caratheodory helly and radon numbers for sublattice and related convexities the caratheodory helly and radon numbers are three main invariants in convexity theory these invariants have been determined exactly or approximately for a number of different convexity structures we consider convexity structures defined by the sublattices and by the convex sublattices of finite dimensional euclidian integer and boolean spaces such sublattices arise in submodular optimization lattice programming and in monotone comparative statics of optimization and fixed point problems we also consider integral l natural convexities induced by dual network flow constraint systems we determine the exact caratheodory helly and radon numbers of most of these convexities and very close upper and lower bounds for the other caratheodory numbers our results imply for example that if a set can be obtained with unions and intersections from a given family of subsets of a finite set then it can be obtained with unions and intersections from a small subfamily we also show that finding the cara

an improvement on delay and its time derivative dependent robust stability of time delayed linear systems with uncertainty in this paper an improvement on the stability result in the above paper by jin hoon see ibid vol 46 2001 is given based on a modified lyapunov function it is shown that our result is much less conservative than that in the paper especially when the size of derivative of the time delay increases for comparison we give two examples

on the φ0 stability of comparison differential systems for many years now the variety of problems of the qualitative properties of differential equations in the context of lyaponov second method has been successfully investigated in a unified way using the comparison principle s in this method the qualitative properties of the system of differential equations are inferred from the corresponding properties of the solutions of the system of comparison equations in order to successfully employ this method it is generally required that the comparison systems possess some special properties the conditions under which the scalar comparison equations possess positivity and stability behaviour have been investigated using scalar lyapunov function method by brauer l siljak and grujic 9 and others ladde 3 gave suficient conditions for nonnegativity and stability of solutions of systems of comparison equations in his investigation of stability of comparison differential systems ladde 3 considered the asymptotic stability and exponential asymptotic stability of the comparison differential system using the method of vector lyapunov functions however imbedded in the method of vector lyapunov function is the requirement of quasimonotone nondecreasing property of the comparison system but quasimonotonicity of the comparison system is not a necessary condition for the system to be stable thus the limitation of the application potential of this general and effective method is due to the fact that

lipschitz stability for nonlinear volterra integrodifferential systems unlike uniform stability the linearized system inherits the property of uniform lipschitz stability from its original nonlinear system in this paper we investigate sufficient conditions for uniform lipschitz stability of nonlinear integro differential systems through their associated variational systems

cone superadditivity of discrete convex functions a function f is said to be cone superadditive if there exists a partition of r n into a family of polyhedral convex cones such that f z x f z y f z f z x y holds whenever x and y belong to the same cone in the family this concept is useful in nonlinear integer programming in that if the objective function is cone superadditive the global minimality can be characterized by local optimality criterion involving hilbert bases this paper shows cone superadditivity of l convex and m convex functions with respect to conic partitions that are independent of particular functions l convex and m convex functions in discrete variables integer vectors as well as in continuous variables real vectors are considered

submodular functions from discrete to continous domains submodular set functions have many applications in combinatorial optimization as they can be minimized and approximately maximized in polynomial time a key element in many of the algorithms and analyses is the possibility of extending the submodular set function to a convex function which opens up tools from convex optimization submodularity goes beyond set functions and has naturally been considered for problems with multiple labels or for functions defined on continuous domains where it corresponds essentially to cross second derivatives being nonpositive in this paper we show that most results relating submodularity and convexity for set functions can be extended to all submodular functions in particular a we naturally define a continuous extension in a set of probability measures b show that the extension is convex if and only if the original function is submodular c prove that the problem of minimizing a submodular function is equivalent to a typically non smooth convex optimization problem and d propose another convex optimization problem with better computational properties e g a smooth dual problem most of these extensions from the set function situation are obtained by drawing links with the theory of multi marginal optimal transport which provides also a new interpretation of existing results for set functions we then provide practical algorithms to minimize generic submodular functions on discrete domains with associated convergence rates

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

delay independent stability conditions for time varying nonlinear uncertain systems a new stability criterion for time varying systems consisting of linear and norm bounded nonlinear terms with uncertain time varying delays is formulated an explicit delay independent sufficient stability condition is formulated in the terms of the transition matrix of the given linear part without delay and the bounds for the uncertain terms the obtained condition turns out to be also necessary if the matrix of the linear part is time invariant and symmetric it is shown that these systems satisfy the well known aizerman s conjecture the obtained criterion is contrasted by some of stability estimates available in the literature for these kinds of systems in all cases the proposed criterion provides less conservative stability bounds

submodular function minimization submodular functions often arise in various fields of operations research including discrete optimization game theory queueing theory and information theory in this survey paper we give overview on the fundamental properties of submodular functions and recent algorithmic devolopments of their minimization

on 0 stability for nonlinear volterra integrodifferential systems 0 stability and lipschitz 0 stability notions of ordinary differential equations odes are introduced in this paper we extend these notions to systems of integro differential equations ides and give some criteria of these notions our technique depends on liapunov s direct method

stability criteria for volterra equations we consider a system of integro differential equations of the form 1 1 x a t x f c t s x s ds with a and c being ni x ni matrices various types of stability are defined and results are obtained showing when one type of stability is equivalent to another type we also construct a number of lyapunov functionals from which we obtain necessary and sufficient conditions for stability of 1 1 finally we prove several results concerning qualitative behavior of solutions of 1 1 introduction we consider the integro differential equation 1 1 xi a t x fc t s x s ds in which a is an n x n matrix continuous for 0 0 and any to 0 there exists a 8 0 such that i q4 t i to imply i x t to q i 0 such that i t i 0 there is a t 0 such that i pqt 0 and a to 0 such that for any 6 0 8 to with i x tl to qp i e definition 7 an n x n matrix is said to be stable if all of its characteristic roots have negative real parts 2 stability the following four papers will have significant bearing on our investigation i in 9 r k miller considered 1 1 with a constant and c c t s and showed that if z t is the n x n matrix satisfying 2 1 z t az t fc t s z s ds z 0 i

stability analysis for neural networks with time varying interval delay this letter is concerned with the stability analysis of neural networks nns with time varying interval delay the relationship between the time varying delay and its lower and upper bounds is taken into account when estimating the upper bound of the derivative of lyapunov functional as a result some improved delay interval dependent stability criteria for nns with time varying interval delay are proposed numerical examples are given to demonstrate the effectiveness and the merits of the proposed method

a system of linear inequalities with a submodular function on 0 1 vectors abstract we consider a system of linear inequalities with 0 1 coefficients and a right hand side given by a submodular function on 0 1 vectors and provide a simple necessary and sufficient condition for the system to be consistent furthermore we show the total dual integrality of the system with some additional conditions

stability analysis of lpv time delayed systems this work provides one of the first attempts to derive computationally tractable criteria for analysing the stability of linear parameter varying lpv time delayed systems we present both delay independent and delay dependent stability conditions which are derived using appropriately selected lyapunov krasovskii functionals according to the system parameter dependence these functionals can be selected to obtain increasingly non conservative results gridding techniques may be used to cast these tests as linear matrix inequalities lmis in cases when the system matrices depend affinely or quadratically on the parameter gridding may be avoided these lmis can be solved efficiently using available software a numerical example of a time delayed system motivated by a metal removal process is used to demonstrate the theoretical results

discrete convexity and unimodularity i abstract in this paper we develop a theory of convexity for the lattice of integer points z n which we call theory of discrete convexity namely we characterize classes of subsets of z n which possess the separation property or equivalently classes of integer polyhedra such that intersection of any two polyhedra of a class is an integer polyhedron need not be in the class specifically we show that these maximal classes are in one to one correspondence with pure systems unimodular systems constitute an important instance of pure systems given a unimodular system we construct a pair of dual discretely convex classes one of which is stable under summation and the other is stable under intersection

discrete convexity and polynomial solvability in minimum 0 extension problems a 0 0 extension of graph vargamma is a metric d d on a set v v containing the vertex set v vargamma v of vargamma such that d d extends the shortest path metric of vargamma and for all x in v x v there exists a vertex s s in vargamma with d x s 0 d x s 0 the minimum 0 0 extension problem 0 ext vargamma on vargamma is given a set v supseteq v vargamma v v and a nonnegative cost function c c defined on the set of all pairs of v v find a 0 0 extension d d of vargamma with sum xy c xy d x y xyc xy d x y minimum the 0 0 extension problem generalizes a number of basic combinatorial optimization problems such as minimum s t s t cut problem and multiway cut problem karzanov proved the polynomial solvability of 0 ext vargamma for a certain large class of modular graphs vargamma and raised the question what are the graphs vargamma for which 0 ext vargamma can be solved in polynomial time he also proved that 0 ext vargamma is np hard if vargamma is not modular or not orientable in a certain sense in this paper we prove the converse if vargamma is orientable and modular then 0 ext vargamma can be solved in polynomial time this completes the classification of graphs vargamma for which 0 ext vargamma is tractable to prove our main result we develop a theory of discrete convex functions on orientable modular graphs analogous to discrete convex analysis by murota and utilize a recent result of thapper and ivn on valued csp

scaling proximity and optimization of integrally convex functions in discrete convex analysis the scaling and proximity properties for the class of l natural convex functions were established more than a decade ago and have been used to design efficient minimization algorithms for the larger class of integrally convex functions of n variables we show here that the scaling property only holds when n le 2 while a proximity theorem can be established for any n but only with a superexponential bound this is however sufficient to extend the classical logarithmic complexity result for minimizing a discrete convex function of one variable to the case of integrally convex functions of any fixed number of variables

note on multimodularity and l convexity multimodular functions and l convex functions have been investigated almost independently but they are in fact equivalent objects that can be related through a unimodular coordinate transformation some facts known for l convex functions can be translated to new results for multimodular functions and vice versa in particular the local optimality condition for global optimality found in the literature of multimodular functions should be rectified and a discrete separation theorem holds for multimodular functions

decentralized stabilization of interconnected systems with time varying delays this technical note establishes decentralized delay dependent stability and stabilization methods for two classes of interconnected continuous time systems the two classes cover the linear case and the lipschitz type nonlinear case in both cases the subsystems are subjected to convex bounded parametric uncertainties and time varying delays within the local subsystems and across the interconnections an appropriate lyapunov functional is constructed to exhibit the delay dependent dynamics at the subsystem level in both cases decentralized delay dependent stability analysis is performed to characterize linear matrix inequalities lmis based conditions under which every local subsystem of the linear interconnected delay system is robustly asymptotically stable with an gamma level l 2 gain then we design a decentralized state feedback stabilization scheme such that the family of closed loop feedback subsystems enjoys the delay dependent asymptotic stability with a prescribed gamma level l 2 gain for each subsystem the decentralized feedback gains are determined by convex optimization over lmis all the developed results are tested on a representative example

an lmi approach to stability of systems with severe time delay this note describes the stability problems of uncertain systems with arbitrarily time varying and severe time delay using new lyapunov krasovskii functionals less conservative stability conditions are obtained for such systems the results are illustrated using the numerical examples based on simple linear matrix inequalities

stability analysis for continuous systems with two additive time varying delay components this paper presents a new result of stability analysis for continuous systems with two additive time varying delay components which represent a general class of delay systems with strong application background in network based control systems this criterion is expressed as a set of linear matrix inequalities which can be readily tested by using standard numerical software a numerical example is provided to show the effectiveness and advantage of the proposed stability condition

delay dependent robust stability criteria for uncertain systems with interval time varying delay this paper proposes an approach for the robust stability of uncertain systems with interval time varying delay the key features of the approach include the introduction of uncorrelated augmented matrix items into the lyapunov functional and the use of a tighter bounding technology unlike existing methodologies the proposed approach involves neither free weighting matrices nor any model transformation it can however lead to much less conservative stability criteria than the existing ones for the systems under consideration numerical examples show that the proposed criteria improve the existing results significantly with much less computational effort

on steepest descent algorithms for discrete convex functions this paper investigates the complexity of steepest descent algorithms for two classes of discrete convex functions m convex functions and l convex functions simple tie breaking rules yield complexity bounds that are polynomials in the dimension of the variables and the size of the effective domain combining the present results with a standard scaling approach leads to an efficient algorithm for l convex function minimization

further results on the robust stability of linear systems with a single time delay abstract for linear systems with a single time varying delay time we propose a method to characterize how large the deviation of the delay time can be compared to the nominal zero value such that the system still preserves its asymptotic stability both cases of linear time delay systems with and without uncertainties are considered the criteria developed are seen to give less conservative results in simulation examples

a unified approach to stability in integrodifferential equations via liapunov functions in this paper we investigate the problems of stability uniform stability uniform lipschitz stability asymptotic stability and uniform asymptotic stability in three classes of integrodifferential systems these are linear nonautonomous systems nonlinear systems and nonlinearly perturbed nonlinear systems a simple method for constructing liapunov functions will be used to unify the treatment of all of the above mentioned stability notions relative to the various classes of integrodifferential systems in our investigation of linear systems we benefited from the work in 4 8 123 for nonlinear systems and their perturbations we have used some of the results obtained recently in is 101 in particular we have used an extension of alekseev s l nonlinear variation of constants formula which was developed in lo the approach we use here was first formulated in 3 and utilized to study uniform lipschitz stability 2 of nonlinear differential systems the method has been extended in 12 to cover all other stability notions in nonlinear differential systems we now give a description of the contents of the paper section 1 includes all the basic definitions and preliminaries in section 2 we investigate the various stability notions of nonautonomous integrodifferential systems this extends the work in 6 81 which mainly dealt with autonomous systems we recall here from 4 that in linear systems the notions of uniform stability and uniform lipschitz stability are equivalent it was shown in 4 however that for nonlinear systems uniform

delay dependent robust stabilization of uncertain systems with multiple state delays this paper deals with the problem of robust stabilization for uncertain systems with multiple state delays the parameter uncertainties are time varying and unknown but are norm bounded and the delays are time varying a new method for achieving robust stabilization is presented for a class of uncertain time delay systems via linear memoryless state feedback control the results depend on the size of the delays and are given in terms of several linear matrix inequalities

technical communique on delay dependent stability and decay estimate for uncertain systems with time varying delay in this note for a class of linear uncertain systems with time varying delay a delay dependent robust stability criterion which can give information on the decay rate of the systems state is presented

technical communique improved delay dependent stability criteria for systems with a delay varying in a range this paper provides improved delay dependent stability criteria for systems with a delay varying in a range the criteria improve over some previous ones in that they have fewer matrix variables yet less conservatism which is established theoretically an example is given to show the advantages of the proposed results

structures of polyhedra determined by submodular functions on crossing families the present paper shows that for any submodular functionf on a crossing family with if the polyhedron is nonempty then there exist a unique distributive lattice with and a unique submodular function with such thatb f coincides with the base polyhedron associated with the submodular system here iff is integer valued thenf 1 is also integer valued based on this fact we also show the relationship between the independent flow problem considered by the author and the minimum cost flow problem considered by j edmonds and r giles

sandwich theorems for set functions abstract in the present paper the following problems are treated when do there exist a a precontent and b a precharge which lies between two given set functions the obtained results yield among others several well known theorems such as bondareva s core theorem kelley s intersection number theorem and sandwich theorems of kranz gol dberg and frank as immediate consequences

notes on l m convex functions and the separation theorems the concepts of l convex function and m convex function have recently been introduced by murota as generalizations of submodular function and base polyhedron respectively and discrete separation theorems are established for l convex concave functions and for m convex concave functions as generalizations of frank s discrete separation theorem for submodular supermodular set functions and edmonds matroid intersection theorem this paper shows the equivalence between murota s l convex functions and favati and tardella s submodular integrally convex functions and also gives alternative proofs of the separation theorems that provide a geometric insight by relating them to the ordinary separation theorem in convex analysis

new delay dependent stability criteria for neural networks with time varying delay in this letter a new method is proposed for stability analysis of neural networks nns with a time varying delay some less conservative delay dependent stability criteria are established by considering the additional useful terms which were ignored in previous methods when estimating the upper bound of the derivative of lyapunov functionals and introducing the new free weighting matrices numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method

theory of submodular programs a fenchel type min max theorem and subgradients of submodular functions we consider submodular programs which are problems of minimizing submodular functions on distributive lattices with or without constraints we define a convex or concave conjugate function of a submodular or supermodular function and show a fenchel type min max theorem for submodular and supermodular functions we also define a subgradient of a submodular function and derive a necessary and sufficient condition for a feasible solution of a submodular program to be optimal which is a counterpart of the karush kuhn tucker condition for convex programs

lipschitz stability of nonlinear systems of differential equations in s the authors introduced the notion of lipschitz stability in differential equations this notion lies somewhere between uniform stability on one side and the notions of asymptotic stability in variation 3 and uniform stability in variation 4 on the other side however lipschitz stability is new only as a nonliner phenomenon since it coincides with uniform stability in linear systems s an important feature of lipschitz stability is that unlike uniform stability the linearized system inherits the property of lipschitz stability from the original nonlinear system 5 in this paper we pursue the study of lipschitz stability that started in s using essentially the techniques of liapunov functions then we give sufficient conditions for the lipschitz stability of certain nonlinearly pertur bed nonlinear systems such systems include among other equations certain integrodifferential and functional differential equations then we give an example which can be investigated successfully using our results but cannot be handled by any previous techniques or results 9

discretized lyapunov functional for uncertain systems with multiple time delay the stability of uncertain systems with multiple time delay is studied using a quadratic lyapunov functional by choosing piecewise linear parameters for the kernel of a quadratic expression the guaranteed stability condition is formulated in the form of linear matrix inequality the extent of conservatism depends on the grid size however numerical results show that even a very coarse discretization can produce quite satisfactory results the possibility of non uniform grid size and more general lyapunov functional is of interest even for a single delay system numerical examples are presented

stability analysis for continuous system with additive time varying delays a less conservative result this paper presents a less conservative result for stability analysis of continuous time systems with additive delays by constructing a new lyapunov krasovskii functional and utilizing free matrix variables in approximating certain integral quadratic terms in obtaining the stability condition in terms of linear matrix inequalities numerical example is provided to show the effectiveness of the proposed method compared to some recent results

proximity theorems of discrete convex functions a proximity theorem is a statement that given an optimization problem and its relaxation an optimal solution to the original problem exists in a certain neighborhood of a solution to the relaxation proximity theorems have been used successfully for example in designing efficient algorithms for discrete resource allocation problems after reviewing the recent results for l convex and m convex functions this paper establishes proximity theorems for larger classes of discrete convex functions l2 convex functions and m2 convex functions that are relevant to the polymatroid intersection problem and the submodular flow problem

on equivalence and efficiency of certain stability criteria for time delay systems in recent years there have been a number of new delay dependent stability criteria based on linear matrix inequalities published in the literature this note aims to theoretically establish the equivalence of seven of these stability criteria moreover the efficiency of these stability criteria is assessed based on the number of unknowns in the linear matrix inequalities

fixed dimensional stochastic dynamic programs an approximation scheme and an inventory application we study fixed dimensional stochastic dynamic programs in a discrete setting over a finite horizon under the primary assumption that the cost to go functions are discrete l convex we propose a pseudo polynomial time approximation scheme that solves this problem to within an arbitrary prespecified additive error of e 0 the proposed approximation algorithm is a generalization of the explicit enumeration algorithm and offers us full control in the trade off between accuracy and running time the main technique we develop for obtaining our scheme is approximation of a fixed dimensional l convex function on a bounded rectangular set using only a selected number of points in its domain furthermore we prove that the approximation function preserves l convexity finally to apply the approximate functions in a dynamic program we bound the error propagation of the approximation our approximation scheme is illustrated on a well known problem in inventory theory the single product problem with lost sales and lead times we demonstrate the practical value of our scheme by implementing our approximation scheme and the explicit enumeration algorithm on instances of this inventory problem

delay and its time derivative dependent robust stability of time delayed linear systems with uncertainty in this paper we consider the robust stability of time delayed linear systems with uncertainties the uncertainties are time varying and unknown but are norm bounded and the time delay is time varying a sufficient condition is presented in the linear matrix inequality form which is dependent on the size of time delay and on the size of time derivative finally we give two examples to compare with the previous results

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

technical communique stability and robust stability for systems with a time varying delay to concern the stability and robust stability criteria for systems with time varying delays this note uses not only the time varying delayed state x t h t but also the delay upper bounded state x email protected to exploit all possible information for the relationship among a current state x t an exactly delayed state x t h t a marginally delayed state x email protected and the derivative of the state email protected t when constructing lyapunov krasovskii functionals and some appropriate integral inequalities originally suggested by park 1999 a delay dependent stability criterion for systems with uncertain time invariant delays ieee transactions on automatic control 44 4 876 877 two fundamental criteria are provided for the cases where no bound of delay derivative is assumed and where an upper bound of delay derivative is assumed examples show the resulting criteria outperform all existing ones in the literature

asymptotic and exponential stability of uncertain system with interval delay abstract this paper considers the problem of asymptotic and exponential stability analysis of the continuous system with interval time varying delay and uncertainties by constructing a new lyapunov krasovskii functional several delay range dependent conditions are derived in terms of the linear matrix inequalities lmis two novel integral equalities are employed to overcome the disadvantages of the methods in existing references the merits of the proposed criteria lie in the exponential stability being a free value and the less conservativeness finally some numerical examples are included to illustrate the effectiveness and the improvement of the proposed method

convexity and steinitz s exchange property abstract convex analysis is developed for functions defined on integer lattice points we investigate the class of functions which enjoy a variant of steinitz s exchange property this includes linear functions on matroids valuations on matroids in the sense of dress and wenzel and separable concave functions on the integral base polytope of submodular systems it is shown that a function has the steinitz exchange property if and only if it can be extended to a concave function such that the maximizers of any linear function form an integral base polytope a frenchel type min max theorem and discrete separation theorems are established which imply as immediate consequences frank s discrete separation theorem for submodular functions edmonds intersection theorem fujishige s fenchel type min max theorem for submodular functions and also frank s weight splitting theorem for weighted matroid intersection

on the subdifferential of a submodular function the author recently introduced a concept of a subdifferential of a submodular function defined on a distributive lattice each subdifferential is an unbounded polyhedron in the present paper we determine the set of all the extreme points and rays of each subdifferential and show the relationship between subdifferentials of a submodular function and subdifferentials in an ordinary sense of convex analysis of lovasz s extension of the submodular function furthermore for a modular function on a distributive lattice we give an algorithm for determining which subdifferential contains a given vector and finding a nonnegative linear combination of extreme vectors of the subdifferential which expresses the given vector minus the unique extreme point of the subdifferential

a framework of discrete dc programming by discrete convex analysis a theoretical framework of difference of discrete convex functions discrete dc functions and optimization problems for discrete dc functions is established standard results in continuous dc theory are exported to the discrete dc theory with the use of discrete convex analysis a discrete dc algorithm which is a discrete analogue of the continuous dc algorithm concave convex procedure in machine learning is proposed the algorithm contains the submodular supermodular procedure as a special case exploiting the polyhedral structure of discrete convex functions the algorithms tailored to specific types of discrete dc functions are proposed

a combinatorial strongly polynomial algorithm for minimizing submodular functions this paper presents a combinatorial polynomial time algorithm for minimizing submodular functions answering an open question posed in 1981 by grotschel lovasz and schrijver the algorithm employs a scaling scheme that uses a flow in the complete directed graph on the underlying set with each arc capacity equal to the scaled parameter the resulting algorithm runs in time bounded by a polynomial in the size of the underlying set and the length of the largest absolute function value the paper also presents a strongly polynomial version in which the number of steps is bounded by a polynomial in the size of the underlying set independent of the function values

new filter design for linear time delay systems abstract this paper develops new robust delay dependent filter design for a class of linear systems with time varying delays and convex bounded parameter uncertainties the design procedure hinges upon the constructive use of an appropriate lyapunov functional plus a free weighting matrices in order to exhibit the delay dependent dynamics the developed approach utilizes smaller number of lmi decision variables thereby leading to less conservative solutions to the delay dependent stability and filtering problems subsequently linear matrix inequalities lmis based conditions are characterized such that the linear delay system is robustly asymptotically stable with an level l 2 gain all the developed results are tested on representative examples

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

brief paper delay dependent robust stability of uncertain fuzzy large scale systems with time varying delays this paper addresses the stability problem of fuzzy large scale systems flsss with uncertainties and arbitrary time varying delays the stability conditions which are less conservative and more applicable than the existing results are derived by a novel lyapunov krasovskii functional method and expressed in terms of linear matrix inequalities lmis two examples are given to demonstrate the correctness and advantage of our theoretical results

m convex function on generalized polymatroid the concept of m convex function introduced by murota 1996 is a quantitative generalization of the set of integral points in an integral base polyhedron as well as an extension of valuated matroid of dress and wenzel 1990 in this paper we extend this concept to functions on generalized polymatroids with a view to providing a unified framework for efficiently solvable nonlinear discrete optimization problems

generalized polymatroids and submodular flows polyhedra related to matroids and sub or supermodular functions play a central role in combinatorial optimization the purpose of this paper is to present a unified treatment of the subject the structure of generalized polymatroids and submodular flow systems is discussed in detail along with their close interrelation in addition to providing several applications we summarize many known results within this general framework

fenchel type duality for matroid valuations the weighted matroid intersection problem has recently been extended to the valuated matroid intersection problem given a pair of valuated matroidsmi v i i i 1 2 defined on a common ground setv find a common baseb 1 2 that maximizes 1 b 2 b this paper develops a fenchel type duality theory related to this problem with a view to establishing a convexity framework for nonlinear integer programming a fenchel type min max theorem and a discrete separation theorem are given furthermore the subdifferentials of matroid valuations are investigated 1998 the mathematical programming society inc published by elsevier science b v

conjugacy relationship between m convex and l convex functions in continuous variables by extracting combinatorial structures in well solved nonlinear combinatorial optimization problems murota 1996 1998 introduced the concepts of m convexity and l convexity to functions defined over the integer lattice recently murota shioura 2000 2001 extended these concepts to polyhedral convex functions and quadratic functions in continuous variables in this paper we consider a further extension to more general convex functions defined over the real space and provide a proof for the conjugacy relationship between general m convex and l convex functions

further improvement of free weighting matrices technique for systems with time varying delay a novel method is proposed in this note for stability analysis of systems with a time varying delay appropriate lyapunov functional and augmented lyapunov functional are introduced to establish some improved delay dependent stability criteria less conservative results are obtained by considering the additional useful terms which are ignored in previous methods when estimating the upper bound of the derivative of lyapunov functionals and introducing the new free weighting matrices the resulting criteria are extended to the stability analysis for uncertain systems with time varying structured uncertainties and polytopic type uncertainties numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method

improved delay dependent robust stability criteria for uncertain time delay systems abstract this paper deals with the robust stability analysis for uncertain systems with time varying delay new delay dependent robust stability criteria of uncertain time delay systems are proposed by exploiting appropriate lyapunov functional candidate these developed results have advantages over some previous ones in that they have fewer matrix variables yet less conservatism due to the introduction of a method to estimate the upper bound of the derivative of lyapunov functional candidate without ignoring the additional useful terms numerical examples are given to demonstrate the effectiveness and the advantage of the proposed method

directed submodularity ditroids and directed submodular flows set relations and operations such as inclusion union and intersection are generalized to directed subsets whose elements are distinguished between forward and backward elements the concepts of submodular functions matroids and polymatroidal network flows are extended to the concepts of directed submodular functions ditroids and directed submodular flows on directed subsets two unrelated matroids submodular functions can be embedded in one ditroid directed submodular function total dual integrality is preserved in these generalizations and proved for very general set function class directed odd submodular functions

odd submodular functions dilworth functions and discrete convex functions three set function classes more general than submodular ones are discussed an odd submodular function defines a box totally dual integral system an integral odd submodular function and its dilworth truncation i e a dilworth function give rise to the same polyhedron with integral vertices the minimum of two submodular functions is an odd submodular function the convolution of two submodular functions is a dilworth function a dilworth function is a discrete convex function a discrete convex function can be characterized by its convex hull subgradients epigraph and general subadditivity discrete convexity is preserved under many natural operations