reduced order observer design for a class of generalized lipschitz nonlinear systems with time varying delay abstract this paper investigates the h reduced order observer design problem for a class of nonlinear systems with interval time varying delay which satisfies the quadratically inner bounded condition and encompasses the family of lipschitz systems a novel reduced order observer design methodology for nonlinear systems is proposed by utilizing a newly extended reciprocal convexity inequality free weighting matrix technique and quadratically inner bounded condition the less conservative existence conditions of the proposed nonlinear h observer are derived the new sufficient conditions in terms of linear matrix inequalities lmis guarantee asymptotic stability of the estimation error dynamics with a prescribed performance two numerical examples are given to illustrate the effectiveness of the proposed approach

a new augmented lyapunov krasovskii functional approach for stability of linear systems with time varying delays abstract this paper proposes improved delay dependent conditions for asymptotic stability of linear systems with time varying delays the proposed method employs a suitable lyapunov krasovskii s functional for new augmented system based on lyapunov method delay dependent stability criteria for the systems are established in terms of linear matrix inequalities lmis which can be easily solved by various optimization algorithms three numerical examples are included to show that the proposed method is effective and can provide less conservative results

the weak lefschetz property of equigenerated monomial ideals abstract we determine a sharp lower bound for the hilbert function in degree d of a monomial algebra failing the weak lefschetz property over a polynomial ring with n variables and generated in degree d for any d 2 and n 3 we consider artinian ideals in the polynomial ring with n variables generated by homogeneous polynomials of degree d invariant under an action of the cyclic group z d z for any n 3 and any d 2 we give a complete classification of such ideals in terms of the weak lefschetz property depending on the action

robust h stabilization for t s fuzzy systems with time varying delays and memory sampled data control abstract in this paper we address the robust h stabilization for t s fuzzy systems with time varying delays based on memory sampled data control by developing some new terms an improved piecewise lyapunov krasovskii functional lkf is constructed to take full advantage of characteristic about real sampling pattern furthermore some relaxed matrices proposed in the lkf are not necessarily positive definite by using the lkf and free matrix based fmb integral inequality some sufficient criteria are established to ensure the stability of fuzzy systems and reduce the influence of external disturbance with an h norm bound then the memory sampled data controller can be derived by solving a group of linear matrix inequalities lmis with the maximal sampling period finally a numerical example is given to demonstrate the benefits and the superiority of the approach proposed

relaxed conditions for stability of time varying delay systems in this paper the problem of delay dependent stability analysis of time varying delay systems is investigated firstly a new inequality which is the modified version of free matrix based integral inequality is derived and then by aid of this new inequality two novel lemmas which are relaxed conditions for some matrices in a lyapunov function are proposed based on the lemmas improved delay dependent stability criteria which guarantee the asymptotic stability of the system are presented in the form of linear matrix inequality lmi two numerical examples are given to describe the less conservatism of the proposed methods

robust exponential h control for uncertain time varying delay systems with input saturation a markov jump model approach abstract this paper is concerned with the state feedback stabilization problem for uncertain time varying delay systems with input saturation based on the stochastic property of time varying delay the considered system can be transformed into a continuous markov jump system with stochastic delays where the growth trend and the maximum value of the time varying delay are limited the problem we address is to design a robust state feedback controller which can switch with time varying delay in terms of markov process such that the system is exponentially mean square stable with disturbance attenuation conditions for the existence of solutions to this problem are obtained in terms of linear matrix equalities lmis when these lmis are feasible the desired robust controller is given finally two examples are provided to demonstrate the effectiveness of the proposed approach

technical communique new conditions for delay derivative dependent stability two recent lyapunov based methods have significantly improved the stability analysis of time delay systems the delay fractioning approach of gouaisbaut and peaucelle 2006 for systems with constant delays and the convex analysis of systems with time varying delays of park and ko 2007 in this paper we develop a convex optimization approach to stability analysis of linear systems with interval time varying delay by using the delay partitioning based lyapunov krasovskii functionals lkfs novel lkfs are introduced with matrices that depend on the time delays these functionals allow the derivation of stability conditions that depend on both the upper and lower bounds on delay derivatives

on the weak lefschetz property for artinian gorenstein algebras of codimension three abstract we study the problem of whether an arbitrary codimension three graded artinian gorenstein algebra has the weak lefschetz property we reduce this problem to checking whether it holds for all compressed gorenstein algebras of odd socle degree in the first open case namely hilbert function 1 3 6 6 3 1 we give a complete answer in every characteristic by translating the problem to one of studying geometric aspects of certain morphisms from p 2 to p 3 and hesse configurations in p 2

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

buchsbaum rim sheaves and their multiple sections abstract this paper begins by introducing and characterizing buchsbaum rim sheaves on z proj r where r is a graded gorenstein k algebra they are reflexive sheaves arising as the sheafification of kernels of sufficiently general maps between free r modules then we study multiple sections of a buchsbaum rim sheaf b i e we consider morphisms p b of sheaves on z dropping rank in the expected codimension where h0 z p is a free r module the main purpose of this paper is to study properties of schemes associated to the degeneracy locus s of it turns out that s is often not equidimensional let x denote the top dimensional part of s in this paper we measure the difference between x and s compute their cohomology modules and describe ring theoretic properties of their coordinate rings moreover we produce graded free resolutions of x and s which are in general minimal among the applications we show how one can embed a subscheme into an arithmetically gorenstein subscheme of the same dimension and prove that zero loci of sections of the dual of a null correlation bundle are arithmetically buchsbaum

novel robust stability criteria for uncertain systems with time varying delay this paper is concerned with the delay dependent stability and robust stability criteria for linear systems with time varying delay and norm bounded uncertainties through constructing a general form of lyapunov krasovskii functional and using integral inequalities some slack matrices and newly established convex combination condition in the calculation the delay dependent stability criteria are derived in terms of linear matrix inequalities numerical examples are given to illustrate the improvement on the conservatism of the delay bound over some reported results in the literature

the weak lefschetz property of gorenstein algebras of codimension three associated to the apery sets abstract it has been conjectured that all graded artinian gorenstein algebras of codimension three have the weak lefschetz property over a field of characteristic zero in this paper we study the weak lefschetz property of associated graded algebras a of the apery set of m pure symmetric numerical semigroups generated by four natural numbers in 2010 bryant proved that these algebras are graded artinian gorenstein algebras of codimension three in a recent article guerrieri showed that if a is not a complete intersection then a is of form a r i with r k x y z and i x a y b x b z z c x a b y b y b z c where 1 b 1 max 1 b a 1 min b 1 c 1 and a c 2 we prove that a has the weak lefschetz property in the following cases max 1 b a c 1 b 1 and a b c 2 2 a 2 b c and a b c 1 b 1 one of a b c is at most five

reducing conservatism of stability criteria for linear systems with time varying delay using an improved triple integral inequality abstract this paper focuses on stability analysis of linear systems with time varying delay where two cases of the time varying delay are discussed that is the time varying delay is either differentiable or just uniformly continuous first an improved triple integral inequality is proposed to estimate triple integrals tightly then by introducing two novel lyapunov krasovskii functionals catering for two cases of time varying delay two sufficient conditions on stability respectively for the system under two cases of time varying delay are derived using the improved triple integral inequality and a necessary and sufficient condition on quadratic matrix inequalities reported recently finally three numerical examples show that the obtained results outperform some existing ones

a new looped functional for stability analysis of sampled data systems abstract in this paper a new two sided looped functional is introduced for stability analysis of sampled data systems the functional fully utilizes the information on both the intervals x t to x t k and x t to x t k 1 based on the two sided functional an improved stability condition is derived in the form of linear matrix inequality lmi numerical examples show that the result computed by the presented condition approximates nearly the theoretical bound bound obtained by eigenvalue analysis and outperforms substantially others in the existing literature

solution algorithms for nonlinear transient heat conduction analysis employing element by element iterative strategies abstract despite continuing advancements in computer technology there are many problems of engineering interest that exceed the combined capabilities of today s numerical algorithms and computational hardware the resources required by traditional finite element algorithms tend to grow geometrically as the problem size is increased thus for the forseeable future there will be problems of interest which cannot be adequately modeled using currently available algorithms for this reason we have undertaken the development of algorithms whose resource needs grow only linearly with problem size in addition these new algorithms will fully exploit the parallel processing capability available in the new generation of multi processor computers the approach taken in the element by element solution procedures is to approximate the global implicit operator by a product of lower order operators this type of product approximation originated with adi techniques and was further refined into the method of fraction steps the current effort involves the use of a more natural operator split for finite element analysis based on element operators this choice of operator splitting based on element operators has several advantages first it fits easily within the architecture of current finite element programs second it allows the development of parallel algorithms finally the computational expense varies only linearly with the number of elements the particular problems considered arise from nonlinear transient heat conduction the nonlinearity enters through both material temperature dependence and radiation boundary conditions the latter condition typically introduces a stiff component in the resultant matrix odes which precludes effective use of explicit solution techniques on the other hand typical implicit techniques involving direct equation solving can be prohibitively expensive instead the matrix equations are solved by combining a modified newton raphson iteration scheme for the nonlinear algebraic problem with an element by element preconditioned conjugate gradient procedure for the linear problems an adaptive intercommunicative strategy is developed for setting termination criteria for the nonlinear and linear equation solving algorithms errors and computational efficiency in the transient solution are controlled by an automatic time step selection strategy the resultant procedure has proven to be both accurate and reliable in the solution of medium size test problems

dynamic output feedback guaranteed cost control for linear systems with interval time varying delays in states and outputs abstract this paper addresses the dynamic output feedback guaranteed cost control problem of a class of time delay systems where the state and output contain interval non differentiable time varying delays the proposed controller uses only the delayed output measurement to stabilize the closed loop system and guarantee an adequate level of system performance by constructing a set of multiple lyapunov krasovskii functionals which include triple integral terms a new criterion for the existence of dynamic output feedback guaranteed cost controllers is established and expressed in terms of linear matrix inequality lmi a numerical example is given to illustrate the obtained results

on the kalman yakubovich popov lemma the purpose of this note is to present a new elementary proof for the multivariable k y p lemma a minimum of linear algebra and finite dimensional convexity theory is used

improved approach to robust stability and h performance analysis for systems with an interval time varying delay abstract an improved delay and range dependent robust stability and h performance analysis criterion for systems with an interval time varying delay is investigated a novel lyapunov krasovskii functional containing triple integral terms is established and an extended free weighting matrix method double integral inequality method is subsequently proposed numerical examples validate the effectiveness of the proposed double integral inequality method and show that our approach is less conservative than existing methods

thin algebras of embedding dimension three let r r0 r1 r2 be a finitely generated commutative graded k algebra with hilbert series hr n 0dimk rn n suppose we require that r have a presentation as r k x1 xg 1 r where g and r and the degrees d1 dr of the homogeneous polynomials 1 r are specified in advance no one knows precisely which hubert series such an r may have a lower bound is the coefficient wise inequality hr 1 g i 1r 1 di absolute value symbols denoting the initial non negative segment of a power series can this lower bound always be attained this deceptively simple sounding question has been answered affirmatively only when g 2 r froberg report no 37 department of mathematics university of stockholm stockholm sweden 1982 a iarrobino memoir no 188 amer math soc providence r i 1977 when r g and when r g 1 and char k 0 a iarrobino compressed algebras trans amer math soc 285 1984 337 378 this paper considers the case g 3 settling it affirmatively whenever k is an infinite field

a novel lyapunov functional for stability of time varying delay systems via matrix refined function this paper is concerned with the development of novel stability criteria for time varying delayed systems to this end a new function which consisted of two quadratic functions with a special structural matrix is established to be a lyapunov functional candidate the proposed lyapunov functional plays key role to decrease the conservatism of derived conditions which is verified by three numerical examples

stability analysis with dissipation inequalities and integral quadratic constraints this technical note considers the stability of a feedback connection of a known linear time invariant system and a perturbation the input output behavior of the perturbation is described by an integral quadratic constraint iqc iqc stability theorems can be formulated in the frequency domain or with a time domain dissipation inequality the two approaches are connected by a non unique factorization of the frequency domain iqc multiplier the factorization must satisfy two properties for the dissipation inequality to be valid first the factorization must ensure the time domain iqc holds for all finite times second the factorization must ensure that a related matrix inequality when feasible has a positive semidefinite solution this technical note shows that a class of frequency domain iqc multipliers has a factorization satisfying these two properties thus the dissipation inequality test with an appropriate factorization can be used with no additional conservatism

robust h filter design for discrete time switched systems with interval time varying delay and linear fractional perturbations lmi optimization approach in this paper the robust h filter scheme for the discrete time switched systems with interval time varying delay and linear fractional perturbations is proposed a convex optimization problem with some lmi constraints is formulated to design the stable switched filter which minimizes the h norm bound for filtering error system some nonnegative inequalities and the free weighting matrix technique are used to provide the additional degree of freedom which improves the conservativeness of the proposed results finally a numerical example is illustrated to show the use of the main results

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

a generalized free matrix based integral inequality for stability analysis of time varying delay systems abstract this paper focuses on the delay dependent stability problem of time varying delay systems a generalized free matrix based integral inequality gfmbii is presented this inequality is able to deal with time varying delay systems without using the reciprocal convexity lemma it overcomes the drawback that the bessel legendre inequality is inconvenient to cope with a time varying delay system as the resultant bound contains a reciprocal convexity through the use of the derived inequality and by constructing a suitable lyapunov krasovskii function lkf improved stability criteria are presented in the form of linear matrix inequalities lmis two numerical examples are carried out to demonstrate that the results outperform the state of the art in the literature

free matrix based integral inequality for stability analysis of systems with time varying delay the free weighting matrix and integral inequality methods are widely used to derive delay dependent criteria for the stability analysis of time varying delay systems because they avoid both the use of a model transformation and the technique of bounding cross terms this technical note presents a new integral inequality called a free matrix based integral inequality that further reduces the conservativeness in those methods it includes well known integral inequalities as special cases using it to investigate the stability of systems with time varying delays yields less conservative delay dependent stability criteria which are given in terms of linear matrix inequalities two numerical examples demonstrate the effectiveness and superiority of the method

novel inequality with application to improve the stability criterion for dynamical systems with two additive time varying delays abstract in this paper the stability of the system with two additive time varying delay components is studied and improved stability condition is obtained it firstly establishes two novel integral inequalities which are better than the same type inequalities found in the literature secondly a new constructed lyapunov functional is constructed based on the additive time varying delays property following two steps to handle the lyapunov functional the delay dependent stability condition is obtained which in terms of linear matrix inequalities finally two numerical examples are given to verify the effectiveness of the proposed method and the superiority of the results

a generalized lower bound theorem for balanced manifolds a simplicial complex of dimension d 1 is said to be balanced if its graph is d colorable juhnke kubitzke and murai proved an analogue of the generalized lower bound theorem for balanced simplicial polytopes we establish a generalization of their result to balanced triangulations of closed homology manifolds and balanced triangulations of orientable homology manifolds with boundary under an additional assumption that all proper links of these triangulations have the weak lefschetz property as a corollary we show that if delta is an arbitrary balanced triangulation of any closed homology manifold of dimension d 1 ge 3 then 2h 2 delta d 1 h 1 delta ge 4 d atopwithdelims 2 tilde beta 1 delta tilde beta 0 delta thus verifying a conjecture by klee and novik to prove these results we develop the theory of flag h vectors

improved stability criteria for linear systems with interval time varying delays this paper suggests first order and second order generalized zero equalities and constructs a new flexible lyapunov krasovskii functional with more state terms also by applying various zero equalities improved stability criteria of linear systems with interval time varying delays are developed using wirtinger based integral inequality jensen inequality and a lower bound lemma the time derivative of the lyapunov krasovskii functional is bounded by the combinations of various state terms including not only integral terms but also their interval normalized versions which contributes to make the stability criteria less conservative numerical examples show the improved performance of the criteria in terms of maximum delay bounds

stability analysis of systems with time varying delay via novel augmented lyapunov krasovskii functionals and an improved integral inequality abstract delay dependent stability analysis of linear systems with a time varying delay is investigated in this paper firstly instead of developing a lyapunov krasovskii functional lkf including augmented non integral quadratic terms as usual this paper proposes two augmented integral function based lkfs which can reflect closer relationships among system states secondly to bound the derivative of lkf more accurately a new integral inequality with several free matrices is developed compared with the free matrix based integral inequality this inequality can provide additional freedom due to the free matrices introduced then by employing those lkfs and the improved integral inequality several delay dependent stability criteria are established for two types of delays finally two numerical examples are given to demonstrate the superiority of the proposed method

looking out for stable syzygy bundles abstract we study slope stability properties of syzygy bundles on a projective space p n given by ideal generators of a homogeneous primary ideal in particular we give a combinatorial criterion for a monomial ideal to have a semistable syzygy bundle restriction theorems for semistable bundles yield the same stability results on the generic complete intersection curve from this we deduce a numerical formula for the tight closure of an ideal generated by monomials or by generic homogeneous elements in a generic two dimensional complete intersection ring

monomial ideals almost complete intersections and the weak lefschetz property many algebras are expected to have the weak lefschetz property though this is often very difficult to establish we illustrate the subtlety of the problem by studying monomial and some closely related ideals our results exemplify the intriguing dependence of the property on the characteristic of the ground field and on arithmetic properties of the exponent vectors of the monomials

element by element penalty uzawa formulation for large scale flow problems abstract a solution procedure for solving large scale unsteady incompressible viscous flow problems is presented it is a velocity explicit pressure implicit method and is based on a penalty uzawa finite element formulation the matrix system is solved by an element by element conjugate gradient method

on higher hessians and the lefschetz properties abstract we deal with a generalization of a theorem of p gordan and m noether on hypersurfaces with vanishing first hessian we prove that for any given n 3 d 3 and 2 k d 2 there are irreducible hypersurfaces x v f p n of degree deg f d not cones and such that their hessian of order k hess f k vanishes identically the vanishing of higher hessians is closely related with the strong or weak lefschetz property for standard graded artinian gorenstein algebra as pointed out first in 31 and later in 24 as an application we construct for each pair n d 3 3 3 4 standard graded artinian gorenstein algebras a of codimension n 1 4 and with socle degree d 3 which do not satisfy the strong lefschetz property failing at an arbitrary step k with 2 k d 2 we also prove that for each pair n d n 3 and d 3 except 3 3 3 4 3 6 and 4 4 there are standard graded artinian gorenstein algebras of codimension n 1 socle degree d with unimodal hilbert vectors and which do not satisfy the weak lefschetz property

dissipativity based sampled data control for fuzzy markovian jump systems abstract in this paper the problems of dissipativity analysis and sampled data control are considered for fuzzy markovian jump systems firstly by constructing a mode dependent lyapunov function consisting of the two sided closed loop function where the information of both intervals x tk to x t and x t to x t k 1 are fully utilized the stochastically stable criteria and strictly q s r dissipative criteria are proposed in the form of linear matrix inequalities lmis then on the basis of the strictly dissipativity criteria a controller with state feedback is designed for the studied systems at last a truck trailer model is shown to demonstrate the efficiency of the presented method

stability analysis of systems with uncertain time varying delays stability of systems in the presence of bounded uncertain time varying delays in the feedback loop is studied the delay parameter is assumed to be an unknown time varying function for which the upper bounds on the magnitude and the variation are given the stability problem is treated in the integral quadratic constraint iqc framework criteria for verifying robust stability are formulated as feasibility problems over a set of frequency dependent linear matrix inequalities the criteria can be equivalently formulated as semi definite programs sdp using kalman yakubovich popov lemma as such checking robust stability can be performed in a computationally efficient fashion

further refinements in stability conditions for time varying delay systems abstract this paper addresses the problem of assessing the stability of linear time invariant lti systems with time varying delay the first contribution is a new stability criterion specified as a negativity condition for a quadratic function parameterized by the delay this result mainly follows from an augmented affine parameter dependent lyapunov krasovskii functional which in turn takes advantages of convexity properties then as a second contribution we invoke a result from robust control literature to show how the proposed stability condition can be checked exactly in terms of linear matrix inequality lmi conditions the improvements obtained by the proposed refinements are illustrated via numerical examples drawn from the literature

togliatti systems and galois coverings abstract we study the homogeneous artinian ideals of the polynomial ring k x y z generated by the homogeneous polynomials of degree d which are invariant under an action of the cyclic group z d z for any d 3 we prove that they are all monomial togliatti systems and that they are minimal if the action is defined by a diagonal matrix having on the diagonal 1 e e a where e is a primitive d th root of the unity we get a complete description when d is prime or a power of a prime we also establish the relation of these systems with linear ceva configurations

delay dependent stability for 2d systems with time varying delay subject to state saturation in the roesser model this paper addresses the problem of delay dependent stability of 2d systems with time varying delay subject to state saturation in the roesser model by introducing diagonally dominant matrices new delay dependent conditions are obtained in terms of linear matrix inequalities lmis where the lower and upper delay bounds along horizontal and vertical directions respectively are known numerical examples are provided to demonstrate the proposed results

the weak and strong lefschetz properties for artinian k algebras abstract let a i 0ai be a standard graded artinian k algebra where chark 0 then a has the weak lefschetz property if there is an element l of degree 1 such that the multiplication l a i a i 1 has maximal rank for every i and a has the strong lefschetz property if l d a i a i d has maximal rank for every i and d the main results obtained in this paper are the following 1 every height three complete intersection has the weak lefschetz property our method surprisingly uses rank two vector bundles on p 2 and the grauert mulich theorem 2 we give a complete characterization including a concrete construction of the hilbert functions that can occur for k algebras with the weak or strong lefschetz property and the characterization is the same one 3 we give a sharp bound on the graded betti numbers achieved by our construction of artinian k algebras with the weak or strong lefschetz property and fixed hilbert function this bound is again the same for both properties some hilbert functions in fact force the algebra to have the maximal betti numbers 4 every artinian ideal in k x y possesses the strong lefschetz property this is false in higher codimension

the lefschetz properties of monomial complete intersections in positive characteristic abstract stanley proved that in characteristic zero all artinian monomial complete intersections have the strong lefschetz property we provide a positive characteristic complement to stanley s result in the case of artinian monomial complete intersections generated by monomials all of the same degree and also for arbitrary artinian monomial complete intersections in characteristic two to establish these results we first prove an a priori lower bound on the characteristics that guarantee the lefschetz properties we then use a variety of techniques to complete the classifications

improved criteria on robust stability and h performance for linear systems with interval time varying delays via new triple integral functionals this paper analyzes delay dependent robust stability and h performance of linear systems with an interval time varying delay based on a new lyapunov krasovskii functional containing new triple integral terms the time derivative of the lyapunov krasovskii functional produces not only the strictly proper rational functions but also the non strictly proper rational functions of the time varying delays with first order denominators the combinations of the rational functions are directly handled via the jensen inequality lemma and the lower bound lemma for reciprocal convexity whereas such combinations were approximated in the literature the proposed criteria become less conservative with the significantly smaller number of decision variables than the existing criteria which will be demonstrated by some numerical examples

extremal point sets and gorenstein ideals the hilbert function of a homogeneous ideal in r k x0 xn k a field is a much studied object this is not surprising since the hilbert function encodes important algebraic combinatorial and geometric information about the ideal the fact that recent computer algebra developments have made the hilbert function computable has not only sustained interest in them but sparked interest in many new questions about them in this paper we will concentrate on the hilbert functions which are the hilbert functions of points in p from 11 we know that this is the same as studying 0 dimensional differentiable o sequences equivalently the hilbert functions of graded artinian quotients of k x1 xn in our earlier paper 9 we began a discussion of n type vectors and showed that they were in 1 1 correspondence with hilbert functions of doi 10 1006 aima 1998 1889 available online at http www idealibrary com on

delay dependent exponential stabilization for uncertain linear systems with interval non differentiable time varying delays abstract in this paper the problem of exponential stabilization for a class of linear systems with time varying delay is studied the time delay is a continuous function belonging to a given interval which means that the lower and upper bounds for the time varying delay are available but the delay function is not necessary to be differentiable based on the construction of improved lyapunov krasovskii functionals combined with leibniz newton s formula new delay dependent sufficient conditions for the exponential stabilization of the systems are first established in terms of lmis numerical examples are given to demonstrate that the derived conditions are much less conservative than those given in the literature

the non lefschetz locus abstract we study the weak lefschetz property of artinian gorenstein algebras and in particular of artinian complete intersections in codimension four and higher it is an open problem whether all complete intersections have the weak lefschetz property for a given artinian gorenstein algebra a we ask what linear forms are lefschetz elements for this particular algebra i e which linear forms l give maximal rank for all the multiplication maps l a i a i 1 this is a zariski open set and its complement is the non lefschetz locus for monomial complete intersections we completely describe the non lefschetz locus for general complete intersections of codimension three and four we prove that the non lefschetz locus has the expected codimension which in particular means that it is empty in a large family of examples for general gorenstein algebras of codimension three with a given hilbert function we prove that the non lefschetz locus has the expected codimension if the first difference of the hilbert function is of decreasing type for completeness we also give a full description of the non lefschetz locus for artinian algebras of codimension two

lyapunov based exact stability analysis and synthesis for linear single parameter dependent systems we propose a class of polynomially parameter dependent quadratic ppdq lyapunov functions for assessing the stability of single parameter dependent linear time invariant s pdlti systems in a non conservative manner it is shown that the stability of s pdlti systems is equivalent to the existence of a ppdq lyapunov function a bound on the degree of the polynomial dependence of the lyapunov function in the system parameter is given explicitly the resulting stability conditions are expressed in terms of a set of matrix inequalities whose feasibility over a compact and connected set can be cast as a convex finite dimensional optimisation problem extensions of the approach to state feedback controller synthesis are also provided

stability analysis of linear systems with interval time varying delays utilizing multiple integral inequalities this paper is devoted to stability analysis of continuous time delay systems with interval time varying delays having known bounds on the delay derivatives a parameterized family of lyapunov krasovskii functionals involving multiple integral terms is introduced and novel multiple integral inequalities are utilized to derive sufficient stability condition for systems with time varying delays the efficiency of the proposed method is illustrated by numerical examples

on the structure of monomial complete intersections in positive characteristic abstract in this paper we study the lefschetz properties of monomial complete intersections in positive characteristic we give a complete classification of the strong lefschetz property when the number of variables is at least three which proves a conjecture by cook ii we also extend earlier results on the weak lefschetz property by dropping the assumption on the residue field being infinite and by giving new sufficient criteria

the weak lefschetz property for monomial ideals of small type abstract in this work a combinatorial approach towards the weak lefschetz property is developed that relates this property to enumerations of signed perfect matchings as well as to enumerations of signed families of non intersecting lattice paths in certain triangular regions this connection is used to study artinian quotients by monomial ideals of a three dimensional polynomial ring extending a main result in the recent memoir 1 we completely classify the quotients of type two that have the weak lefschetz property in characteristic zero we also derive results in positive characteristic for quotients whose type is at most two

integral quadratic constraints for delayed nonlinear and parameter varying systems the stability and performance of nonlinear and linear parameter varying lpv time delayed systems are analyzed first the input output behavior of the time delay operator is bounded in the frequency domain by integral quadratic constraints iqcs a simple geometric interpretation is used to derive new iqcs for both constant and varying delays second the performance of nonlinear and lpv delayed systems is bounded using dissipation inequalities that incorporate iqcs the nonlinear or lpv part of the system is treated directly in the analysis and not bounded by iqcs this step makes use of recent results that show under mild technical conditions that an iqc has an equivalent representation as a finite horizon time domain constraint a numerical example with a nonlinear delayed system is provided to demonstrate the effectiveness of the method

an efficient and rapid numerical quadrature to generate element matrices for quadrilateral and hexahedral elements in functionally graded materials fgms abstract this research paper introduces a robust efficient and stabilized midpoint quadrature to generate element stiffness matrices for quadrilateral and hexahedral elements in finite element method fem this new quadrature is established based on passive richardson extrapolation which has the inherent ability to stabilize and improve the accuracy of the extrapolated results the new quadrature includes a simple artificial stabilizing function with gauss one point quadrature 1gp as an anti hourglass effect for the first approximation the 1gp sampling point to be considered at origin 0 0 is done to evaluate element matrices thermal conductivity matrices capacitance matrices etc in the 4 square element 2 2 x 2 2 in the plane as a stabilizing function sampling points are considered to be either at the center of the four element edges or center of the four quadrants in the reference square element with appropriate constant weighting functions for hexahedral elements also the element stiffness coefficients are calculated only in the center of the element and center of all the octants of the reference cubic element 2 2 x 2 2 x 2 2 the proposed method deals mostly with integer variables and sampling at 0 0 0 whereas gauss quadrature uses lengthy float variables corresponding to irrational numbers in terms of decimals in the stiffness matrix calculations thus consuming time a number of standard example problems are demonstrated to assess the efficiency of the proposed method the results of all the numerical examples are found to be in good agreement with the exact results and conventional gauss quadrature results

an improved reciprocally convex inequality and an augmented lyapunov krasovskii functional for stability of linear systems with time varying delay this paper is concerned with stability of a linear system with a time varying delay first an optimal reciprocally convex inequality is proposed compared with the extended reciprocally convex inequality recently reported the optimal reciprocally convex inequality not only provides an optimal bound for the reciprocally convex combination but also introduces less slack matrix variables second a new lyapunov krasovskii functional is tailored for the use of auxiliary function based integral inequality third based on the optimal reciprocally convex inequality and the new lyapunov krasovskii functional a stability criterion is derived for the system under study finally two well studied numerical examples are given to show that the obtained stability criterion can produce a larger upper bound of the time varying delay than some existing methods

novel delay dependent robust h control of uncertain systems with distributed time varying delays this paper investigates the problem of delay dependent robust h control for a class of uncertain systems with distributed time varying delays the aim is to design a delay dependent robust h control which ensures robust asymptotic stability of the system the delay derivative dependent robust h control criteria are obtained in terms of linear matrix inequalities lmis numerical examples are given to illustrate the effectiveness of the proposed method the results are also compared with the existing results to show the conservativeness

the dilworth number of artin gorenstein rings 1let a be an artin local ring the dilworth number of a is defined to be the supremum of p z for ideals z in a where p is the minimal number of generators in my paper 4 i developed some methods to compute this number when a is homogeneously graded over a field k and especially if a is gorenstein and ch k 0 i showed that it is the dominating case that the dilworth number is attained by a power of the maximal ideal in such a case we shall say that a has the sperner property in the present paper we consider artin rings a m not necessarily graded and compare the dilworth number of a and that of gr a and it will be shown that the main result of 4 is valid without the assumption that the rings are homogeneous our main result is theorem 7 where we prove that most artin gorenstein rings have the sperner property actually we prove a stronger result which says that it has the weak stanley property to explain the term most we represent an artin gorenstein ring a in the

free resolutions of artinian compressed algebras abstract we construct free resolutions of compressed therefore generic artinian graded algebra quotients of polynomial rings and give a method to reduce them to a minimal resolutions this yields results on the form of the resolution and the degrees of the forms in the matrices of the differentials but not precise betti numbers in addition we discuss how this construction is related to a conjecture of boij last we treat the noncompressed case

notes on stability of time delay systems bounding inequalities and augmented lyapunov krasovskii functionals the bounding inequalities and the lyapunov krasovskii functionals lkfs are important for the stability analysis of time delay systems much attention has been paid to develop tighter inequalities for improving stability criteria while the contribution of the lkfs has not been considered when discussing the relationship between the tightness of inequalities and the conservatism of criteria this note is concerned with this issue firstly it is proved that when a simple lkf is applied the stability criteria obtained by the wirtinger based inequality and the jensen inequality are equivalent although the wirtinger based inequality is tighter it means that the tighter inequality does not always lead to a less conservative criterion secondly it is found that a suitable augmented lkf with necessary integral vectors in its derivative is required to achieve the advantage of the wirtinger based inequality based on this observation two delay product type terms are introduced into the lkf to establish new stability criteria finally a numerical example is given to verify the equivalence statements and to show the benefit of the proposed criteria

streamline upwind petrov galerkin formulations for convection dominated flows with particular emphasis on the incompressible navier stokes equations abstract a new finite element formulation for convection dominated flows is developed the basis of the formulation is the streamline upwind concept which provides an accurate multidimensional generalization of optimal one dimensional upwind schemes when implemented as a consistent petrov galerkin weighted residual method it is shown that the new formulation is not subject to the artificial diffusion criticisms associated with many classical upwind methods the accuracy of the streamline upwind petrov galerkin formulation for the linear advection diffusion equation is demonstrated on several numerical examples the formulation is extended to the incompressible navier stokes equations an efficient implicit pressure explicit velocity transient algorithm is developed which accomodates several treatments of the incompressibility constraint and allows for multiple iterations within a time step the effectiveness of the algorithm is demonstrated on the problem of vortex shedding from a circular cylinder at a reynolds number of 100