pseudo time stepping methods for space time discontinuous galerkin discretizations of the compressible navier stokes equations the space time discontinuous galerkin discretization of the compressible navier stokes equations results in a non linear system of algebraic equations which we solve with pseudo time stepping methods we show that explicit runge kutta methods developed for the euler equations suffer from a severe stability constraint linked to the viscous part of the equations and propose an alternative to relieve this constraint while preserving locality to evaluate its effectiveness we compare with an implicit explicit runge kutta method which does not suffer from the viscous stability constraint we analyze the stability of the methods and illustrate their performance by computing the flow around a 2d airfoil and a 3d delta wing at low and moderate reynolds numbers

extended dissipative analysis for neural networks with time varying delays in this brief an extended dissipativity analysis was conducted for a neural network with time varying delays the concept of the extended dissipativity can be used to solve for the h l2 l passive and dissipative performance by adjusting the weighting matrices in a new performance index in addition the activation function dividing method is modified by introducing a tuning parameter examples are provided to show the effectiveness and less conservatism of the proposed method

improved linear matrix inequality approach to stability analysis of linear systems with interval time varying delays this paper investigates the problem of stability analysis for a class of linear systems with interval time varying delay in order to develop a less conservative stability condition a lyapunov krasovskii functional comprising novel integral terms is introduced convex combination idea is utilized to derive a stability criterion in terms of linear matrix inequalities lmis without any additional free weighting matrices which increase drastically the computational burden of the stability test numerical examples are presented to illustrate the superiority of the proposed approach compared to some existing ones in the literature

a less conservative robust stability test for linear uncertain time delay systems this note concerns with the robust stability of linear uncertain systems with state delay the uncertainty is assumed to be of polytopic type a less conservative delay dependent linear matrix inequality lmi method is presented based on a new lyapunov krasovskii functional the present method incorporates a relaxed parameter dependent technique combined with a recently proposed idea of introducing free weighting matrices when confined to delay free case the present result is also less conservative than existing stability tests using parameter dependent methods numerical examples are given to show the less conservativeness of the results

further results on exponential stability of neural networks with time varying delay this paper investigates the problem of the exponential stability for a class of neural networks with time varying delay a triple integral term and a term considering the delay information in a new way are introduced to the lyapunov krasovskii functional lkf the obtained criterion show advantages over the existing ones since not only a novel lkf is constructed but also several techniques such as wirtinger based inequality and convex combination technique are used to estimate the upper bound of the derivative of the lkf finally a numerical example is provided to verify the effectiveness and benefit of the proposed criterion

the determinant and adjoint of a square fuzzy matrix abstract the theory of the determinant and adjoint of a square fuzzy matrix will be studied also we define the circular fuzzy matrices and show that some properties of a square fuzzy matrix such as reeflexivity transitivity circularity are carried over to the adjoint of the matrix finally we show how to construct a transitive fuuzzy matrix from a given one through the adjoint matrix

operators that preserve semiring matrix functions abstract characterizations are obtained of those linear operators over certain semirings that preserve 1 the rth coefficient of the rook polynomial those that preserve 2 the term rank of matrices with term rank r and those that preserve 3 the rth elementary symmetric permanental function our results apply to many algebraic systems of combinatorial interest including the nonnegative integer matrices boolean matrices and fuzzy matrices

analysis of semi implicit dgfem for nonlinear convection diffusion problems on nonconforming meshes the paper deals with the numerical analysis of a scalar nonstationary nonlinear convection diffusion equation the space discretization is carried out by the discontinuous galerkin finite element method dgfem on general nonconforming meshes formed by possibly nonconvex elements with nonsymmetric treatment of stabilization terms and interior and boundary penalty the time discretization is carried out by a semi implicit euler scheme in which the diffusion and stabilization terms are treated implicitly whereas the nonlinear convective terms are treated explicitly we derive a priori asymptotic error estimates in the discrete l l2 l l2 norm l2 h1 l2 h1 seminorm and l h1 l h1 seminorm with respect to the mesh size h and time step numerical examples demonstrate the accuracy of the method and manifest the effect of nonconvexity of elements and nonconformity of the mesh

further improvement of jensen inequality and application to stability of time delayed systems this paper is concerned with the delay dependent stability for the linear systems with a time varying delay to get a result in the form of lmi from a lyapunov krasovskii functional an integral inequality is necessary and jensen inequality has been a most powerful inequality in the last few years recently based on wirtinger inequality an improved integral inequality encompassing jensen inequality was proposed and its application to the stability showed a quite improvement in this paper without using wirtinger inequality a further improved integral inequality in the form of infinite series is derived and based on this a delay dependent stability condition in the form of lmi is derived finally its contribution on the stability criterion is shown by well known two examples

new stability results for delayed neural networks this paper is concerned with the stability for delayed neural networks by more fully making use of the information of the activation function a new lyapunov krasovskii functional lkf is constructed then a new integral inequality is developed and more information of the activation function is taken into account when the derivative of the lkf is estimated by lyapunov stability theory a new stability result is obtained finally three examples are given to illustrate the stability result is less conservative than some recently reported ones

a discontinuous hp finite element method for diffusion problems 1 d analysis abstract this paper presents the mathematical analysis of a new variant of the discontinuous galerkin method which is applicable to the numerical solution of diffusion problems not requiring auxiliary variables such as those used in mixed methods the focus of this study is on a class of linear second order boundary value problems for which we prove stability and a priori error estimates in both the finite and infinite dimensional spaces

adaptive discontinuous galerkin finite element methods for nonlinear hyperbolic conservation laws we consider the a posteriori error analysis and adaptive mesh design for discontinuous galerkin finite element approximations to systems of nonlinear hyperbolic conservation laws in particular we discuss the question of error estimation for general target functionals of the solution typical examples include the outflow flux local average and pointwise value as well as the lift and drag coefficients of a body immersed in an inviscid fluid by employing a duality argument we derive so called weighted or type i a posteriori error bounds these error estimates include the product of the finite element residuals with local weighting terms involving the solution of a certain dual or adjoint problem that must be numerically approximated based on the resulting approximate type i bound we design and implement an adaptive algorithm that produces meshes specifically tailored to the efficient computation of the given target functional of practical interest the performance of the proposed adaptive strategy and the quality of the approximate type i a posteriori error bound is illustrated by a series of numerical experiments in particular we demonstrate the superiority of this approach over standard mesh refinement algorithms which employ type ii error indicators

recent developments on the stability of systems with aperiodic sampling an overview this article presents basic concepts and recent research directions about the stability of sampled data systems with aperiodic sampling we focus mainly on the stability problem for systems with arbitrary time varying sampling intervals which has been addressed in several areas of research in control theory systems with aperiodic sampling can be seen as time delay systems hybrid systems input output interconnections discrete time systems with time varying parameters etc the goal of the article is to provide a structural overview of the progress made on the stability analysis problem without being exhaustive which would be neither possible nor useful we try to bring together results from diverse communities and present them in a unified manner for each of the existing approaches the basic concepts fundamental results converse stability theorems when available and relations with the other approaches are discussed in detail results concerning extensions of lyapunov and frequency domain methods for systems with aperiodic sampling are recalled as they allow to derive constructive stability conditions furthermore numerical criteria are presented while indicating the sources of conservatism the problems that remain open and the possible directions of improvement at last some emerging research directions such as the design of stabilizing sampling sequences are briefly discussed

space time discontinuous galerkin finite element method with dynamic grid motion for inviscid compressible flows ii efficient flux quadrature a new and efficient quadrature rule for the flux integrals arising in the space time discontinuous galerkin discretization of the euler equations in a moving and deforming space time domain is presented and analyzed the quadrature rule is a factor three more efficient than the commonly applied quadrature rule and does not affect the local truncation error and stability of the numerical scheme the local truncation error of the resulting numerical discretization is determined and is shown to be the same as when product gauss quadrature rules are used details of the approximation of the dissipation in the numerical flux are presented which render the scheme consistent and stable the method is successfully applied to the simulation of a three dimensional transonic flow over a deforming wing

analysis of a bdf dgfe scheme for nonlinear convection diffusion problems we deal with the numerical solution of a scalar nonstationary nonlinear convection diffusion equation we employ a combination of the discontinuous galerkin finite element method for the space semi discretization and the k step backward difference formula for the time discretization the diffusive and stabilization terms are treated implicitly whereas the nonlinear convective term is treated by a higher order explicit extrapolation method which leads to the necessity to solve only a linear algebraic problem at each time step we analyse this scheme and derive a priori asymptotic error estimates in the discrete l l 2 norm and the l 2 h 1 seminorm with respect to the mesh size h and time step for k 2 3 numerical examples verifying the theoretical results are presented

on delay dependent stability under model transformations of some neutral linear systems this paper focuses on the stability analysis of a class of neutral linear systems some sufficient delay dependent stability conditions are derived in terms of an appropriate model transformation of the original system transformation similar to the one used in the retarded case the analysis makes use of an appropriate construction of a degenerate lyapunov krasovskii functional several computational schemes and frequency domain interpretations as well as an example are also presented

new insights on stability of sampled data systems with time delay abstract this paper analyses the stability of sampled data systems with time delay by employing a two sided looped functional approach some improved conditions are derived to guarantee the stability of the system under consideration then based the conditions some intrinsic relationships between sampled data period and time delay are obtained from the illustrative example being solved by the proposed approach it is observed that the results obtained are significantly better than those obtained by existing methods more importantly from the simulation being carried out it is discovered that contrary to the findings in previous studies time delays in a system may enlarge the interval of sampled data periods and accelerate the rate of convergence of the system states rather than deteriorate the system performance

discontinuous galerkin method for the solution of a transport level set problem the subject of the paper is the numerical analysis of the transport level set problem discretized by the discontinuous galerkin method without the assumption that the first order nonstationary transport equation contains a reaction term which is used in a standard literature we prove error estimates in the l l 2 norm in the case of the space semidiscretization method of lines and in the case of the space time discontinuous galerkin method in the l 2 l 2 norm numerical experiments support the derived error estimates and show that they are not sharp in the case of the space time discontinuous galerkin method

technical communique improved delay range dependent stability criteria for linear systems with time varying delays this paper is concerned with the stability analysis of linear systems with time varying delays in a given range a new type of augmented lyapunov functional is proposed which contains some triple integral terms in the proposed lyapunov functional the information on the lower bound of the delay is fully exploited some new stability criteria are derived in terms of linear matrix inequalities without introducing any free weighting matrices numerical examples are given to illustrate the effectiveness of the proposed method

delay dependent stability criteria for generalized neural networks with two delay components this paper investigates the delay dependent stability for generalized continuous neural networks with time varying delays a novel lyapunov krasovskii functional lkf that considers more information on activation functions of delayed neural networks and delay upper bounds is developed simultaneously most commonly used techniques for treating the derivative of the lkf are reviewed and compared with each other with the way of introducing slack matrices those techniques are classified into two categories including free weighting matrix fwm based techniques and reciprocally convex combination based techniques it is found that the introduced slack matrices play an important role in conservatism reducing and those four types of fwm based methods lead to same results and are equivalent moreover the obtained criteria are extended to the system with a single time varying delay two numerical examples are given to verify the effectiveness of the proposed method

stability for neural networks with time varying delays via some new approaches this paper considers the problem of delay dependent stability criteria for neural networks with time varying delays first by constructing a newly augmented lyapunov krasovskii functional a less conservative stability criterion is established in terms of linear matrix inequalities second by proposing novel activation function conditions which have not been proposed so far further improved stability criteria are proposed finally three numerical examples used in the literature are given to show the improvements over the existing criteria and the effectiveness of the proposed idea

determinant theory for fuzzy matrices abstract we study determinant theory for fuzzy square matrices including some boolean matrices and consider the cayley hamilton theorem for these matrices we prove that det a adj a det a det adj a a where adj a denotes the adjoint matrix of a fuzzy matrix a

stability analysis of neural networks with two delay components based on dynamic delay interval method in this paper a dynamic delay interval ddi method is proposed to deal with the stability problem of neural networks with two delay components this method extends the fixed interval of a time varying delay to a dynamic one which relaxes the restriction on upper and lower bounds of the delay intervals combining the reciprocally convex combination technique and wirtinger integral inequality the ddi method leads to some much less conservative delay dependent stability criteria based on a linear matrix inequality for neural networks with two delay components furthermore the criteria for the system with a single time varying delay are provided some examples are given to illustrate the effectiveness of the obtained results

space time discontinuous galerkin finite element method with dynamic grid motion for inviscid compressible flows i general formulation a new space time discontinuous galerkin finite element method for the solution of the euler equations of gas dynamics in time dependent flow domains is presented the discontinuous galerkin discretization results in an efficient elementwise conservative upwind finite element method which is particularly well suited for local mesh refinement the upwind scheme uses a formulation of the hllc flux applicable to moving meshes and several formulations for the stabilization operator to ensure that monotone solutions around discontinuities are investigated the non linear equations of the space time discretization are solved using a multigrid accelerated pseudo time integration technique with an optimized runge kutta method the linear stability of the pseudo time integration method is investigated for the linear advection equation the numerical scheme is demonstrated with simulations of the flow field in a shock tube a channel with a bump and an oscillating naca 0012 airfoil these simulations show that using the data at the superconvergence points the accuracy of the numerical discretization is o h5 2 in space for smooth subsonic flows both on structured and on locally refined meshes and that the space time adaptation can significantly improve the accuracy and efficiency of the numerical method

wirtinger based integral inequality application to time delay systems in the last decade the jensen inequality has been intensively used in the context of time delay or sampled data systems since it is an appropriate tool to derive tractable stability conditions expressed in terms of linear matrix inequalities lmis however it is also well known that this inequality introduces an undesirable conservatism in the stability conditions and looking at the literature reducing this gap is a relevant issue and always an open problem in this paper we propose an alternative inequality based on the fourier theory more precisely on the wirtinger inequalities it is shown that this resulting inequality encompasses the jensen one and also leads to tractable lmi conditions in order to illustrate the potential gain of employing this new inequality with respect to the jensen one two applications on time delay and sampled data stability analysis are provided

partially implicit bdf2 blends for convection dominated flows in this paper we consider various blends of implicit and explicit time integration schemes based on the well known bdf2 method applied to convection diffusion problems with dominating convection a fully implicit treatment of convection terms is often not very efficient we shall deal with second order schemes that are implicit in the convection terms only locally in space without introducing the internal inconsistencies that are common with many time splitting methods along with implementation aspects of the implicit relations we shall discuss accuracy of the schemes positivity and monotonicity properties

novel delay dependent stability criterion for time varying delay systems with parameter uncertainties and nonlinear perturbations this study proposes a novel approach to obtain less conservative conditions for the robust stability analysis for time varying delay systems with parameter uncertainties and nonlinear perturbations specifically first we divide the time varying delay into non uniformly subintervals and decompose the corresponding integral intervals to estimate the bounds of integral terms more exactly second novel delay derivation dependent stability criteria are derived by introducing a parameter c in the lyapunov krasovskii functional third we define some new variables to deal with uncertain parameters finally two numerical examples are presented to demonstrate the effectiveness and advantages of the theoretical results

multistability of complex valued neural networks with time varying delays in this paper the multistability problem is studied for an n dimensional delayed complex valued neural networks with two general classes of activation functions after splitting the state space to multiple subsets based on the fixed point theorem it is shown that such complex valued neural networks can have 9n equilibria each of which is located in one of the subsets furthermore some sufficient conditions are derived for the local exponential stability of some equilibria by employing the property of activation functions and inequality technique as an application of these results some criteria are obtained for checking the coexistence and exponential stability of multiple equilibria of real valued neural networks two examples are performed to illustrate and validate the theoretical findings

analysis on robust h performance and stability for linear systems with interval time varying state delays via some new augmented lyapunov krasovskii functional in this paper the problem of h performance and stability analysis for linear systems with interval time varying delays is considered first by constructing a newly augmented lyapunov krasovskii functional which has not been proposed yet an improved h performance criterion with the framework of linear matrix inequalities lmis is introduced next the result and method are extended to the problem of a delay dependent stability criterion finally numerical examples are given to show the superiority of proposed method

on the stability of linear systems with uncertain delay this paper focuses on the stability of some class of delay systems including uncertainty in the delays more precisely we are interested in guaranteeing the stability of perturbed delay systems by assuming the stability of the nominal system if the delay perturbation is constant necessary and sufficient conditions are derived in terms of generalized eigenvalue distribution of some finite dimensional constant matrix pencil if the delay perturbation is time varying some sufficient stability conditions are derived using exact lyapunov krasovskii functionals illustrative examples are also included

analysis of the discontinuous galerkin method for nonlinear convection diffusion problems abstract the subject matter is the analysis of the discontinuous galerkin finite element method applied to a nonlinear convection diffusion problem in the contrary to the standard fem the requirement of the conforming properties is omitted this allows us to consider general polyhedral elements with mutually disjoint interiors we do not require their convexity but assume only that they are star shaped we present an error analysis for the case of a nonsymmetric discretization of diffusion terms theoretical results are accompanied by numerical experiments

stability analysis of fractional order complex valued neural networks with both leakage and discrete delays in this paper the problem of uniform stability for fractional order complex valued neural networks with both leakage and discrete delays is considered base on the contracting mapping principle a sufficient condition is proposed for the existence and uniqueness of the equilibrium point of the addressed neural networks by employing analysis technique some delay dependent criteria are established for checking the global uniform stability of the fractional order complex valued neural networks two numerical examples are presented to demonstrate the validity and feasibility of the proposed results

analysis of space time discontinuous galerkin method for nonlinear convection diffusion problems the paper presents the theory of the discontinuous galerkin finite element method for the space time discretization of a nonstationary convection diffusion initial boundary value problem with nonlinear convection and linear diffusion the problem is not singularly perturbed with dominating convection the discontinuous galerkin method is applied separately in space and time using in general different space grids on different time levels and different polynomial degrees p and q in space and time dicretization in the space discretization the nonsymmetric symmetric and incomplete interior and boundary penalty nipg sipg iipg approximation of diffusion terms is used the paper is concerned with the proof of error estimates in l 2 l 2 and dg norm formed by the l 2 h 1 seminorm and penalty terms a special technique based on the use of the gauss radau interpolation and numerical integration has been used for the derivation of an abstract error estimate in the dg norm the error estimates are optimal with respect to the size of the space grid they are optimal with respect to the time step if the dirichlet boundary condition has behaviour in time as a polynomial of degree q

reciprocally convex approach to stability of systems with time varying delays whereas the upper bound lemma for matrix cross product introduced by park 1999 and modified by moon park kwon and lee 2001 plays a key role in guiding various delay dependent criteria for delayed systems the jensen inequality has become an alternative as a way of reducing the number of decision variables it directly relaxes the integral term of quadratic quantities into the quadratic term of the integral quantities resulting in a linear combination of positive functions weighted by the inverses of convex parameters this paper suggests the lower bound lemma for such a combination which achieves performance behavior identical to approaches based on the integral inequality lemma but with much less decision variables comparable to those based on the jensen inequality lemma

on h control for linear systems with interval time varying delay this paper deals with the problem of delay dependent robust h control for linear time delay systems with norm bounded and possibly time varying uncertainty the time delay is assumed to be a time varying continuous function belonging to a given interval which means that the lower and upper bounds for the time varying delay are available and no restriction on the derivative of the time varying delay is needed which allows the time delay to be a fast time varying function based on an integral inequality which is introduced in this paper and lyapunov krasovskii functional approach a delay dependent bounded real lemma brl is first established without using model transformation and bounding techniques on the related cross product terms then employing the obtained brl a delay dependent condition for the existence of a state feedback controller which ensures asymptotic stability and a prescribed h performance level of the closed loop systems for all admissible uncertainties is proposed in terms of a linear matrix inequality lmi a numerical example is also given to illustrate the effectiveness of the proposed method

implicit explicit methods for time dependent partial differential equations implicit explicit imex schemes have been widely used especially in conjunction with spectral methods for the time integration of spatially discretized partial differential equations pdes of diffusion convection type typically an implicit scheme is used for the diffusion term and an explicit scheme is used for the convection term reaction diffusion problems can also be approximated in this manner in this work we systematically analyze the performance of such schemes propose improved new schemes and pay particular attention to their relative performance in the context of fast multigrid algorithms and of aliasing reduction for spectral methods for the prototype linear advection diffusion equation a stability analysis for first second third and fourth order multistep imex schemes is performed stable schemes permitting large time steps for a wide variety of problems and yielding appropriate decay of high frequency error modes are identified numerical experiments demonstrate that weak decay

finite time h fuzzy control of nonlinear markovian jump delayed systems with partly uncertain transition descriptions abstract this paper addresses a finite time h fuzzy control problem for a class of nonlinear markovian jump delayed systems with partly uncertain transition descriptions which is represented as a takagi sugeno t s fuzzy model a new homogeneous polynomial of partly uncertain transition rates is chosen free matrix based and double integral forms of the wirtinger based integral inequalities are employed to make the proposed approach less conservative then sufficient conditions are derived such that the fuzzy nonlinear makovian jump delayed system exhibits stochastic finite time boundedness finally two numerical examples are given to illustrate the effectiveness of the proposed design methodology

improved delay dependent stability criteria for time delay systems this note provides an improved asymptotic stability condition for time delay systems in terms of a strict linear matrix inequality unlike previous methods the mathematical development avoids bounding certain cross terms which often leads to conservatism when time varying norm bounded uncertainties appear in a delay system an improved robust delay dependent stability condition is also given examples are provided to demonstrate the reduced conservatism of the proposed conditions

lmi based approach for global asymptotic stability analysis of recurrent neural networks with various delays and structures global asymptotic stability problem is studied for a class of recurrent neural networks with distributed delays satisfying lebesgue stieljies measures on the basis of linear matrix inequality the concerned network model includes many neural network models with various delays and structures as its special cases such as the delays covering the discrete delays and distributed delays and the network structures containing the neutral type networks and high order networks therefore many new stability criteria for the above neural network models have also been derived from the present stability analysis method all the obtained stability results have similar matrix inequality structures and can be easily checked three numerical examples are used to show the effectiveness of the obtained results

space time discontinuous galerkin method for the compressible navier stokes equations a space time discontinuous galerkin finite element method for the compressible navier stokes equations is presented we explain the space time setting derive the weak formulation and discuss our choices for the numerical fluxes the resulting numerical method allows local grid adaptation as well as moving and deforming boundaries which we illustrate by computing the flow around a 3d delta wing on an adapted mesh and by simulating the dynamic stall phenomenon of a 2d airfoil in rapid pitch up maneuver

new lyapunov krasovskii functionals for global asymptotic stability of delayed neural networks this brief deals with the problem of global asymptotic stability for a class of delayed neural networks some new lyapunov krasovskii functionals are constructed by nonuniformly dividing the delay interval into multiple segments and choosing proper functionals with different weighting matrices corresponding to different segments in the lyapunov krasovskii functionals then using these new lyapunov krasovskii functionals some new delay dependent criteria for global asymptotic stability are derived for delayed neural networks where both constant time delays and time varying delays are treated these criteria are much less conservative than some existing results which is shown through a numerical example

a delay dependent stability criterion for systems with uncertain time invariant delays this paper provides a new stability criterion for systems with time invariant uncertain delays based on an improved upper bound for the inner product of two vectors a new delay dependent robust stability criterion is derived which is shown by an example less conservative than existing stability criteria

a discontinuoushpfinite element method for diffusion problems we present an extension of the discontinuous galerkin method which is applicable to the numerical solution of diffusion problems the method involves a weak imposition of continuity conditions on the solution values and on fluxes across interelement boundaries within each element arbitrary spectral approximations can be constructed with different orderspin each element we demonstrate that the method is elementwise conservative a property uncharacteristic of high order finite elements for clarity we focus on a model class of linear second order boundary value problems and we developpriorierror estimates convergence proofs and stability estimates the results of numerical experiments onh andp convergence rates for representative two dimensional problems suggest that the method is robust and capable of delivering exponential rates of convergence

cramer and cayley hamilton in the max algebra abstract cramer s rule and the cayley hamilton theorem are formulated and provided in the so called max algebra which consists of the set of reals provided with two operations maximization and addition it is surprising to see that these well known theorems carry over to the max algebra almost without any changes provided that the conventional addition and multiplication are replaced by maximization and addition respectively the definitions of determinant and eigenvalue have to be adjusted to this new formulation the role of the determinant is taken over by the permanent and a refinement of this latter concept called the dominant

technical communique delay range dependent stability for systems with time varying delay this paper is concerned with the stability analysis for systems with time varying delay in a range an appropriate type of lyapunov functionals is proposed to investigate the delay range dependent stability problem the present results may improve the existing ones due to a method to estimate the upper bound of the derivative of lyapunov functional without ignoring some useful terms and the introduction of additional terms into the proposed lyapunov functional which take into account the range of delay numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method

brief paper new delay dependent stability criteria for systems with interval delay this paper provides a new delay dependent stability criterion for systems with a delay varying in an interval with a different lyapunov functional defined a tight upper bound of its derivative is given the resulting criterion has advantages over some previous ones in that it involves fewer matrix variables but has less conservatism which is established theoretically examples are provided to demonstrate the advantage of the stability result

new approaches on stability criteria for neural networks with interval time varying delays abstract this paper concerns the problem of delay dependent stability criteria for neural networks with interval time varying delays first by constructing a newly augmented lyapunov krasovskii functional and combining with a reciprocally convex combination technique less conservative stability criterion is established in terms of linear matrix inequalities lmis which will be introduced in theorem 1 second by taking different interval of integral terms of lyapunov krasovskii functional utilized in theorem 1 further improved stability criterion is proposed in theorem 2 third a novel approach which divides the bounding of activation function into two subinterval are proposed in theorem 3 to reduce the conservatism of stability criterion finally through two well known numerical examples used in other literature it will be shown the proposed stability criteria achieves the improvements over the existing ones and the effectiveness of the proposed idea

stability analysis of lur e systems with additive delay components via a relaxed matrix inequality abstract this paper is concerned with the stability analysis of lur e systems with sector bounded nonlinearity and two additive time varying delay components in order to accurately understand the effect of time delays on the system stability the extended matrix inequality for estimating the derivative of the lyapunov krasovskii functionals lkfs is employed to achieve the conservatism reduction of stability criteria it reduces estimation gap of the popular reciprocally convex combination lemma rccl combining the extended matrix inequality and two types of lkfs lead to several stability criteria which are less conservative than the rccl based criteria under the same lkfs finally the advantages of the proposed criteria are demonstrated through two examples

a novel summation inequality for stability analysis of discrete time neural networks in this paper based on the discrete wirtinger inequality a novel summation inequality is established which extends the jensen inequality by the technique of the novel inequality a sufficient criterion on asymptotic stability of discrete neural networks with time varying delays is obtained a numerical example is given to demonstrate the effectiveness of the inequality

global asymptotic stability for a class of generalized neural networks with interval time varying delays this paper is concerned with global asymptotic stability for a class of generalized neural networks nns with interval time varying delays which include two classes of fundamental nns i e static neural networks snns and local field neural networks lfnns as their special cases some novel delay independent and delay dependent stability criteria are derived these stability criteria are applicable not only to snns but also to lfnns it is theoretically proven that these stability criteria are more effective than some existing ones either for snns or for lfnns which is confirmed by some numerical examples

discontinuous hp finite element methods for advection diffusion reaction problems we consider the hp version of the discontinuous galerkin finite element method dgfem for second order partial differential equations with nonnegative characteristic form this class of equations includes second order elliptic and parabolic equations advection reaction equations as well as problems of mixed hyperbolic elliptic parabolic type our main concern is the error analysis of the method in the absence of streamline diffusion stabilization in the hyperbolic case an hp optimal error bound is derived here we consider only advection reaction problems which satisfy a certain standard positivity condition in the self adjoint elliptic case an error bound that is h optimal and p suboptimal by frac 1 2 a power of p is obtained these estimates are then combined to deduce an error bound in the general case for elementwise analytic solutions the method exhibits exponential rates of convergence under p refinement the theoretical results are illustrated by numerical experiments

the determinant of a fuzzy matrix with respect to t and co t norms abstract we study determinants of square matrices over the interval 0 1 when ordinary multiplication is replaced by a triangular norm and ordinary addition is replaced by a triangular conorm

improved delay dependent stabilization for a class of networked control systems with nonlinear perturbations and two delay components abstract this paper focuses on the problem of delay dependent state feedback control for a class of networked control systems ncss with nonlinear perturbations and two delay components based on the dynamic delay interval ddi method and the wirtinger integral inequality some improved delay dependent stability analysis are obtained furthermore the results are extended to the conditions of ncss with one time delay and the corresponding stability analysis results and state feedback controller are obtained finally some numerical examples and simulations are given to show the effectiveness of the proposed methods

h state estimation for neural networks with general activation function and mixed time varying delays this article deals with h state estimation of neural networks with mixed delays in order to make full use of delay information novel delay product lyapunov krasovskii functional lkf by using parameterized delay interval is first constructed then generalized free weighting matrix integral inequality is used to estimate the derivative of lkf to reduce the conservatism also a more general activation function is further applied by combining with parameterized delay interval in order to obtain a more accurate estimator model finally sufficient conditions are derived to confirm that the estimation error system is asymptotically stable with a prescribed h performance numerical examples are simulated to show the benefits of our proposed method