fixed time consensus of complex dynamical networks with nonlinear coupling and fuzzy state dependent uncertainties abstract in this paper the fixed time consensus problem for complex dynamical networks with nonlinear coupling and fuzzy state dependent uncertainties is discussed different from most existing publications the controller is designed as a fuzzy logic system which is applicable for complex dynamical networks with system uncertainties and unknown topology to ensure the fixed time consensus furthermore compared with the initial condition based finite time consensus the settling time is bounded by a constant within fixed time regardless of the initial condition based on the lyapunov stability theory and inequality techniques some sufficient criteria for fixed time consensus are obtained finally two numerical examples are granted to display the performance of the obtained results

the lagrangian relaxation method for solving integer programming problems this article originally appeared in management science january 1981 volume 27 number 1 pp 1 18 published by the institute of management sciences one of the most computationally useful ideas of the 1970s is the observation that many hard integer programming problems can be viewed as easy problems complicated by a relatively small set of side constraints dualizing the side constraints produces a lagrangian problem that is easy to solve and whose optimal value is a lower bound for minimization problems on the optimal value of the original problem the lagrangian problem can thus be used in place of a linear programming relaxation to provide bounds in a branch and bound algorithm this approach has led to dramatically improved algorithms for a number of important problems in the areas of routing location scheduling assignment and set covering this paper is a review of lagrangian relaxation based on what has been learned in the last decade

on equivalence of two stability criteria for continuous time switched systems with dwell time constraint in this note a study on the equivalence of two stability criteria for continuous time switched linear systems with dwell time constraint is presented it is demonstrated that for any dwell time satisfying the conditions in stability criterion proposed in geromel and colaneri 2006 the conditions in stability criterion of allerhand and shaked 2011 also hold as long as the number of decision variables and related lmis is sufficiently large which implies the two stability criteria are intrinsically equivalent the equivalence is obtained by showing that two criteria can be derived from each other with a sufficiently large number of decision variables and lmis a numerical example is proposed to illustrate the theoretical results and an extension to uncertain case is briefly presented

nonlinear feedback design for fixed time stabilization of linear control systems two types of nonlinear control algorithms are presented for uncertain linear plants controllers of the first type are stabilizing polynomial feedbacks that allow to adjust a guaranteed convergence time of system trajectories into a prespecified neighborhood of the origin independently on initial conditions the control design procedure uses block control principles and finite time attractivity properties of polynomial feedbacks controllers of the second type are modifications of the second order sliding mode control algorithms they provide global finite time stability of the closed loop system and allow to adjust a guaranteed settling time independently on initial conditions control algorithms are presented for both single input and multi input systems theoretical results are supported by numerical simulations

synchronization of ts fuzzy complex dynamical networks with time varying impulsive delays and stochastic effects in this paper global exponential synchronization of takagi sugeno ts fuzzy complex dynamical networks with multiple time varying delays and stochastic perturbations is studied via delayed impulsive distributed control both impulsive and continuous parts of the fuzzy model have different multiple time varying delays which make the considered model general and practical a novel lemma on exponential stability of impulsive delayed differential equations was established in which the impulsive functions exhibit multiple time varying delays by utilizing the proposed lemma lyapunov functions the stochastic analysis techniques and the kronecker product general criteria ensuring global exponential synchronization in mean square of the addressed ts fuzzy complex networks are obtained moreover the theory of function minimum value is utilized to reduce the conservativeness of the obtained synchronization criteria which also makes them simple and easy to be verified in practical applications results of this paper improve and extend some existing ones numerical simulations including small world network coupled with time delayed lorenz system are given to show the effectiveness of the theoretical results

robust stability and stabilization of linear switched systems with dwell time sufficient conditions are given for the stability of linear switched systems with dwell time and with polytopic type parameter uncertainty a lyapunov function in quadratic form which is non increasing at the switching instants is assigned to each subsystem during the dwell time this function varies piecewise linearly in time after switching occurs it becomes time invariant afterwards this function leads to asymptotic stability conditions for the nominal set of subsystems that can be readily extended to the case where these subsystems suffer from polytopic type parameter uncertainties the method proposed is then applied to stabilization via state feedback both for the nominal and the uncertain cases

the stochastic location model with risk pooling abstract in this paper we present a stochastic version of the location model with risk pooling lmrp that optimizes location inventory and allocation decisions under random parameters described by discrete scenarios the goal of our model called the stochastic lmrp or slmrp is to find solutions that minimize the expected total cost including location transportation and inventory costs of the system across all scenarios the location model explicitly handles the economies of scale and risk pooling effects that result from consolidating inventory sites the slmrp framework can also be used to solve multi commodity and multi period problems we present a lagrangian relaxation based exact algorithm for the slmrp the lagrangian subproblem is a non linear integer program but it can be solved by a low order polynomial algorithm we discuss simple variable fixing routines that can drastically reduce the size of the problem we present quantitative and qualitative computational results on problems with up to 150 nodes and 9 scenarios describing both algorithm performance and solution behavior as key parameters change

pressure stability in fractional step finite element methods for incompressible flows abstract the objective of this paper is to analyze the pressure stability of fractional step finite element methods for incompressible flows that use a pressure poisson equation for the classical first order projection method it is shown that there is a pressure control which depends on the time step size and therefore there is a lower bound for this time step for stability reasons the situation is much worse for a second order scheme in which part of the pressure gradient is kept in the momentum equation the pressure stability in this case is extremely weak to overcome these shortcomings a stabilized fractional step finite element method is also considered and its stability is analyzed some simple numerical examples are presented to support the theoretical results

stability and synchronization of discrete time neural networks with switching parameters and time varying delays this paper is concerned with the problems of exponential stability analysis and synchronization of discrete time switched delayed neural networks using the average dwell time approach together with the piecewise lyapunov function technique sufficient conditions are proposed to guarantee the exponential stability for the switched neural networks with time delays benefitting from the delay partitioning method and the free weighting matrix technique the conservatism of the obtained results is reduced in addition the decay estimates are explicitly given and the synchronization problem is solved the results reported in this paper not only depend upon the delay but also depend upon the partitioning which aims at reducing the conservatism numerical examples are presented to demonstrate the usefulness of the derived theoretical results

a tree search algorithm for the p median problem abstract in this paper we present two lower bounds for the p median problem the problem of locating p facilities medians on a network these bounds are based on two separate lagrangean relaxations of a zero one formulation of the problem with subgradient optimisation being used to maximise these bounds penalty tests based on these lower bounds and a heuristically determined upper bound to the problem are developed and shown to result in a large reduction in problem size the incorporation of the lower bounds and the penalty tests into a tree search procedure is described and computational results are given for problems with an arbitrary number of medians and having up to 200 vertices a comparison is also made between these algorithms and the dual based algorithm of erlenkotter

the meshless finite element method a meshless method is presented which has the advantages of the good meshless methods concerning the ease of introduction of node connectivity in a bounded time of order n and the condition that the shape functions depend only on the node positions furthermore the method proposed also shares several of the advantages of the finite element method such as a the simplicity of the shape functions in a large part of the domain b c0 continuity between elements which allows the treatment of material discontinuities and c ease of introduction of the boundary conditions copyright 2003 john wiley sons ltd

impulsive synchronization of reaction diffusion neural networks with mixed delays and its application to image encryption this paper presents a new impulsive synchronization criterion of two identical reaction diffusion neural networks with discrete and unbounded distributed delays the new criterion is established by applying an impulse time dependent lyapunov functional combined with the use of a new type of integral inequality for treating the reaction diffusion terms the impulse time dependent feature of the proposed lyapunov functional can capture more hybrid dynamical behaviors of the impulsive reaction diffusion neural networks than the conventional impulse time independent lyapunov functions functionals while the new integral inequality which is derived from wirtinger s inequality overcomes the conservatism introduced by the integral inequality used in the previous results numerical examples demonstrate the effectiveness of the proposed method later the developed impulsive synchronization method is applied to build a spatiotemporal chaotic cryptosystem that can transmit an encrypted image the experimental results verify that the proposed image encrypting cryptosystem has the advantages of large key space and high security against some traditional attacks

stabilization of switched positive system with impulse and marginally stable subsystems a mode dependent dwell time method abstract in this article the problem of stabilization for the switched positive linear system spls with impulse and marginally stable subsystems is studied in which both the continuous time case and the discrete time case are taken into account by the usage of a piecewise weak linear copositive lyapunov function lclf and the mode dependent dwell time mdt time dependent switching control laws are designed to guarantee the asymptotic stability of the system furthermore based on the comparison principal for positive systems the main results are generalized to the time variant spls two examples are worked out to indicate that our results have advantages over some known results in the literature

on the exact solution of large scale simple plant location problems abstract the simple plant location problem deals with the selection of facility sites from a set of possible locations with the intention of serving a given set of customers from the chosen locations the objective is to minimize the sum of the fixed charges for establishing the facilities and the transportation costs corresponding to the supply of the demands we show how to modify a primal dual version of erlenkotter s exact algorithm to get an improved procedure computational experience with large scale problems indicates that compared with erlenkotter s code an implementation of the modified algorithm is faster by more than one order of magnitude for real life problems with 1500 potential facility sites the increase of computational speed may even exceed the factor of 100

derivation of stabilized equations for numerical solution of advective diffusive transport and fluid flow problems abstract the concept of the so called artificial or balancing diffusion used to stabilize the numerical solution of advective diffusive transport and fluid flow problems is revised in this paper it is shown that the standard forms of the balancing diffusion terms usually chosen in a heuristic manner can be naturally found by introducing higher order approximations in the derivation of the governing differential equations via standard conservation or equilibrium principles this allows us to reinterpret many stabilization algorithms and concepts used in every day practice by numerical analysts and also provides an expression for computing the stabilization parameter

quasi synchronization of heterogeneous dynamic networks via distributed impulsive control this paper studies leader follower synchronization in heterogeneous dynamic networks via distributed impulsive control the goal is to drive the followers to approximately synchronize with the leader within a nonzero error bound referred to as quasi synchronization some fundamental and yet challenging problems are addressed 1 how to obtain a tight quasi synchronization error bound 2 how many and which nodes should be controlled 3 how to design the coupling strength to select the pinned nodes and to determine the impulse intervals to optimize the error bound or to achieve quasi synchronization within a prescribed error bound first some general quasi synchronization conditions are derived with explicit expressions of the error bound second the pinning strategy and the coupling strength in achieving quasi synchronization are explored and expressed in term of impulse intervals it is interesting to find that a large coupling strength will destroy synchrony in contrast to continuous pinning control furthermore the common requirement that the leader has a directed path to every node is needed only in the case that the impulse intervals can be arbitrarily small a new concept referred to as impulse pinning controllability is introduced to the case that impulses cannot take place too frequently third an optimization of the error bound is discussed and formulated under a prescribed error bound the design problem of the coupling strength pinned nodes and impulse intervals is solved finally three examples are given to verify the theoretical results

an overview of representative problems in location research we present a survey of over 50 representative problems in location research our goal is not to review all variants of different location models or to describe solution results but rather to provide a broad overview of major location problems that have been studied indicating briefly how they are formulated and how they relate to one another we review standard problems such as median center and warehouse location problems as well as less traditional location problems which have emerged in recent years our primary focus is on problems for which operations research type models have been developed most of the problems we review have been formulated as optimization problems

a stabilized finite element method for incompressible viscous flows using a finite increment calculus formulation abstract a stabilized finite element formulation for incompressible viscous flows is derived the starting point are the modified navier stokes equations incorporating naturally the necessary stabilization terms via a finite increment calculus fic procedure application of the standard finite element galerkin method to the modified differential equations leads to a stabilized discrete system of equations overcoming the numerical instabilities emanating from the advective terms and those due to the lack of compatibility between approximate velocity and pressure fields the fic method also provides a natural explanation for the stabilization terms appearing in all equations for both the navier stokes and the simpler stokes equations transient solution schemes with enhanced stabilization properties are also proposed finally a procedure for computing the stabilization parameters is presented

finite time synchronization of coupled networks with markovian topology and impulsive effects this note considers globally finite time synchronization of coupled networks with markovian topology and distributed impulsive effects the impulses can be synchronizing or desynchronizing with certain average impulsive interval by using m matrix technique and designing new lyapunov functions and controllers sufficient conditions are derived to ensure the synchronization within a setting time and the conditions do not contain any uncertain parameter it is demonstrated theoretically and numerically that the number of consecutive impulses with minimum impulsive interval of the desynchronizing impulsive sequence should not be too large it is interesting to discover that the setting time is related to initial values of both the network and the markov chain numerical simulations are provided to illustrate the effectiveness of the theoretical analysis

partitioned procedures for the transient solution of coupled aroelastic problems part i model problem theory and two dimensional application abstract in order to predict the dynamic response of a flexible structure in a fluid flow the equations of motion of the structure and the fluid must be solved simultaneously in this paper we present several partitioned procedures for time integrating this focus coupled problem and discuss their merits in terms of accuracy stability heterogeneous computing i o transfers subcycling and parallel processing all theoretical results are derived for a one dimensional piston model problem with a compressible flow because the complete three dimensional aeroelastic problem is difficult to analyze mathematically however the insight gained from the analysis of the coupled piston problem and the conclusions drawn from its numerical investigation are confirmed with the numerical simulation of the two dimensional transient aeroelastic response of a flexible panel in a transonic non linear euler flow regime

fluid structure interaction using the particle finite element method abstract in the present work a new approach to solve fluid structure interaction problems is described both the equations of motion for fluids and for solids have been approximated using a material lagrangian formulation to approximate the partial differential equations representing the fluid motion the shape functions introduced by the meshless finite element method mfem have been used thus the continuum is discretized into particles that move under body forces gravity and surface forces due to the interaction with neighboring particles all the physical properties such as density viscosity conductivity etc as well as the variables that define the temporal state such as velocity and position and also other variables like temperature are assigned to the particles and are transported with the particle motion the so called particle finite element method pfem provides a very advantageous and efficient way for solving contact and free surface problems highly simplifying the treatment of fluid structure interactions

computational study of large scale p median problems given a directed graph g v a the p median problem consists of determining p nodes the median nodes minimizing the total distance from the other nodes of the graph we present a branch and cut and price algorithm yielding provably good solutions for instances with v 3795 key ingredients of the algorithm are a delayed column and row generation technique exploiting the special structure of the formulation to solve the lp relaxation and cutting planes to strengthen the formulation and limit the size of the enumeration tree

the synchronization of instantaneously coupled harmonic oscillators using sampled data with measurement noise in this brief we propose an effective algorithm for synchronization of instantaneously coupled harmonic oscillators by using sampled data which may contain measurement noise we discuss the convergence of this algorithm for both fixed and switching directed network topologies in the presence or absence of leaders we also establish sufficient conditions under which the coupled harmonic oscillators could attain synchronized oscillatory motions in the presence of noise and moreover it is shown that synchronization can be attained even when the velocity information is exchanged only at discrete time instants finally we give some numerical examples to illustrate the effectiveness of the theoretical results

synchronization of coupled reaction diffusion neural networks with time varying delays via pinning impulsive controller in this paper global exponential synchronization stability in an array of linearly diffusively coupled reaction diffusion neural networks with time varying delays is investigated by adding impulsive controller to a small fraction of nodes pinning impulsive controller in order to overcome the difficulty resulting from the fact that the impulsive controller affects only the dynamical behaviors of the controlled nodes a new analysis method is developed by using the developed method two known lemmas on stability of delayed functional differential equation with and without impulses and lyapunov stability theory several novel and easily verified synchronization criteria guaranteeing the whole network will be pinned to a homogenous solution are derived moreover the effects of the pinning impulsive controller and the dynamics of the uncontrolled nodes and the diffusive couplings on the synchronization process are explicitly expressed in the obtained criteria our results also show that we can always de

brief paper a unified synchronization criterion for impulsive dynamical networks this paper focuses on the problem of globally exponential synchronization of impulsive dynamical networks two types of impulses are considered synchronizing impulses and desynchronizing impulses in previous literature all of the results are devoted to investigating these two kinds of impulses separately thus a natural question arises is there any unified synchronization criterion which is simultaneously effective for synchronizing impulses and desynchronizing impulses in this paper a unified synchronization criterion is derived for directed impulsive dynamical networks by proposing a concept named average impulsive interval the derived criterion is theoretically and numerically proved to be less conservative than existing results numerical examples including scale free and small world structures are given to show that our results are applicable to large scale networks

fixed time synchronization of complex networks with impulsive effects via nonchattering control dealing with impulsive effects is one of the most challenging problems in the field of fixed time control in this paper we solve this challenging problem by considering fixed time synchronization of complex networks cns with impulsive effects by designing a new lyapunov function and constructing comparison systems a sufficient condition formulated by matrix inequalities is given to ensure that all the dynamical subsystems in the cns are synchronized with an isolated system in a settling time which is independent of the initial values of both the cns and the isolated system then by partitioning impulse interval and using the convex combination technique sufficient conditions in terms of linear matrix inequalities are provided our synchronization criteria unify synchronizing and desynchronizing impulses compared with the existing controllers for fixed time and finite time techniques the designed controller is continuous and does not include any sign function and hence the chattering phenomenon in most of the existing results is overcome an optimal algorithm is proposed for the estimation of the settling time numerical examples are given to show the effectiveness of our new results

moment exponential stability of stochastic delay systems with delayed impulse effects at random times and applications in the stabilisation of stochastic neural networks in this paper we investigate the exponential stability for a class of impulsive stochastic functional differential equations with delayed impulse effects the impulse instants considered in this p

finite time consensus in networks of integrator like dynamic agents with directional link failure this technical note proposes a general class of nonlinear protocols in the form of continuous state feedbacks for finite time consensus in networks of integrator like dynamic agents with directional link failure these protocols with adjustable terms are applicable in a wide range of situations such as with input saturation restrictions and with convergence rate constraints based on the assumption of a common positive dwell time for all active information links it is shown that if the union of the interaction topology over some fixed length of time always contains a spanning tree then the system will solve an asymptotical consensus problem in addition if the length sum of time intervals over which the interaction topology contains a spanning tree is larger than a threshold determined by the state differences between agents then the system will solve a finite time consensus problem the validity of the protocols is proven in the case with external reference inputs finally simulations are presented to demonstrate the effectiveness of the theoretical results

multi agent consensus with relative state dependent measurement noises in this note the distributed consensus corrupted by relative state dependent measurement noises is considered each agent can mea sure or receive its neighbors state information with random noises whose intensity is a vector function of agents relative states by investigating the structure of this interaction and the tools of stochastic differential equa tions we develop several small consensus gain theorems to give sufficient conditions in terms of the control gain the number of agents and the noise intensity function to ensure mean square m s and almost sure a s consensus and quantify the convergence rate and the steady state error especially for the case with homogeneous communication and control channels a necessary and sufficient condition to ensure m s consensus on the control gain is given and it is shown that the control gain is independent of the specific network topology but only depends on the number of nodes and the noise coefficient constant for symmetric measurement models the almost sure convergence rate is estimated by the iterated logarithm law of brownian motions index terms distributed consensus distributed coordination fading channel measurement noises multi agent system

the particle finite element method a powerful tool to solve incompressible flows with free surfaces and breaking waves summary particle methods are those in which the problem is represented by a discrete number of particles each particle moves accordingly with its own mass and the external internal forces applied to it particle methods may be used for both discrete and continuous problems in this paper a particle method is used to solve the continuous fluid mechanics equations to evaluate the external applied forces on each particle the incompressible navier stokes equations using a lagrangian formulation are solved at each time step the interpolation functions are those used in the meshless finite element method and the time integration is introduced by an implicit fractional step method in this manner classical stabilization terms used in the momentum equations are unnecessary due to lack of convective terms in the lagrangian formulation once the forces are evaluated the particles move independently of the mesh all the information is transmitted by the particles fluid structure interaction problems including free fluid surfaces breaking waves and fluid particle separation may be easily solved with this methodology copyright 2004 john wiley sons ltd

fixed time synchronization of markovian jump fuzzy cellular neural networks with stochastic disturbance and time varying delays abstract this paper mainly studies the fixed time synchronization of markovian jump fuzzy cellular neural networks with stochastic perturbations and time varying delays in the leakage term by designing delay dependent controllers with or without fuzzy terms constructing a suitable stochastic lyapunov functional and using matrix analysis techniques this paper derives some novel and useful sufficient conditions to guarantee the fixed time synchronization of the addressed drive response systems and the conditions are delay dependent which has less conservative results the finite time is also independent of the initial states finally numerical examples are given to illustrate the effectiveness of the proposed main results

probabilistic analysis of a relaxation for the k median problem this paper provides a probabilistic analysis of the so called strong linear programming relaxation of the k median problem when the number of points say n goes to infinity the analysis is performed under four classical models in location theory the euclidean network tree and uniform cost models for example we show that for the euclidean model and k k o n log n the value of the relaxation is almost surely within 0 3 percent of the optimum k median value for the uniform cost model and the same conditions on k we show that the value of the relaxation is almost surely 50 percent of the optimum k median value we also show that under various assumptions branch and bound algorithms that use the strong linear programming relaxation as a bound must almost surely expand a nonpolynomial number of nodes to solve the k median problem to optimality finally we report extensive computational experiments as predicted by the probabilistic analysis the relaxation was not as tight for the problem

finite time cluster synchronization of t s fuzzy complex networks with discontinuous subsystems and random coupling delays this paper is concerned with the cluster synchronization in finite time for a class of complex networks with nonlinear coupling strengths and probabilistic coupling delays the complex networks consist of several clusters of nonidentical discontinuous systems suffered from uncertain bounded external disturbance based on the takagi sugeno t s fuzzy interpolation approach we first obtain a set of t s fuzzy complex networks with constant coupling strengths by developing some novel lyapunov functionals and using the concept of filippov solution some new analytical techniques are established to derive sufficient conditions ensuring the cluster synchronization in a setting time in particular this paper extends the pinning control strategies for networks with continuous time dynamics to discontinuous networks numerical simulations demonstrate that the theoretical results are effective and the t s fuzzy approach is important for relaxed results

synchronization stability of riemann liouville fractional delay coupled complex neural networks abstract this paper focuses on discussing the synchronization stability problem of the riemann liouville fractional coupled complex interconnected delayed neural networks several globally asymptotic stability criteria for considered network systems are established in terms of lyapunov functional approach and linear matrix inequality technique the relationships between the stability of fractional order isolated neural networks and the synchronization of fractional order coupled complex neural networks are discussed in detail the main advantage is to avoid calculating the fractional derivative of lyapunov functional to discuss the synchronization stability conditions a numerical example is also performed to demonstrate the validity and feasibility of the proposed results

possibilities of finite calculus in computational mechanics abstract the expression finite calculus refers to the derivation of the governing differential equations in mechanics by invoking balance of fluxes forces etc in a domain of finite size the governing equations resulting from this approach are different from those of infinitessimal calculus theory and they incorporate new terms depending on the dimensions of the balance domain the new modified equations allow to derive naturally stabilized numerical schemes using finite element finite difference finite volume or meshless methods the paper briefly discusses the possibilities of the modified governing equations derived via the finite calculus technique for the numerical solution of convection diffusion problems incompressible flow and incompressible solid mechanic problems and strain localization problems

lagrangian finite element analysis of newtonian fluid flows a fully lagrangian nite element method for the analysis of newtonian ows is developed the approach furnishes in eect a lagrangian implementation of the compressible navier stokes equations as the ow proceeds the mesh is maintained undistorted through continuous and adaptive remeshing of the uid mass the principal advantage of the present approach lies in the treatment of boundary conditions at material surfaces such as free boundaries uid uid or uid solid interfaces in contrast to eulerian approaches boundary conditions are enforced at material surfaces ab initio and therefore require no special attention consistent tangents are obtained for lagrangian implicit analysis of a newtonian uid ow which may exhibit compressibility eects the accuracy of the approach is assessed by comparison of the solution for a sloshing problem with existing numerical results and its versatility demonstrated through a simulation of wave breaking the nite element mesh is maintained undistorted throughout the computation by recourse to frequent and adaptive remeshing 1998 john wiley sons ltd

multidimensional extensions and a nested dual approach for the m median problem abstract a general framework for modeling median type locational decisions where i travel costs and demands may be stochastic ii multiple services or commodities need to be considered and or iii multiple median type objectives might exist is presented using the concept of multidimensional networks the classical m median problem the stochastic m median problem the multicommodity m median problem and and multiobjective m median problem are defined within this framework by an appropriate transformation of variables the multidimensional m median problem simplifies to the classical m median problem but with a k fold increase in the number of nodes where k is the number of dimensions of the network a nested dual approach to solve the resulting classical m median problem that uses erlenkotter s facility location scheme as a subroutine is presented computational results indicate that the procedure may perhaps be the best available one to solve the m median problem exactly

new results on finite fixed time synchronization of delayed diffusive fuzzy hnns with discontinuous activations abstract in this paper the problem of finite fixed time synchronization ffts is studied for delayed diffusive hopfield neural networks by employing filippov regularization approaches inequality techniques and a generalized finite fixed time stability theorem a novel state feedback controller is designed to realize the ffts of the considered network model the obtained theoretical results generalize and improve existing ones in the literature finally a numerical example is presented to show the effectiveness of the theoretical results

polyhedrization of an arbitrary 3d point set abstract given a 3d point set the problem of defining the volume associated dividing it into a set of regions elements and defining a boundary surface is tackled several physical problems need to define volume domains boundary surfaces and approximating functions from a given point distribution this is for instance the case of particle methods in which all the information is the particle positions and there are not boundary surfaces definition until recently all the fem mesh generators were limited to the generation of simple elements as tetrahedral or hexahedral elements or triangular and quadrangular in 2d problems the reason of this limitation was the lack of any acceptable shape function to be used in other kind of geometrical elements nowadays there are several acceptable shape functions for a very large class of polyhedra these new shape functions together with a generalization of the delaunay tessellation presented in this paper gives an optimal marriage and a powerful tool to solve a large variety of physical problems by numerical methods the domain partition into polyhedra presented here is not a standard mesh generation the problem here is for a given node distribution to find a suitable boundary surface and a suitable mesh to be used in the solution of a physical problem by a numerical method to include new nodes or change their positions is not allowed