new criteria of passivity analysis for fuzzy time delay systems with parameter uncertainties this paper investigates the passivity problem for a class of uncertain stochastic fuzzy nonlinear systems with mixed delays and nonlinear noise disturbances by employing an improved free weighting matrix approach the fuzzy system is based on the takagi sugeno model that is often used to represent the complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning to reflect more realistic dynamical behaviors of the system the parameter uncertainties the stochastic disturbances and nonlinearities are considered where the parameter uncertainties enter into all the system matrices the stochastic disturbances are given in the form of a brownian motion the mixed delays comprise both discrete and distributed time varying delays by taking the relationship among the time delays their lower and upper bounds into account some less conservative linear matrix inequality based delay dependent passivity criteria are obtained without ignoring any useful terms in the derivative of lyapunov functional finally numerical examples are given to demonstrate the effectiveness and merits of the proposed methods

dissipativity analysis for singular systems with time varying delays this paper is concerned with the dissipativity analysis problem for singular systems with time varying delays a delay dependent criterion is established to guarantee the dissipativity of the underlying systems using the delay partitioning technique all the results given in this paper are not only dependent upon the time delay but also dependent upon the number of delay partitions the effectiveness and the reduced conservatism of the derived results are demonstrated by two illustrative examples

brief delay dependent robust h control of uncertain linear state delayed systems this paper examines the problems of robust stabilization and robust h control for linear systems with a constant time delay in the state and subject to parameter uncertainty systems with norm bounded parameter uncertainty will be considered and attention is focused on the design of linear memoryless state feedback controllers we develop methods of robust stabilization and robust h control which are dependent on the size of the delay and are based on the solution of linear matrix inequalities the proposed methods can be easily extended to uncertain linear polytopic systems as well as to the case of multiple time delays

stability of takagi sugeno fuzzy delay systems with impulse the takagi sugeno t s model of fuzzy delay systems with impulse is first presented in this paper by means of classical analysis methods and razumikhin technique the criteria of uniform stability and uniform asymptotic stability for t s fuzzy delay systems with impulse are obtained respectively three numerical examples are also discussed to illustrate the efficiency of the obtained results

unconditionally convergent l1 galerkin fems for nonlinear time fractional schrodinger equations in this paper a linearized l1 galerkin finite element method is proposed to solve the multidimensional nonlinear time fractional schrodinger equation in terms of a temporal spatial error splitting argument we prove that the finite element approximations in the l 2 norm and l infty norm are bounded without any time step size conditions more importantly by using a discrete fractional gronwall type inequality optimal error estimates of the numerical schemes are obtained unconditionally while the classical analysis for multidimensional nonlinear fractional problems always required certain time step restrictions dependent on the spatial mesh size numerical examples are given to illustrate our theoretical results

numerical solution of the space fractional fokker planck equation the traditional second order fokker planck equation may not adequately describe the movement of solute in an aquifer because of large deviation from the dynamics of brownian motion densities of stable type have been used to describe the probability distribution of these motions the resulting governing equation of these motions is similar to the traditional fokker planck equation except that the order of the highest derivative is fractional in this paper a space fractional fokker planck equation sffpe with instantaneous source is considered a numerical scheme for solving sffpe is presented using the riemann liouville and grunwald letnikov definitions of fractional derivatives the sffpe is transformed into a system of ordinary differential equations ode then the ode system is solved by a method of lines numerical results for sffpe with a constant diffusion coefficient are evaluated for comparison with the known analytical solution the numerical approximation of sffpe with a time dependent diffusion coefficient is also used to simulate levy motion with stable densities we will show that the numerical method of sffpe is able to more accurately model these heavy tailed motions

limit theorems for coupled continuous time random walks scaling limits of continuous time random walks are used in physics to model anomalous diffusion in which a cloud of particles spreads at a different rate than the classical brownian motion governing equations for these limit processes generalize the classical diffusion equation in this article we characterize scaling limits in the case where the particle jump sizes and the waiting time between jumps are dependent this leads to an efficient method of computing the limit and a surprising connection to fractional derivatives

numerical methods and analysis for a class of fractional advection dispersion models in this paper a class of fractional advection dispersion models fadms is considered these models include five fractional advection dispersion models i e the time fadm the mobile immobile time fadm with a time caputo fractional derivative 0 c 1 the space fadm with two sides riemann liouville derivatives the time space fadm and the time fractional advection diffusion wave model with damping with index 1 c 2 these equations can be used to simulate the regional scale anomalous dispersion with heavy tails we propose computationally effective implicit numerical methods for these fadms the stability and convergence of the implicit numerical methods are analysed and compared systematically finally some results are given to demonstrate the effectiveness of theoretical analysis

preconditioned iterative methods for fractional diffusion equation in this paper we are concerned with numerical methods for the solution of initial boundary value problems of anomalous diffusion equations of order 1 2 the classical crank nicholson method is used to discretize the fractional diffusion equation and then the spatial extrapolation is used to obtain temporally and spatially second order accurate numerical estimates two preconditioned iterative methods namely the preconditioned generalized minimal residual preconditioned gmres method and the preconditioned conjugate gradient for normal residual preconditioned cgnr method are proposed to solve relevant linear systems numerical experiments are given to illustrate the efficiency of the methods

the fractional order governing equation of levy motion a governing equation of stable random walks is developed in one dimension this fokker planck equation is similar to and contains as a subset the second order advection dispersion equation ade except that the order a of the highest derivative is fractional e g the 1 65th derivative fundamental solutions are levy s a stable densities that resemble the gaussian except that they spread proportional to time 1 a have heavier tails and incorporate any degree of skewness the measured variance of a plume undergoing levy motion would grow faster than fickian plume at a rate of time 2 a where 0 a 2 the equation is parsimonious since the parameters are not functions of time or distance the scaling behavior of plumes that undergo levy motion is accounted for by the fractional derivatives which are appropriate measures of fractal functions in real space the fractional derivatives are integrodifferential operators so the fractional ade describes a spatially nonlocal process that is ergodic and has analytic solutions for all time and space

a class of second order difference approximations for solving space fractional diffusion equations a class of second order approximations called the weighted and shifted grunwald difference wsgd operators are proposed for riemann liouville fractional derivatives with their effective applications to numerically solving space fractional diffusion equations in one and two dimensions the stability and convergence of our difference schemes for space fractional diffusion equations with constant coefficients in one and two dimensions are theoretically established several numerical examples are implemented to test the efficiency of the numerical schemes and confirm the convergence order and the numerical results for variable coefficients problem are also presented

robust fuzzy control of nonlinear systems with parametric uncertainties addresses the robust fuzzy control problem for nonlinear systems in the presence of parametric uncertainties the takagi sugeno t s fuzzy model is adopted for fuzzy modeling of the nonlinear system two cases of the t s fuzzy system with parametric uncertainties both continuous time and discrete time cases are considered in both continuous time and discrete time cases sufficient conditions are derived for robust stabilization in the sense of lyapunov asymptotic stability for the t s fuzzy system with parametric uncertainties the sufficient conditions are formulated in the format of linear matrix inequalities the t s fuzzy model of the chaotic lorenz system which has complex nonlinearity is developed as a test bed the effectiveness of the proposed controller design methodology is finally demonstrated through numerical simulations on the chaotic lorenz system

robust fuzzy control for uncertain stochastic time delay takagi sugeno fuzzy models for achieving passivity this paper focuses on the robust passive stability and stabilization problems for uncertain nonlinear stochastic time delay systems via the fuzzy modeling approach the nonlinear stochastic system is described by takagi sugeno t s fuzzy model in which the consequent parts are presented by linear stochastic time delay differential equation with lyapunov krasovskii function and improved jensen s inequality the stability criteria are derived in addition the passivity theory is employed to discuss external disturbance effect on system for achieving attenuation performance according to the proposed design method the fuzzy controller is carried out by parallel distributed compensation pdc concept to guarantee the robust asymptotical stability and attenuation performance of system in the sense of mean square finally a synchronous generator power system is presented to manifest the application and effectiveness of the proposed fuzzy control method

robust h control for a class of nonlinear discrete time delay stochastic systems with missing measurements this paper is concerned with the problem of robust h output feedback control for a class of uncertain discrete time delayed nonlinear stochastic systems with missing measurements the parameter uncertainties enter into all the system matrices the time varying delay is unknown with given low and upper bounds the nonlinearities satisfy the sector conditions and the missing measurements are described by a binary switching sequence that obeys a conditional probability distribution the problem addressed is the design of an output feedback controller such that for all admissible uncertainties the resulting closed loop system is exponentially stable in the mean square for the zero disturbance input and also achieves a prescribed h performance level by using the lyapunov method and stochastic analysis techniques sufficient conditions are first derived to guarantee the existence of the desired controllers and then the controller parameters are characterized in terms of linear matrix inequalities lmis a numerical example is exploited to show the usefulness of the results obtained

robust passivity and passification of stochastic fuzzy time delay systems in this paper the passivity and passification problems are investigated for a class of uncertain stochastic fuzzy systems with time varying delays the fuzzy system is based on the takagi sugeno t s model that is often used to represent the complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning to reflect more realistic dynamical behaviors of the system both the parameter uncertainties and the stochastic disturbances are considered where the parameter uncertainties enter into all the system matrices and the stochastic disturbances are given in the form of a brownian motion we first propose the definition of robust passivity in the sense of expectation then by utilizing the lyapunov functional method the ito differential rule and the matrix analysis techniques we establish several sufficient criteria such that for all admissible parameter uncertainties and stochastic disturbances the closed loop stochastic fuzzy time delay system is robustly passive in the sense of expectation the derived criteria which are either delay independent or delay dependent are expressed in terms of linear matrix inequalities lmis that can be easily checked by using the standard numerical software illustrative examples are presented to demonstrate the effectiveness and usefulness of the proposed results

an implicit difference scheme with the kps preconditioner for two dimensional time space fractional convection diffusion equations abstract this paper deals with the numerical computation and analysis for a class of two dimensional time space fractional convection diffusion equations an implicit difference scheme is derived for solving this class of equations it is proved under some suitable conditions that the derived difference scheme is stable and convergent moreover the convergence orders of the scheme in time and space are also given in order to accelerate the convergence rate by combining the kronecker product splitting kps preconditioner with the generalized minimal residual gmres method a preconditioning strategy for implementing the difference scheme is introduced finally several numerical examples are presented to illustrate the computational accuracy and efficiency of the methods

fuzzy affine model based memory filter design of nonlinear systems with time varying delay this paper studies the piecewise affine memory mathscr h infty filtering problem for nonlinear systems with time varying delay in a delay dependent framework the nonlinear plant is characterized by a continuous time takagi sugeno fuzzy affine model with parametric uncertainties the purpose is to develop a new approach for filter synthesis procedure with less conservatism specifically by constructing a novel lyapunov krasovskii functional together with a wirtinger based integral inequality reciprocally convex inequality and s procedure an improved criterion is first attained for analyzing the mathscr h infty performance of the filtering error system and then via some linearization techniques the piecewise affine memory filter synthesis is carried out it is shown that the existence of desired filter gains can be explicitly determined by the solution of a convex optimization problem finally simulation studies are presented to reveal the effectiveness and less conservatism of the developed approaches it is anticipated that the proposed scheme can be further extended to the analysis and synthesis of continuous time fuzzy affine dynamic systems with integrated communication delays in the networked circumstance

multigrid method for fractional diffusion equations the fractional diffusion equation is discretized by the implicit finite difference scheme with the shifted grunwald formula the scheme is unconditionally stable and the coefficient matrix possesses the toeplitz like structure a multigrid method is proposed to solve the resulting system meanwhile the fast toeplitz matrix vector multiplication is utilized to lower the computational cost with only o nlogn complexity where n is the number of the grid points numerical experiments are given to demonstrate the efficiency of the method

finite difference approximations for fractional advection dispersion flow equations fractional advection dispersion equations are used in groundwater hydrology to model the transport of passive tracers carried by fluid flow in a porous medium in this paper we develop practical numerical methods to solve one dimensional fractional advection dispersion equations with variable coefficients on a finite domain the practical application of these results is illustrated by modeling a radial flow problem use of the fractional derivative allows the model equations to capture the early arrival of tracer observed at a field site

passivity and passification of time delay systems in this paper the problems of passivity and passification of a class of linear time delay systems are investigated a new state transformation is developed to exhibit the delay dependence it is established that the passivity condition can be cast in a linear matrix inequality lmi format for state feedback passification it is proven that it is indifferent to use instantaneous or delayed state feedback the case of dynamic output feedback passification is also treated numerical examples are provided

an approach to fuzzy control of nonlinear systems stability and design issues presents a design methodology for stabilization of a class of nonlinear systems first the authors represent a nonlinear plant with a takagi sugeno fuzzy model then a model based fuzzy controller design utilizing the concept of the so called parallel distributed compensation is employed the main idea of the controller design is to derive each control rule so as to compensate each rule of a fuzzy system the design procedure is conceptually simple and natural moreover the stability analysis and control design problems can be reduced to linear matrix inequality lmi problems therefore they can be solved efficiently in practice by convex programming techniques for lmis the design methodology is illustrated by application to the problem of balancing and swing up of an inverted pendulum on a cart

a counterexample to the lazer mckenna conjecture on donne un contre exemple complet a une conjecture de lazer et mckenna si f r r est c 1 si f 1 y quand y si 1 si l et si contient au moins k 1 valeurs propres de sur alors l equation u f u t 1 v dans u 0 sur a au moins 2 k 1 solutions pour t positif grand

delay dependent guaranteed cost control for t s fuzzy systems with time delays this study introduces a guaranteed cost control method for nonlinear systems with time delays which can be represented by takagi sugeno t s fuzzy models with time delays the state feedback and generalized dynamic output feedback approaches are considered the generalized dynamic output feedback controller is presented by a new fuzzy controller architecture which is of dual indexed rule base it considers both the dynamic part and the output part of t s fuzzy model which guarantees that the controller without any delay information can stabilize time delay t s fuzzy systems based on delay dependent lyapunov functional approach some sufficient conditions for the existence of state feedback controller are provided via parallel distributed compensation pdc first second the corresponding conditions are extended into the generalized dynamic output feedback closed loop system via so called generalized pdc technique the upper bound of time delay can be obtained using convex optimization such that the system can be stabilized for all time delays whose sizes are not larger than the bound the minimizing method is also proposed to search the suboptimal upper bound of guaranteed cost function the effectiveness of the proposed method can be shown by the simulation examples

technical communique reliable h control for discrete time piecewise linear systems with infinite distributed delays in this paper the reliable h control problem is investigated for discrete time piecewise linear systems with time delays and actuator failures the time delays are assumed to be infinitely distributed in the discrete time domain and the possible failure of each actuator is described by a variable varying in a given interval the aim of the addressed reliable h control problem is to design a controller such that for the admissible infinite distributed delays and possible actuator failures the closed loop system is exponentially stable with a given disturbance attenuation level c the controller gain is characterized in terms of the solution to a linear matrix inequality that can be easily solved by using standard software packages a simulation example is exploited in order to illustrate the effectiveness of the proposed design procedures

stochastic h sub 2 h sub spl infin control with state dependent noise this paper discusses the stochastic h sub 2 h sub spl infin control problem with state dependent noise by means of the stabilization exact observability and stochastic detectability of stochastic systems the infinite horizon stochastic h sub 2 h sub spl infin control design is developed for the finite horizon h sub 2 h sub spl infin control problem our results generalize the corresponding deterministic ones to the stochastic models finally the observer based suboptimal stochastic h sub 2 h sub spl infin control is discussed in which the state variables cannot be measured directly and a feasible design algorithm is proposed

technical communique absolute stability of time delay systems with sector bounded nonlinearity this paper deals with the problem of absolute stability of time delay systems with sector bounded nonlinearity some new delay dependent stability criteria are obtained and formulated in the form of linear matrix inequalities lmis neither model transformation nor bounding technique for cross terms is involved through derivation of the stability criteria numerical examples show that the results obtained in this paper improve the estimate of the stability limit over some existing result

passivity analysis for discrete time stochastic markovian jump neural networks with mixed time delays in this paper passivity analysis is conducted for discrete time stochastic neural networks with both markovian jumping parameters and mixed time delays the mixed time delays consist of both discrete and distributed delays the markov chain in the underlying neural networks is finite piecewise homogeneous by introducing a lyapunov functional that accounts for the mixed time delays a delay dependent passivity condition is derived in terms of the linear matrix inequality approach the case of markov chain with partially unknown transition probabilities is also considered all the results presented depend upon not only discrete delay but also distributed delay a numerical example is included to demonstrate the effectiveness of the proposed methods

global synchronization for discrete time stochastic complex networks with randomly occurred nonlinearities and mixed time delays in this paper the problem of stochastic synchronization analysis is investigated for a new array of coupled discrete time stochastic complex networks with randomly occurred nonlinearities rons and time delays the discrete time complex networks under consideration are subject to 1 stochastic nonlinearities that occur according to the bernoulli distributed white noise sequences 2 stochastic disturbances that enter the coupling term the delayed coupling term as well as the overall network and 3 time delays that include both the discrete and distributed ones note that the newly introduced rons and the multiple stochastic disturbances can better reflect the dynamical behaviors of coupled complex networks whose information transmission process is affected by a noisy environment e g internet based control systems by constructing a novel lyapunov like matrix functional the idea of delay fractioning is applied to deal with the addressed synchronization analysis problem by employing a combination of the linear matrix inequality lmi techniques the free weighting matrix method and stochastic analysis theories several delay dependent sufficient conditions are obtained which ensure the asymptotic synchronization in the mean square sense for the discrete time stochastic complex networks with time delays the criteria derived are characterized in terms of lmis whose solution can be solved by utilizing the standard numerical software a simulation example is presented to show the effectiveness and applicability of the proposed results

brief paper a note on control of a class of discrete time stochastic systems with distributed delays and nonlinear disturbances this paper is concerned with the state feedback control problem for a class of discrete time stochastic systems involving sector nonlinearities and mixed time delays the mixed time delays comprise both discrete and distributed delays and the sector nonlinearities appear in the system states and all delayed states the distributed time delays in the discrete time domain are first defined and then a special matrix inequality is developed to handle the distributed time delays within an algebraic framework an effective linear matrix inequality lmi approach is proposed to design the state feedback controllers such that for all admissible nonlinearities and time delays the overall closed loop system is asymptotically stable in the mean square sense sufficient conditions are established for the nonlinear stochastic time delay systems to be asymptotically stable in the mean square sense and then the explicit expression of the desired controller gains is derived a numerical example is provided to show the usefulness and effectiveness of the proposed design method

passivity analysis and passification of discrete time hybrid systems for discrete time hybrid systems in piecewise affine or piece wise polynomial pwp form this note proposes sufficient passivity analysis and synthesis criteria based on the computation of piecewise quadratic or pwp storage functions by exploiting linear matrix inequality techniques and sum of squares decomposition methods passivity analysis and synthesis of passifying controllers can be carried out through standard semidefinite programming packages providing a tool particularly important for stability of interconnected heterogeneous dynamical systems

fourth order accurate scheme for the space fractional diffusion equations because of the nonlocal properties of fractional operators higher order schemes play a more important role in discretizing fractional derivatives than classical ones the striking feature is that higher order schemes of fractional derivatives can keep the same computation cost with first order schemes but greatly improve the accuracy nowadays there are already two types of second order discretization schemes for space fractional derivatives the first type is given and discussed in sousa and li arxiv 1109 2345v1 2011 chen and deng appl math model 38 2014 pp 3244 3259 chen deng and wu appl numer math 70 2013 pp 22 41 and the second type is a class of schemes presented in tian zhou and deng math comp to appear also available online from arxiv 1201 5949 2012 the core object of this paper is to derive a class of fourth order approximations called the weighted and shifted lubich difference operators for space fractional derivatives then we use the derived schemes t

delay dependent robust h sub spl infin and l sub 2 l sub spl infin filtering for a class of uncertain nonlinear time delay systems this note presents delay dependent robust h sub spl infin and l sub 2 l sub spl infin filter designs for a class of nonlinear systems with multiple time varying delays in the state and parameter uncertainties residing in a polytope the nonlinearities are assumed to satisfy global lipschitz conditions attention is focused on the design of robust full order and reduced order filters guaranteeing a prescribed noise attenuation level in an h sub spl infin or l sub 2 l sub spl infin sense the admissible filters can be obtained from the solution of convex optimization problems in terms of linear matrix inequalities which can be solved via efficient interior point algorithms

a kronecker product splitting preconditioner for two dimensional space fractional diffusion equations abstract we study preconditioned iterative methods for the linear system arising in the numerical discretization of a two dimensional space fractional diffusion equation our approach is based on a formulation of the discrete problem that is shown to be the sum of two kronecker products by making use of an alternating kronecker product splitting iteration technique we establish a class of fixed point iteration methods theoretical analysis shows that the new method converges to the unique solution of the linear system moreover the optimal choice of the involved iteration parameters and the corresponding asymptotic convergence rate are computed exactly when the eigenvalues of the system matrix are all real the basic iteration is accelerated by a krylov subspace method like gmres the corresponding preconditioner is in a form of a kronecker product structure and requires at each iteration the solution of a set of discrete one dimensional fractional diffusion equations we use structure preserving approximations to the discrete one dimensional fractional diffusion operators in the action of the preconditioning matrix numerical examples are presented to illustrate the effectiveness of this approach

fast adi method for high dimensional fractional diffusion equations in conservative form with preconditioned strategy in this paper high dimensional two sided space fractional diffusion equations derived from the fractional ficks law and with monotonic variable diffusion coefficients are solved by alternating direction implicit method each linear system corresponding to each spatial direction thus resulted is solved by krylov subspace method the method is accelerated by applying an approximate inverse preconditioner where under certain conditions we showed that the normalized preconditioned matrix is equal to a sum of identity matrix a matrix with small norm and a matrix with low rank such that the preconditioned krylov subspace method converges superlinearly we also briefly present some fast algorithms whose computational cost for solving the linear systems is o nlogn where n is the matrix size the results are illustrated by some numerical examples

passivity and passification of fuzzy systems with time delays takagi sugeno t s fuzzy model provides an effective representation of complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning applied to a set of linear input output submodels recently a number of authors studied the t s fuzzy systems with time delays in this paper the passivity and feedback passification of t s fuzzy systems with time delays are considered both delay independent and delay dependent results are presented and the theoretical results are given in terms of linear matrix inequalities lmis numerical examples are given which illustrate the effectiveness of the theoretical results

a direct o nlog2n finite difference method for fractional diffusion equations fractional diffusion equations model phenomena exhibiting anomalous diffusion that can not be modeled accurately by the second order diffusion equations because of the nonlocal property of fractional differential operators the numerical methods have full coefficient matrices which require storage of o n 2 and computational cost of o n 3 where n is the number of grid points in this paper we develop a fast finite difference method for fractional diffusion equations which only requires storage of o n and computational cost of o nlog 2n while retaining the same accuracy and approximation property as the regular finite difference method numerical experiments are presented to show the utility of the method

a fourth order approximation of fractional derivatives with its applications a new fourth order difference approximation is derived for the space fractional derivatives by using the weighted average of the shifted grunwald formulae combining the compact technique the properties of proposed fractional difference quotient operator are presented and proved then the new approximation formula is applied to solve the space fractional diffusion equations by the energy method the proposed quasi compact difference scheme is proved to be unconditionally stable and convergent in l2 norm for both 1d and 2d cases several numerical examples are given to confirm the theoretical results

analysis and synthesis of nonlinear time delay systems via fuzzy control approach takagi sugeno ts fuzzy models 1985 1992 can provide an effective representation of complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning applied to a set of linear input output i o submodels in this paper the ts fuzzy model approach is extended to the stability analysis and control design for both continuous and discrete time nonlinear systems with time delay the ts fuzzy models with time delay are presented and the stability conditions are derived using lyapunov krasovskii approach we also present a stabilization approach for nonlinear time delay systems through fuzzy state feedback and fuzzy observer based controller sufficient conditions for the existence of fuzzy state feedback gain and fuzzy observer gain are derived through the numerical solution of a set of coupled linear matrix inequalities an illustrative example based on the cstr model is given to design a fuzzy controller

fractal mobile immobile solute transport 1 a fractal mobile immobile model for solute transport assumes power law waiting times in the immobile zone leading to a fractional time derivative in the model equations the equations are equivalent to previous models of mobile immobile transport with power law memory functions and are the limiting equations that govern continuous time random walks with heavy tailed random waiting times the solution is gained by performing an integral transform on the solution of any boundary value problem for transport in the absence of an immobile phase in this regard the output from a multidimensional numerical model can be transformed to include the effect of a fractal immobile phase the solutions capture the anomalous behavior of tracer plumes in heterogeneous aquifers including power law breakthrough curves at late time and power law decline in the measured mobile mass the made site mobile tritium mass decline is consistent with a fractional time derivative of order 0 33 while haggerty et al s 2002 stream tracer test is well modeled by a fractional time derivative of order 0 3

a generalized hopfield network for nonsmooth constrained convex optimization lie derivative approach this paper proposes a generalized hopfield network for solving general constrained convex optimization problems first the existence and the uniqueness of solutions to the generalized hopfield network in the filippov sense are proved then the lie derivative is introduced to analyze the stability of the network using a differential inclusion the optimality of the solution to the nonsmooth constrained optimization problems is shown to be guaranteed by the enhanced fritz john conditions the convergence rate of the generalized hopfield network can be estimated by the second order derivative of the energy function the effectiveness of the proposed network is evaluated on several typical nonsmooth optimization problems and used to solve the hierarchical and distributed model predictive control four tank benchmark

delay dependent robust h sub spl infin control for t s fuzzy systems with time delay this paper focuses on the problem of delay dependent robust fuzzy control for a class of nonlinear delay systems via state feedback the takagi sugeno t s fuzzy model is adopted for representing a nonlinear system with time delayed state a delay dependent stabilization criterion is first presented then the methods of robust stabilization and robust h sub spl infin control are developed which are dependent on the size of the delay and are based on the solutions of linear matrix inequalities lmis finally a design example of robust h sub spl infin controller for uncertain nonlinear systems is given to illustrate the effectiveness of the approaches proposed in this paper

a circulant preconditioner for fractional diffusion equations the implicit finite difference scheme with the shifted grunwald formula which is unconditionally stable is employed to discretize fractional diffusion equations the resulting systems are toeplitz like and then the fast fourier transform can be used to reduce the computational cost of the matrix vector multiplication the preconditioned conjugate gradient normal residual method with a circulant preconditioner is proposed to solve the discretized linear systems the spectrum of the preconditioned matrix is proven to be clustered around 1 if diffusion coefficients are constant hence the convergence rate of the proposed iterative algorithm is superlinear numerical experiments are carried out to demonstrate that our circulant preconditioner works very well even though for cases of variable diffusion coefficients

new delay dependent stabilization conditions of t s fuzzy systems with constant delay this paper focuses on the problem of robust control for takagi sugeno t s fuzzy systems with time delay the delay dependent stability analysis and controller synthesis have been addressed the free weighting matrix method has been used for stability analysis and controller synthesis new and less conservative delay dependent stability conditions are proposed in terms of linear matrix inequalities lmi finally some examples are given to illustrate the effectiveness of the proposed approaches

multiple solutions of positively homogeneous equations where h r rn is a continuous and t periodic function v is a vector to be 5xed are real numbers and a is a symmetric n n matrix given u rn we write u u u where u denotes the vector whose components are the positive parts of those of u and similarly for u this kind of systems appear e g after discretization in space of partial di0erential equations like the wave or beam equations they also provide a mathematical model of a system of coupled oscillators with several springs and stops let 1 2 n be the eigenvalues of a in increasing order and assume i 1 6 2 6 6 n i 2