superfast solution of linear convolutional volterra equations using qtt approximation we address a linear fractional differential equation and develop effective solution methods using algorithms for the inversion of triangular toeplitz matrices and the recently proposed qtt format the inverses of such matrices can be computed by the divide and conquer and modified bini s algorithms for which we present the versions with the qtt approximation we also present an efficient formula for the shift of vectors given in qtt format which is used in the divide and conquer algorithm as a result we reduce the complexity of inversion from the fast fourier level o n log n to the speed of superfast fourier transform i e o log 2 n the results of the paper are illustrated by numerical examples

robust stabilization of nonlinear multiple time delay large scale systems via decentralized fuzzy control to overcome the effect of modeling errors between nonlinear multiple time delay subsystems and takagi sugeno t s fuzzy models with multiple time delays a robustness design of fuzzy control is proposed in this work in terms of lyapunov s direct method a delay dependent stability criterion is hence derived to guarantee the asymptotic stability of nonlinear multiple time delay large scale systems based on this criterion and the decentralized control scheme a set of model based fuzzy controllers is then synthesized via the technique of parallel distributed compensation pdc to stabilize the nonlinear multiple time delay large scale system finally a numerical example with simulations is given to demonstrate the concepts discussed throughout this work

delay dependent robust h control for t s fuzzy system with interval time varying delay this paper is concerned with the problem of robust h control for uncertain t s fuzzy systems with interval time varying delay that is the delay is assumed to be a time varying function belonging to an interval by defining new lyapunov functions and making use of novel techniques to achieve delay dependence new conditions for the existence of robust h controller are obtained based on the parallel distributed compensation pdc method in this article all the conditions are shown in terms of linear matrix inequalities lmis which can be solved efficiently by using the lmi optimization techniques two numerical examples are given to illustrate the less conservatism of the proposed method

regularity of invariant measures on finite and infinite dimensional spaces and applications abstract in this paper we prove new results on the regularity i e smoothness of measures solving the equation l 0 for operators of type l b on finite and infinite dimensional state spaces e in particular we settle a conjecture of i shigekawa in the situation where h is the gross laplacian e h is an abstract wiener space and b id e v where v takes values in the cameron martin space h using gross logarithmic sobolev inequality in an essential way we show that is always absolutely continuous w r t the gaussian measure and that the square root of the density is in the malliavin test function space of order 1 in l 2 furthermore we discuss applications to infinite dimensional stochastic differential equations and prove some new existence results for l 0 these include results on the inverse problem i e we give conditions ensuring that b is the vector logarithmic derivative of a measure we also prove necessary and sufficient conditions for to be symmetrizing i e l is symmetric on l 2 finally a substantial part of this work is devoted to the uniqueness of symmetrizing measures for l we characterize the cases where we have uniqueness by the irreducibility of the associated classical dirichlet forms

modeling identification and control of a class of nonlinear systems in this paper we propose a new fuzzy hyperbolic model for a class of complex systems which is difficult to model the fuzzy hyperbolic model is a nonlinear model in nature and can be easily derived from a set of fuzzy rules it can also be seen as a feedforward neural network model and so we can identify the model parameters by bp algorithm we prove that the stable controller can be designed based on linear system theory two methods of designing the controller for the fuzzy hyperbolic model are proposed the results of simulation support the effectiveness of the model and the control scheme

the logarithmic sobolev inequality for discrete spin systems on a lattice for finite range lattice gases with a finite spin space it is shown that the dobrushin shlosman mixing condition is equivalent to the existence of a logarithmic sobolev inequality for the associated unique gibbs state in addition implications of these considerations for the ergodic properties of the corresponding glauber dynamics are examined

analytic and geometric background of recurrence and non explosion of the brownian motion on riemannian manifolds we provide an overview of such properties of the brownian motion on complete non compact riemannian manifolds as recurrence and non explosion it is shown that both properties have various analytic characterizations in terms of the heat kernel green function liouville properties etc on the other hand we consider a number of geometric conditions such as the volume growth isoperimetric inequalities curvature bounds etc which are related to recurrence and non explosion

approach to equilibrium of glauber dynamics in the one phase region i the attractive case various finite volume mixing conditions in classical statistical mechanics are reviewed and critically analyzed in particular somefinite size conditions are discussed together with their implications for the gibbs measures and for the approach to equilibrium of glauber dynamics inarbitrarily large volumes it is shown that dobrushin shlosman s theory ofcomplete analyticity and its dynamical counterpart due to stroock and zegarlinski cannot be applied in general to the whole one phase region since it requires mixing properties for regions ofarbitrary shape an alternative approach based on previous ideas of oliveri and picco is developed which allows to establish results on rapid approach to equilibrium deeply inside the one phase region in particular in the ferromagnetic case we considerably improve some previous results by holley and aizenman and holley our results are optimal in the sene that for example they show for the first time fast convergence of the dynamicsfor any temperature above the critical one for thed dimensional ising model with or without an external field in part ii we extensively consider the general case not necessarily attractive and we develop a new method based on renormalizations group ideas and on an assumption of strong mixing in a finite cube to prove hypercontractivity of the markov semigroup of the glauber dynamics

ergodicity ofl2 semigroups and extremality of gibbs states we extend the classical results of holley stroock on the characterization of extreme gibbs states for the ising model in terms of the irreducibility resp ergodicity of the corresponding glauber dynamics to the case of lattice systems with unbounded linear spin spaces we first develop a general framework to discuss questions of this type using classical dirichlet forms on infinite dimensional state spaces and their associated diffusions we then describe concrete applications to lattice models with polynomial interactions i e the discretep d models of euclidean quantum field theory in addition we prove the equivalence of extremality and shift ergodicity for tempered gibbs states of these models and also discuss this question in the general framework

fuzzy h_ infty filter design for a class of nonlinear discrete time systems with multiple time delays this paper studies the fuzzy hinfin filter design problem for signal estimation of nonlinear discrete time systems with multiple time delays and unknown bounded disturbances first the takagi sugeno t s fuzzy model is used to represent the state space model of nonlinear discrete time systems with time delays next we design a stable fuzzy hinfin filter based on the t s fuzzy model which guarantees asymptotic stability and a prescribed hinfin index for the filtering error system irrespective of the time delays and uncertain disturbances a sufficient condition for the existence of such a filter is established by using the linear matrix inequality lmi approach the proposed lmi problem can be efficiently solved with global convergence guarantee using convex optimization techniques such as the interior point algorithm simulation examples are provided to illustrate the design procedure of the present method

new approach to delay dependent stability analysis and stabilization for continuous time fuzzy systems with time varying delay this paper is concerned with delay dependent stability analysis and stabilization problems for continuous time takagi and sugeno t s fuzzy systems with a time varying delay a new method for the delay dependent stability analysis and stabilization is suggested which is less conservative than other existing ones first based on a fuzzy lyapunov krasovskii functional lkf a delay dependent stability criterion is derived for the open loop fuzzy systems in the derivation process some free fuzzy weighting matrices are introduced to express the relationships among the terms of the system equation and among the terms in the leibniz newton formula then a delay dependent stabilization condition based on the so called parallel distributed compensation pdc scheme is worked out for the closed loop fuzzy systems the proposed stability criterion and stabilization condition are represented in terms of linear matrix inequalities lmis and compared with the existing ones via two examples finally application to control of a truck trailer is also given to illustrate the effectiveness of the proposed design method

decentralized stabilization of large scale interconnected systems with delays in this note we study the decentralized stabilization problem of linear time invariant large scale interconnected systems with delays without any assumption of system structure our main result here is the sufficient condition for the decentralized stabilization one application of the procedures to the decentralized observers is also presented

stability analysis of product t methods for abel integral equations of the second kind stability analysis of product methods for abel integral equations of the second kind based on the test equation y t 1 lambda int limits 0 1 frac y s t s alpha ds t geqq 0 0 0 and we investigate whether this property is inherited by numerical approximations toy

on monotone abel volterra integral equations on the half line in this paper we reanalyze the trapezoidal method for the solution of nonlinear abel volterra integral equations on the half line we prove the convergence of the method in the uniform norm provided the nonlinearity is lipschitz continuous and strictly monotone

a priori estimates for symmetrizing measures and their applications to gibbs states abstract we prove existence and uniform a priori estimates for tempered gibbs states of certain classical lattice systems with unbounded spins nonharmonic pair potentials and infinite radius of interaction we use an alternative characterization of gibbs measures in terms of their radon nikodym derivatives w r t local shifts of the configuration space and corresponding integration by parts formulas

ito type measure valued stochastic differential equations a class of ito type measure valued stochastic differential equations is studied on a locally compact polish space the sdes are driven by countably many brownian motions with interactions caused by the diffusion and the drift coefficients through countably many continuous functions explicit conditions are presented for the existence uniqueness and ergodicity of the solution

spectral gap and logarithmic sobolev inequality for kawasaki and glauber dynamics we prove that the spectral gap of the kawasaki dynamics shrink at the rate of 1 l2 for cubes of sizel provided that some mixing conditions are satisfied we also prove that the logarithmic sobolev inequality for the glauber dynamics in standard cubes holds uniformly in the size of the cube if the dobrushin shlosman mixing condition holds for standard cubes

delay dependent robust and reliable h fuzzy hyperbolic decentralized control for uncertain nonlinear interconnected systems this paper develops the delay dependent robust and reliable h fuzzy hyperbolic control for nonlinear large scale interconnected systems with parameter uncertainties firstly the modeling method of fuzzy hyperbolic model fhm is given for the general large scale interconnected systems the main advantages of using fhm over t s fuzzy model are that neither premise structure identification nor completeness design of premise variables space is needed therefore the required computational effort is less than that of using t s fuzzy model especially when a lot of fuzzy rules are needed to model complex nonlinear systems then according to the lyapunov direct method and the decentralized control theory of large scale interconnected systems linear matrix inequality lmi based conditions with some free weighting matrices are derived which guarantee the closed loop interconnected systems to be robustly stable with the h performance even in the presence of some possible actuator failures moreover precise failure parameters of actuators are not required and the only requirements are the lower and upper bounds of failure parameters the restriction that the derivative of the time varying delay is smaller than one is removed therefore the results obtained are less conservative three simulation examples are provided to show the effectiveness of the proposed approach

stability results for collocation methods for volterra integral equations abstract stability behavior is investigated for polynomial spline collocation applied to volterra integral equations with special emphasis on a weakly singular test equation the characterization of the corresponding stability domain is related to stability results for solutions of finite recursion relations as they occur for methods applied to ordinary differential equations estimates of the stability domains are established and as a consequence conditions for a 2 stability are obtained exploiting these estimates collocation approximations with constant linear and continuous splines are considered in more depth and several numerical illustrations are presented

hypercontractivity and spectral gap of symmetric diffusions with applications to the stochastic ising models abstract we describe some results relating the spectral gap and logarithmic sobolev constants we work initially in the context of symmetric diffusions on a finite dimensional manifold and later apply our results to the analysis of certain infinite systems of mildly interacting diffusions

on the ergodic properties of glauber dynamics we show that if there is an infinite volume gibbs measure which satisfies a logarithmic sobolev inequality with local coefficients of moderate growth then the corresponding stochastic dynamics decays to equilibrium exponentially fast in the uniform norm

reliable mixed l2 h fuzzy static output feedback control for nonlinear systems with sensor faults this paper is concerned with the design of reliable mixed l 2 h static output feedback sof fuzzy controllers for nonlinear continuous time systems with complete sensor faults the takagi and sugeno t s fuzzy model is employed to represent a nonlinear system a sufficient condition for the existence of reliable mixed l 2 h sof fuzzy controllers is presented in terms of a set of quadratic matrix inequalities qmis which not only guarantees that the closed loop fuzzy system satisfies a desired h disturbance attenuation constraint for all admissible operating regimes including the normal and sensor fault cases but also provides different upper bounds on the l 2 performance criterion for different operating regimes a suboptimal reliable fuzzy controller is obtained by the proposed iterative linear matrix inequality ilmi algorithm for minimizing the normal l 2 performance bound while maintaining acceptable lower levels of the bounds in the sensor fault cases finally a numerical example is given to illustrate the effectiveness of the proposed design method

relative entropy and mixing properties of infinite dimensional diffusions let be a diffusion process taking values on the infinite dimensional space t z where t is the circle and with components satisfying the equations d i i dw i b i dt for some coefficients i and b i i z suppose we have an initial distribution and a sequence of times t n such that lim n s tn exists where s t is the semi group of the process we prove that if i and b i are bounded of finite range have uniformly bounded second order partial derivatives and inf i i 0 then is invariant

new approaches to h controller designs based on fuzzy observers for t s fuzzy systems via lmi the problems of relaxed quadratic stability conditions fuzzy observer designs and h controller designs for t s fuzzy systems have been studied first new stability conditions are obtained by relaxing the stability conditions derived in previous papers secondly new fuzzy observers based on the relaxed stability conditions for the t s fuzzy systems have been proposed thirdly two sufficient lmi conditions which guarantee the existence of the h controllers based on fuzzy observers for the t s fuzzy systems have been proposed the conditions are not only simple but also consider the interactions among the fuzzy subsystems finally by some examples using the lmi technique we show that the regulators the fuzzy observers and the h controller designs based on new observers for the t s fuzzy systems are very practical and efficient

elliptic equations for measures on infinite dimensional spaces and applications we introduce and study a new concept of a weak elliptic equation for measures on infinite dimensional spaces this concept allows one to consider equations whose coefficients are not globally integrable by using a suitably extended lyapunov function technique we derive a priori estimates for the solutions of such equations and prove new existence results as an application we consider stochastic burgers reaction diffusion and navier stokes equations and investigate the elliptic equations for the corresponding invariant measures our general theorems yield a priori estimates and existence results for such elliptic equations we also obtain moment estimates for gibbs distributions and prove an existence result applicable to a wide class of models

improved delay dependent robust stabilization conditions of uncertain t s fuzzy systems with time varying delay this paper aims to develop simplified yet improved delay dependent robust control for uncertain t s fuzzy systems with time varying delay this is achieved through constructing new lyapunov krasovskii functionals and improving jensen s inequality unlike existing work in this area the approach developed in this paper employs neither free weighing matrices nor model transformations as a result simplified yet improved stability conditions are obtained for t s fuzzy systems with norm bounded type uncertainties for controller synthesis of the fuzzy systems the stabilization problem with memoryless state feedback control is solved via utilizing a cone complementarity minimization algorithm numerical examples are given to demonstrate the effectiveness of the proposed approach

a novel approach to h_ bm infty decentralized fuzzy observer based fuzzy control design for nonlinear interconnected systems in general due to the interactions among subsystems it is difficult to design an h infin decentralized output feedback controller for nonlinear interconnected systems this study introduces h infin decentralized fuzzy observer based fuzzy control design where the premise variables depend on the state variables estimated by a fuzzy observer for nonlinear interconnected systems via t s fuzzy models the fuzzy control design for this case is more flexible but much more complex than that for the case where the premise variables depend on the state variables only a novel decoupled method is proposed in this study to transform the non linear matrix inequality non lmi conditions into some lmi forms by the proposed decoupled method the problem of h infin decentralized fuzzy observer based fuzzy control design for nonlinear interconnected systems is characterized in terms of solving an eigenvalue problem evp with five prespecified scalars for each subsystem in general it is a difficult task to solve the evp with five prespecified scalars fortunately this special evp can be easily solved by using a genetic algorithm and an lmi based optimization method finally a simulation example is given to illustrate the design procedure and robust performance of the proposed methods

the logarithmic sobolev inequality for continuous spin systems on a lattice abstract in this article we give cf theorem 1 6 a sufficient condition on a local specification for the associated gibbs state to satisfy a logarithmic sobolev inequality in the final section cf theorem 3 10 we relate our condition to the type of mixing condition introduced by dobrushin and shlosman in connection with their work on complete analyticity

approaches to quadratic stability conditions and h sub spl infin control designs for t s fuzzy systems in this paper the problems of quadratic stability conditions and h sub spl infin control designs for takagi sugeno t s fuzzy systems have been studied first a new quadratic stability condition which is more simple than that in a previous paper has been proposed second two new sufficient conditions in the terms of linear matrix inequalities lmis which guarantee the existence of the state feedback h sub spl infin control for the t s fuzzy systems have been proposed the conditions are not only simple but also consider the interactions among the fuzzy subsystems finally based on the lmis the h sub spl infin controller designing methods for the t s fuzzy systems have been given

the equivalence of the logarithmic sobolev inequality and the dobrushin shlosman mixing condition given a finite range lattice gas with a compact continuous spin space it is shown cf theorem 1 2 that a uniform logarithmic sobolev inequality cf 1 4 holds if and only if the dobrushin shlosman mixing condition cf 1 5 holds as a consequence of our considerations we also show cf theorems 3 2 and 3 6 that these conditions are equivalent to a statement about the uniform rate at which the associated glauber dynamics tends to equilibrium in this same direction we show cf theorem 3 19 that these ideas lead to a surprisingly strong large deviation principle for the occupation time distribution of the glauber dynamics

compactness and the maximal gibbs state for random gibbs fields on a lattice we prove for a general class of gibbsian random field on that the set of tempered gibbs states is compact this class contains the euclidean random fields moreover if the interaction is attractive there is a unique minimal and maximal gibbs state and are unique translation invariant ant and have the global markov property we also prove that uniqueness of the tempered gibbs state is equivalent to the magnetizationsm qx being equal which is true if the pressure is differentiable

dobrushin uniqueness theorem and logarithmic sobolev inequalities we formulate a condition on a local specification e on a countable product space m m being a riemannian manifold or a discrete set 1 1 assuring that the corresponding set of gibbs measures consists of a unique measure satisfying a logarithmic sobolev inequality

the log sobolev inequality for unbounded spin systems abstract in this note we would like to give a proof of log sobolev inequality for un bounded spin systems with weaker assumptions on the potentials than previously obtained

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

approach to equilibrium of glauber dynamics in the one phase region ii the general case we develop a new method based on renormalization group ideas block decimation procedure to prove under an assumption of strong mixing in a finite cube 0 a logarithmic sobolev inequality for the gibbs state of a discrete spin system as a consequence we derive the hypercontractivity of the markov semigroup of the associated glauber dynamics and the exponential convergence to equilibrium in the uniform norm in all volumes multiples of the cube 0

new approaches on h control of t s fuzzy systems with interval time varying delay this paper considers the delay dependent stabilization problems and h control problems for uncertain t s fuzzy system with time varying delay in a range a new method is proposed by defining new lyapunov functionals and introducing some integral inequalities the merit of the proposed conditions lies in the less conservativeness than the existing ones which is achieved by paying careful attention to the subtle difference between the two integral terms which is always ignored in the existing literatures and the free variables which replace the leibniz newton formula with integral inequalities the fuzzy state feedback gains are derived through the numerical solution of a set of linear matrix inequalities lmis the efficiency and the benefits of our method are demonstrated by the numerical examples

uniform error estimates of galerkin methods for monotone abel volterra integral equations on the half line we consider galerkin methods for monotone abel volterra integral equations of the second kind on the half line the l2 theory follows from kolodner s theory of monotone hammerstein equations we derive the loo theory from the l2 theory by relating the l2and loo spectra of operators of the form x b ax to one another here denotes convolution and b e l1 and a e loo as an extra condition we need b t o t a 1 with a 0 we also prove the discrete analogue in particular we verify that the galerkin matrix satisfies the discrete conditions

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

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

a family of methods for abel integral equations of the second kind abstract a class of methods depending on some parameters are introduced for the numerical solution of the abel integral equations of the second kind some bounds on the parameters are determined so that the corresponding methods have infinite stability intervals

stability and stabilization of fuzzy large scale systems this paper investigates the stability and stabilization problems for the fuzzy large scale system in which the system is composed of a number of takagi sugeno fuzzy model subsystems with interconnections the stability criterion of the fuzzy large scale system without control is derived first instead of fuzzy parallel distributed compensation design linear state feedback control is used in the stabilization work each local control is obtained from riccati equation of the corresponding subsystem and the interconnection terms are used to determine the local feedback gain determination based on lyapunov criterion some conditions are derived under which the whole fuzzy large scale system is stabilized asymptotically a numerical example is given to illustrate the control design procedure and its effectiveness

a perspective on the numerical treatment of volterra equations abstract we discuss the properties and numerical treatment of various types of volterra and abel volterra integral and integro differential equations

reliable rm h_infty fuzzy control for continuous time nonlinear systems with actuator failures this paper is concerned with the design of reliable hinfin fuzzy controllers for continuous time nonlinear systems with actuator failures the takagi and sugeno fuzzy model is employed to represent a nonlinear system the objective is to find a stabilizing state feedback fuzzy controller such that the nominal hinfin performance is optimized while satisfying a prescribed hinfin performance constraint in the actuator failure cases based on the linear matrix inequality lmi techniques two efficient methods for the design of a suboptimal reliable hinfin fuzzy controller are proposed different lyapunov functions are used during the design for the nominal and actuator failure cases which lead to a less conservative controller design in the first method a single lyapunov function is used for the actuator failure cases the second method adopts a parameter dependent lyapunov function for the actuator failure cases which further reduces the conservatism of the design finally numerical simulations on the chaotic rossler system are given to illustrate the effectiveness of the proposed design methods

regularity of invariant measures the case of non constant diffusion part we prove regularity i e smoothness of measures on rdsatisfying the equationl 0 wherelis an operator of typelu tr au b u hereais a lipschitz continuous uniformly elliptic matrix valued map andbis merely square integrable we also treat a class of corresponding infinite dimensional cases where rdis replaced by a locally convex topological vector spacex in this cases is proved to be absolutely continuous w r t a gaussian measure onxand the square root of the radon nikodym density belongs to the malliavin test function space d2 1

reversibility in infinite hamiltonian systems with conservative noise the set of stationary measures of an infinite hamiltonian system with noise is investigated the model consists of particles moving in r 3 with bounded velocities and subject to a noise that does not violate the classical laws of conservation see ovy following lo we assume that the noise has also a finite radius of interaction and prove that translation invariant stationary states of finite specific entropy are reversible with respect to the stochastic component of the evolution therefore the results of lo imply that such invariant measures are superpositions of gibbs states

invariance implies gibbsian some new results we investigate stationary distributions of stochastic gradient systems in riemannian manifolds and prove that under certain assumptions such distributions are symmetric these results are extended to countable products of finite dimensional manifolds and applied to gibbs distributions in the case where the single spin spaces are riemannian manifolds in particular we obtain a new result concerning the question whether all invariant measures are gibbsian actually we consider a more general object weak elliptic equations for measures which on the one hand yields the results obtained stronger than the above mentioned statements and on the other hand enables us to give simpler proofs of more general than previously known facts applications to concrete models of lattice systems over d with not necessarily compact spin space are presented also in the case d 3 under certain assumptions of decay of interaction