nonlinearities promote sharp and sudden flutter onset for small change of the reduced velocity in a stochastic context this behavior translates to steep solution gradients developing in the parametric space a remedy is to expand the stochastic response of the airfoil on a piecewise generalized polynomial chaos basis accurate approximation andaffordable computational costs are obtained using sensitivity based adaptivity for various types of supersonic stochastic responses depending on the selected values of the mach number on the bifurcation map sensitivity analysis via sobol indices shows how the probability density function of the peak pitch amplitude responds to combined uncertainties e g the elastic axis location torsional stiffness and flap angle we believe that this work demonstrates the capability and flexibility of the approach for more reliable predictions of realistic aeroelastic systems subject to a moderate number of uncertainties

subcell resolution in simplex stochastic collocation for spatial discontinuities subcell resolution has been used in the finite volume method fvm to obtain accurate approximations of discontinuities in the physical space stochastic methods are usually based on local adaptivity for resolving discontinuities in the stochastic dimensions however the adaptive refinement in the probability space is ineffective in the non intrusive uncertainty quantification framework if the stochastic discontinuity is caused by a discontinuity in the physical space with a random location the dependence of the discontinuity location in the probability space on the spatial coordinates then results in a staircase approximation of the statistics which leads to first order error convergence and an underprediction of the maximum standard deviation to avoid these problems we introduce subcell resolution into the simplex stochastic collocation ssc method for obtaining a truly discontinuous representation of random spatial discontinuities in the interior of the cells discretizing the probability space the presented ssc sr method is based on resolving the discontinuity location in the probability space explicitly as function of the spatial coordinates and extending the stochastic response surface approximations up to the predicted discontinuity location the applications to a linear advection problem the inviscid burgers equation a shock tube problem and the transonic flow over the rae 2822 airfoil show that ssc sr resolves random spatial discontinuities with multiple stochastic and spatial dimensions accurately using a minimal number of samples

brief h control and robust stabilization of two dimensional systems in roesser models feedback control of two dimensional 2 d systems is a problem of considerable importance in both theory and practical applications in this paper we present a state space solution to the problem of h control of 2 d systems for a linear discrete time 2 d system described by a 2 d state space roesser model a 2 d dynamic output feedback controller is designed to achieve the closed loop system asymptotic stability and a specified h performance using a linear matrix inequality lmi approach we further give a solution for robust stabilization of 2 d systems subject to a class of norm bounded uncertainties the results are demonstrated by an application example of stabilization of processes expressed in a darboux equation

the wiener askey polynomial chaos for stochastic differential equations we present a new method for solving stochastic differential equations based on galerkin projections and extensions of wiener s polynomial chaos specifically we represent the stochastic processes with an optimum trial basis from the askey family of orthogonal polynomials that reduces the dimensionality of the system and leads to exponential convergence of the error several continuous and discrete processes are treated and numerical examples show substantial speed up compared to monte carlo simulations for low dimensional stochastic inputs

stochastic investigation of flows about airfoils at transonic speeds aerodynamics nonlinearities are reported in the uncertain probabilistic space the efficiency of the present methodology are evaluated for the propagation of random disturbances associated with the angle of attack and the freestreammachnumber anerroranalysisiscarriedoutinordertodetermineappropriatephysicalandstochastic discretization levels different stochastic flow regimes are analyzed in details by means of various postprocessing procedures including error bars probabilistic density function of the aerodynamic field and sobol s coefficients

kalman filtering for continuous time uncertain systems with markovian jumping parameters studies the problem of kalman filtering for a class of uncertain linear continuous time systems with markovian jumping parameters the system under consideration is subjected to time varying norm bounded parameter uncertainties in the state and measurement equations stochastic quadratic stability of the above system is analyzed a state estimator is designed such that the covariance of the estimation error is guaranteed to be within a certain bound for all admissible uncertainties which is in terms of solutions of two sets of coupled algebraic riccati equations

h model reduction of markovian jump linear systems abstract in this paper the h model reduction problem for linear systems that possess randomly jumping parameters is studied the development includes both the continuous and discrete cases it is shown that the reduced order models exist if a set of matrix inequalities is feasible an effective iterative algorithm involving linear matrix inequalities is suggested to solve the matrix inequalities characterizing the model reduction solutions using the numerical solutions of the matrix inequalities the reduced order models can be obtained an example is given to illustrate the proposed model reduction method

robust cal h _ infty filtering for markovian jump systems with randomly occurring nonlinearities and sensor saturation the finite horizon case this paper addresses the robust h filtering problem for a class of discrete time varying markovian jump systems with randomly occurring nonlinearities and sensor saturation two kinds of transition probability matrices for the markovian process are considered namely the one with polytopic uncertainties and the one with partially unknown entries the nonlinear disturbances are assumed to occur randomly according to stochastic variables satisfying the bernoulli distributions the main purpose of this paper is to design a robust filter over a given finite horizon such that the h disturbance attenuation level is guaranteed for the time varying markovian jump systems in the presence of both the randomly occurring nonlinearities and the sensor saturation sufficient conditions are established for the existence of the desired filter satisfying the h performance constraint in terms of a set of recursive linear matrix inequalities simulation results demonstrate the effectiveness of the developed filter design scheme

non intrusive iterative stochastic spectral representation with application to compressible gas dynamics in this paper we propose a new iterative formulation improving the convergence of standard non intrusive stochastic spectral method for uncertainty quantification we demonstrate that the method is more accurate than the classical approach with the same level of approximation and at no significant additional computational or memory cost since it is deployed in a post processing stage moreover the accuracy of the representation improves no matter the regularity of the random quantity of interest therefore the method is particularly well suited when nonlinear transformations of random variables are in play and can be viewed as a new way of tackling the gibbs phenomenon we apply the method to several test cases with different levels of regularity dimensionality and complexity including the case of compressible gas dynamics and long time integration problems the new and the classical approaches are compared for the resolution of a stochastic riemann problem governed by an euler system

controllability stabilizability and continuous time markovian jump linear quadratic control consideration is given to the control of continuous time linear systems that possess randomly jumping parameters which can be described by finite state markov processes the relationship between appropriately defined controllability stabilizability properties and the solution of the infinite time jump linear quadratic jlq optimal control problems is also examined although the solution of the continuous time markov jlq problem with finite or infinite time horizons is known only sufficient conditions for the existence of finite cost constant stabilizing controls for the infinite time problem appear in the literature in this paper necessary and sufficient conditions are established these conditions are based on new definitions of controllability observability stabilizability and detectability that are appropriate for continuous time markovian jump linear systems these definitions play the same role for the jlq problem as the deterministic properties do for the linear quadratic regulator lqr problem

robust decentralized stabilization of markovian jump large scale systems a neighboring mode dependent control approach abstract this paper is concerned with the decentralized stabilization problem for a class of uncertain large scale systems with markovian jump parameters the controllers use local subsystem states and neighboring mode information to generate local control inputs a sufficient condition involving rank constrained linear matrix inequalities is proposed for the design of such controllers a numerical example is given to illustrate the developed theory

double b tensors and quasi double b tensors abstract in this paper we propose two new classes of tensors double b tensors and quasi double b tensors give some properties of double b tensors and quasi double b tensors discuss their relationships with b tensors and positive definite tensors and show that even order symmetric double b tensors and even order symmetric quasi double b tensors are positive definite these give some checkable sufficient conditions for the positive definiteness of tensors

filtering design for two dimensional markovian jump systems with state delays and deficient mode information this paper is concerned with the problem of h filtering for a class of two dimensional markovian jump linear systems described by the fornasini marchesini local state space model the systems under consideration are subject to state delays and deficient mode information in the markov chain the description of deficient mode information is comprehensive that simultaneously includes the exactly known partially unknown and uncertain transition probabilities by invoking the properties of the transition probability matrix together with the convexification of uncertain domains a new h performance analysis criterion for the filtering error system is firstly derived then via some matrix inequality linearisation procedures two approaches for the filter synthesis are proposed it is shown that both the full order and reduced order filters can be constructed by solving a set of linear matrix inequalities finally simulation studies are provided to illustrate the effectiveness of the proposed design methods

robust mixed spl hscr sub 2 spl hscr sub spl infin filtering of 2 d systems this paper deals with several challenging problems of robust filtering for two dimensional 2 d systems first of all new linear matrix inequality lmi characterizations for the spl hscr sub spl infin and spl hscr 2 norms of 2 d systems are introduced and thoroughly established based on these preparatory results convex lmi characterizations for robust spl hscr sub spl infin spl hscr sub 2 and robust mixed spl hscr sub 2 spl hscr sub spl infin filtering are derived the efficiency and viability of the proposed techniques and tools are demonstrated through a set of numerical examples

e cospectral hypergraphs and some hypergraphs determined by their spectra two k uniform hypergraphs are said to be cospectral e cospectral if their adjacency tensors have the same characteristic polynomial e characteristic polynomial a k uniform hypergraph h is said to be determined by its spectrum if there is no non isomorphic k uniform hypergraph cospectral with h in this note we give a method for constructing e cospectral hypergraphs which is similar with godsil mckay switching some hypergraphs are shown to be determined by their spectra

calculation of gauss kronrod quadrature rules the jacobi matrix of the 2n 1 point gauss kronrod quadrature rule for a given measure is calculated efficiently by a five term recurrence relation the algorithm uses only rational operations and is therefore also useful for obtaining the jacobi kronrod matrix analytically the nodes and weights can then be computed directly by standard software for gaussian quadrature formulas

a stochastic collocation method for elliptic partial differential equations with random input data in this paper we propose and analyze a stochastic collocation method to solve elliptic partial differential equations with random coefficients and forcing terms input data of the model the input data are assumed to depend on a finite number of random variables the method consists in a galerkin approximation in space and a collocation in the zeros of suitable tensor product orthogonal polynomials gauss points in the probability space and naturally leads to the solution of uncoupled deterministic problems as in the monte carlo approach it can be seen as a generalization of the stochastic galerkin method proposed in i babuscka r tempone and g e zouraris siam j numer anal 42 2004 pp 800 825 and allows one to treat easily a wider range of situations such as input data that depend nonlinearly on the random variables diffusivity coefficients with unbounded second moments and random variables that are correlated or even unbounded we provide a rigorous convergence analysis and demonstrate exponential convergence of the probability error with respect to the number of gauss points in each direction in the probability space under some regularity assumptions on the random input data numerical examples show the effectiveness of the method

technical communique exponential stabilizability of stochastic systems with markovian jumping parameters altfn this paper was not presented at any ifac meeting this paper was recommended for publication in revised form by editor peter dorato this paper deals with the exponential stabilizability of the class of stochastic systems with jumps for the case of linear uncertain stochastic system we have designed an optimal control law that guarantees the exponential stability robustness of systems with markovian jumps for the nonlinear case with matching conditions we have established a similar result

generalized h2 fault detection for two dimensional markovian jump systems this paper is concerned with the generalized h 2 fault detection for two dimensional 2 d discrete time markovian jump systems the mathematical model of the 2 d system is established upon the well known roesser model and the measurement missing phenomenon which appears typically in a network environment is modeled by a stochastic variable satisfying the bernoulli random binary distribution in addition the transition probabilities of the markovian jump process are assumed to be partly accessed that is the transition probabilities are partly known our attention is focused on the design of a fault detection filter or a residual generation system which guarantees the fault detection system to be mean square asymptotically stable and to have a prescribed generalized h 2 performance sufficient conditions for the existence of a desired fault detection filter are established in terms of linear matrix inequalities lmis a numerical example is provided to illustrate the effectiveness of the proposed design method

brief paper h filtering for 2d markovian jump systems this paper is concerned with the problem of h filtering for 2d discrete markovian jump systems the mathematical model of 2d jump systems is established upon the well known roesser model our attention is focused on the design of a full order filter which guarantees the filtering error system to be mean square asymptotically stable and has a prescribed h disturbance attenuation performance sufficient conditions for the existence of a desired filter are established in terms of linear matrix inequalities lmis and the corresponding filter design is cast into a convex optimization problem which can be efficiently solved by using commercially available numerical software a numerical example is provided to illustrate the effectiveness of the proposed design method

robust h sub spl infin control of uncertain markovian jump systems with time delay this paper is concerned with the robust stochastic stabilizability and robust h sub spl infin disturbance attenuation for a class of uncertain linear systems with time delay and randomly jumping parameters the transition of the jumping parameters is governed by a finite state markov process sufficient conditions on the existence of a robust stochastic stabilizing and spl gamma suboptimal h sub spl infin state feedback controller are presented using the lyapunov functional approach it is shown that a robust stochastically stabilizing h sub spl infin state feedback controller can be constructed through the numerical solution of a set of coupled linear matrix inequalities

treatment of uncertain material interfaces in compressible flows abstract to treat uncertain interface position is an important issue for complex applications in this paper we address the characterization of randomly perturbed interfaces between fluids thanks to stochastic modeling and uncertainty quantification through the 2d euler system the perturbed interface is modeled as a random field and represented by a karhunen loeve expansion the stochastic 2d euler system is solved applying polynomial chaos theory through the intrusive polynomial moment method ipmm this stochastic resolution method is fully explained and studied theoretically and numerically stochastic richtmyer meshkov unstable flows are solved and presented for several configurations of the uncertain interface different rugosities between the fluids the probability density functions of the mass density of the fluid in the vicinity of the interface are computed built and compared for the different simulations the system exhibits strong sensitivity with respect to the stochastic initially leading modes