effective digital implementation of fuzzy control systems based on approximate discrete time models this paper addresses an effective digital implementation of fuzzy control systems via an intelligent digital redesign idr approach the purpose of idr is to effectively convert an existing continuous time fuzzy controller to an equivalent sampled data fuzzy controller in the sense of the state matching the authors show that under reasonable assumptions the idr based on the exact discrete time models can be reduced to the idr based on the approximate discrete time models the state matching error between the closed loop trajectories is carefully analyzed using the integral quadratic functional approach the estimation of the state matching error is presented using the linear matrix inequality lmi techniques the problem of designing the sampled data fuzzy controller to minimize the estimation as well as to guarantee the stability is formulated and solved as the convex optimization problem with lmi constraints it is also shown that the resulting sampled data fuzzy controller recovers the performance of the continuous time fuzzy controller as the sampling period approaches zero a numerical example is used to demonstrate the effectiveness of the proposed design technique

design of a polynomial fuzzy observer controller with sampled output measurements for nonlinear systems considering unmeasurable premise variables in this paper we propose a polynomial fuzzy observer controller for nonlinear systems where the design is achieved through the stability analysis of polynomial fuzzy model based pfmb observer control system the polynomial fuzzy observer estimates the system states using estimated premise variables the estimated states are then employed by the polynomial fuzzy controller for the feedback control of nonlinear systems represented by the polynomial fuzzy model the system stability of the pfmb observer control system is analyzed based on the lyapunov stability theory although using estimated premise variables in polynomial fuzzy observer can handle a wider class of nonlinear systems it leads to a significant drawback that the stability conditions obtained are nonconvex matrix decoupling technique is employed to achieve convex stability conditions in the form of sum of squares we further extend the design and analysis to polynomial fuzzy observer controller using a sampled data technique for nonlinear systems where only sampled output measurements are available simulation examples are presented to demonstrate the feasibility and validity of the design and analysis results

scalar curvature and projective embeddings i we prove that a metric of constant scalar curvature on a polarised kahler manifold is the limit of metrics induced from a specific sequence of projective embeddings satisfying a condition introduced by h luo this gives as a corollary the uniqueness of constant scalar curvature kahler metrics in a given rational cohomology class the proof uses results in the literature on the asymptotics of the bergman kernel the arguments are presented in a general framework involving moment maps for two different group actions

on the decomposition of global conformal invariants i this is the first of two papers where we address and partially confirm a conjecture of deser and schwimmer originally postulated in high energy physics the objects of study are scalar riemannian quantities constructed out of the curvature and its covariant derivatives whose integrals over compact manifolds are invariant under conformal changes of the underlying metric our main conclusion is that each such quantity that locally depends only on the curvature tensor without covariant derivatives can be written as a linear combination of the chern gauss bonnet integrand and a scalar conformal invariant

cr invariants of weight five in the bergman kernel abstract fefferman s program 1979 c fefferman adv math 31 131 262 of getting a biholomorphically invariant asymptotic expansion of the bergman kernel for smoothly bounded strictly pseudoconvex domains is realized in dimension 2 with the identification of universal constants according to the program the expansion is in terms of an approximately invariant smooth defining function of the domain which we refer to as fefferman s defining function and the coefficients are functions in the domain constructed by using derivatives of fefferman s defining function consequently the invariant expansion is necessarily a finite sum with a remainder term and the ambiguity estimate is crucial in the problem we get an expansion such that the boundary values of the coefficients are cr invariants of weight 5 this refines earlier results of c r graham 1987 in lecture notes in math vol 1276 pp 108 135 springer verlag new york berlin and the authors 1993 k hirachi g komatsu and n nakazawa in lecture notes in pure and appl math vol 143 pp 77 96 dekker new york the refinement becomes possible by appropriate extensions inside the domain of the cr invariants of weight 4 due to the ambiguity estimate of these extensions our expansion is optimal as far as fefferman s defining function is used a similar result for the szego kernel is also obtained

sampled data h h fault detection and isolation for nonlinear systems in t s form a direct discrete time design methodology for the sampled data fault detection and isolation fdi problem is proposed for a nonlinear system in takagi sugeno form the generalized observer scheme is adopted accompanied by a bank of the sensors number of observers a sufficient condition to find observer and residual gains based on an accessible approximate rather than unavailable exact discrete time model is proposed in terms of matrix inequalities so that it exhibits h h performance and asymptotic stability an algorithm involving a convex optimization is presented using the cone complementary linearization technique we show that the fdi observer ensures modified h h performance and lagrange stability when it is connected to the actual nonlinear system

stabilization of a class of underactuated mechanical systems via interconnection and damping assignment we consider the application of a formulation of passivity based control pbc known as interconnection and damping assignment ida to the problem of stabilization of underactuated mechanical systems which requires the modification of both the potential and the kinetic energies our main contribution is the characterization of a class of systems for which ida pbc yields a smooth asymptotically stabilizing controller with a guaranteed domain of attraction the class is given in terms of solvability of certain partial differential equations one important feature of ida pbc stemming from its hamiltonian formulation is that it provides new degrees of freedom for the solution of these equations using this additional freedom we are able to show that the method of controlled lagrangians in its original formulation may be viewed as a special case of our approach as illustrations we design asymptotically stabilizing ida pbcs for the classical ball and beam system and a novel inertia wheel pendulum

integral kahler invariants and the bergman kernel asymptotics for line bundles abstract on a compact kahler manifold one can define global invariants by integrating local invariants of the metric assume that a global invariant thus obtained depends only on the kahler class then we show that the integrand can be decomposed into a chern polynomial the integrand of a chern number and divergences of one forms which do not contribute to the integral we apply this decomposition formula to describe the asymptotic expansion of the bergman kernel for positive line bundles and to show that the cr q curvature on a sasakian manifold is a divergence

positive solutions of the dirichlet problem for the prescribed mean curvature equation in minkowski space abstract we prove the existence of multiple positive solutions of the dirichlet problem for the prescribed mean curvature equation in minkowski space div u 1 u 2 f x u u in u 0 on here is a bounded regular domain in r n and the function f f x s is either sublinear or superlinear or sub superlinear near s 0 the proof combines topological and variational methods

determination of a riemannian metric from the first variation of its spectrum on determine la metrique g par une etude du comportement d ordre 1 du spectre sous perturbations de la metrique inconnue g par des 2 tenseurs covariants symetriques connus

brief paper fault tolerant control for a class of nonlinear sampled data systems via a euler approximate observer in this paper a fault tolerant control ftc scheme is developed for a class of nonlinear sampled data systems first a euler approximate discrete model is used to describe the plant under the sampling under this model an observer based fault estimation method is proposed to guarantee the accuracy of both the state and fault estimation values the conditions to make the approximate model consistent with the exact model are presented then an active fault tolerant controller which has a constraint condition for the sampling time is designed to make the faulty system stable finally an inverted pendulum is used to show the efficiency of the proposed method

sampled data h fuzzy filtering for nonlinear systems with missing measurements in this paper a sampled data h fuzzy filtering problem is considered for nonlinear systems with missing measurements the nonlinear sampled data system and missing measurements are assumed to be represented by a takagisugeno ts fuzzy system and an independent identically distributed bernoulli random process respectively based on the fuzzy system the h fuzzy filtering problem is formulated to design the sampled data fuzzy filter by using the exponential mean square stability definition the stability condition with an h performance is guaranteed for the fuzzy system with the sampled data fuzzy filter and its sufficient condition is converted into the linear matrix inequality lmi format finally an example is provided to verify the effectiveness of the proposed fuzzy filtering technique

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

logarithmic singularity of the szego kernel and a global invariant of strictly pseudoconvex domains this paper is a continuation of fefferman s program 7 for studying the geometry and analysis of strictly pseudoconvex domains the key idea of the program is to consider the bergman and szeg kernels of the domains as analogs of the heat kernel of riemannian manifolds in riemannian or confor mai geometry the coefficients of the asymptotic expansion of the heat kernel can be expressed in terms of the curvature of the metric by integrating the co efficients one obtains index theorems in various settings for the bergman and szeg kernels there has been much progress made on the description of their asymptotic expansions based on invariant theory 7 1 15 we now seek for invariants that arise from the integral of the coefficients of the expansions we here prove that the integral of the coefficient of the logarithmic sin gularity of the szeg kernel gives a biholomorphic invariant of a domain ft or a cr invariant of the boundary dft and moreover that the invariant is un changed under perturbations of the domain theorem 1 we also show that the same invariant appears as the coefficient of the logarithmic term of the volume expansion of the domain with respect to the bergman volume element theorem 2 this second result is an analogue of the derivation of a conformai invariant from the volume expansion of conformally compact einstein mani folds which arises in the ads cft correspondence see 10 for a discussion and references the proofs of these results are based on kashiwara s microlocal analysis of the bergman kernel in 17 where he showed that the reproducing prop erty of the bergman kernel on holomorphic functions can be quantized to a reproducing property of the microdifferential operators i e classical ana lytic pseudodifferential operators this provides a system of microdifferential equations that characterizes the singularity of the bergman kernel which can be formulated as a microfunction up to a constant multiple such an argument

adaptive observers for ts fuzzy systems with unknown polynomial inputs a large class of nonlinear systems can be well approximated by takagi sugeno ts fuzzy models with linear or affine consequents however in practical applications the process under consideration may be affected by unknown inputs such as disturbances faults or unmodeled dynamics in this paper we consider the problem of simultaneously estimating the state and unknown inputs in ts systems the inputs considered in this paper are 1 polynomials in time such as a bias in the model or an unknown ramp input acting on the model and 2 unmodeled dynamics the proposed observer is designed based on the known part of the fuzzy model conditions on the asymptotic convergence of the observer are presented and the design guarantees an ultimate bound on the error signal the results are illustrated on a simulation example

observer based h_ infty sampled data fuzzy control for a class of nonlinear parabolic pde systems in this paper an observer based h infty sampled data fuzzy control problem is addressed for a class of nonlinear parabolic partial differential equation pde systems with the aid of the modal decomposition technique a nonlinear ordinary differential equation ode model is initially derived to describe the dominant slow dynamics of the pde system subsequently the resulting nonlinear ode model is accurately represented by the takagi sugeno t s fuzzy model then based on the t s fuzzy model a finite dimensional observer based sampled data fuzzy control design with h infty performance is developed for the pde system via employing a novel time dependent functional the outcome of the observer based h infty sampled data fuzzy control problem can be formulated as a bilinear matrix inequality optimization problem moreover an iterative optimization algorithm based on the linear matrix inequalities is given to obtain a suboptimal h infty sampled data fuzzy controller finally simulation results on the fisher equation and a temperature cooling fin of high speed aerospace vehicle illustrate that the proposed design method is effective

sampled data observer based output feedback fuzzy stabilization of nonlinear systems exact discrete time design approach this paper presents a new direct discrete time design methodology of a sampled data observer based output feedback fuzzy controller for a class of nonlinear system that is exactly modeled in takagi sugeno s form at least locally a fundamental yet challenging issue in this direction is the unavailability of the exact discrete time model of the nonlinear plant in a closed form in contrast to the earlier works that are based on an approximate discrete time model thus the stability obtained in the design step is not preserved in the implementation step we employ an exact discrete time fuzzy model in an integral form sufficient asymptotic stabilization conditions are investigated in the discrete time lyapunov sense we then show that the resulting sampled data controller indeed asymptotically stabilizes the nonlinear plant an example is provided to illustrate the effectiveness of the proposed methodology

nonconstant positive radial solutions for neumann problem involving the mean extrinsic curvature operator abstract let b be the unit ball in r n with n 2 let f c 1 0 r f 0 0 f for some 0 f s s for s 0 f s s for s and f k r where k r is the k th radial eigenvalue of i in the unit ball with neumann boundary condition we use the unilateral global bifurcation theorem to show the existence of nonconstant positive radial solutions of the quasilinear neumann problem div u 1 u 2 u f u in b u 0 on b

on the lower order terms of the asymptotic expansion of tian yau zelditch we compute the first three coefficients of the asymptotic expansion of tian yau zelditch we also prove that in general the fcth coefficient is a polynomial of the curvature and its derivative of weight k

brief paper stability connection between sampled data fuzzy control systems with quantization and their approximate discrete time model this paper concerns the stability of a sampled data takagi sugeno t s fuzzy control system with quantization when a controller design is based on an approximate discrete time model of the plant without quantization the motivations come from the facts that digital devices for interfacing a plant with a controller quantize signals and an exact discrete time model of the t s fuzzy system is generally not amenable to synthesis process we show that the concerned system is lagrange stabilizable by the controller asymptotically stabilizing the approximate discrete time model a constructive design algorithm for the developed stability analysis is proposed in terms of linear matrix inequalities

fuzzy dynamic output feedback control through nonlinear takagi sugeno models we present a convex way to design a fuzzy dynamic output feedback compensator for locally stabilizing a class of nonlinear discrete time systems this class consists of the systems described by takagi sugeno t s models with a sector bounded nonlinear additive term and saturated control signals the local stabilization takes into account the domain of validity of these t s models which is a key issue for practical applications two types of nonlinear fuzzy compensators are considered one having all matrices of the controller depending on fuzzy grade membership functions and the other with only a subset of the matrices with such a dependency the controller design includes a fuzzy anti windup gain that handles saturating actuators besides a time performance index based on the contractivity of the level set of the fuzzy lyapunov function is proposed regarding the closed loop system examples are given to illustrate the effectiveness of this proposal

brief paper robust sampled data h control with stochastic sampling in this paper the problem of robust h control is investigated for sampled data systems with probabilistic sampling the parameter uncertainties are time varying norm bounded and appear in both the state and input matrices for the simplicity of technical development only two different sampling periods are considered whose occurrence probabilities are given constants and satisfy bernoulli distribution which can be further extended to the case with multiple stochastic sampling periods by applying an input delay approach the probabilistic sampling system is transformed into a continuous time delay system with stochastic parameters in the system matrices by linear matrix inequality lmi approach sufficient conditions are obtained which guarantee the robust mean square exponential stability of the system with an h performance moreover an h controller design procedure is then proposed an illustrative example is included to demonstrate the effectiveness of the proposed techniques

invariants of conformal laplacians the conformal laplacian d d d n 2 s 4 n 1 acting on functions on a riemannian manifold mn with scalar curvature s is a conformally invariant operator in this paper we will use d to construct new conformal invariants one of these is a pointwise invariant one is the integral of a local expression and one is a nonlocal spectral invariant derived from functional determinants we begin in 1 by describing the laplacian d and its green function in the context of conformal geometry we then derive a basic formula giving the variation in the heat kernel of d this formula is strikingly simpler than the corresponding formula for the ordinary laplacian given by ray and singer 15 the heat kernel of d has an asymptotic expansion k t x x 4 t n 2 ak x tk in 2 we prove that a n 2 2 is a pointwise conformal invariant of weight 2 i e it satisfies a n 2 2 x 2g 2a n 2 2 x g where g is the metric and is any smooth positive function in particular this shows the existence of a nontrivial locally computable conformally invariant density naturally associated to the conformal structure of an even dimensional manifold the key to the proof is to consider the parametrix of the green s function which is obtained from the heat kernel by an integral transform one finds that a n 2 2 occurs as the coefficient of the first log term in this parametrix and its conformal invariance then follows directly from the conformal invariance of the green s function in 3 we show that an 2 is a global conformal invariant the calculations in 4 show that it is not a pointwise invariant the proof is a direct calculation of the invariant of an 2 using equation 1 10

decentralized sampled data fuzzy observer design for nonlinear interconnected systems this paper presents the decentralized sampled data fuzzy observer design techniques for nonlinear interconnected systems which are assumed to be composed of fuzzy subsystems and unknown interconnections to design the decentralized fuzzy observer the estimation error dynamics is obtained and the performance function is defined based on the estimation error dynamics and the performance function the continuous time decentralized fuzzy observer is first proposed to minimize the interconnection bound to attenuation degree ratio in addition the decentralized sampled data fuzzy observers are designed by using the approximate discretization and the exact discrete time design approaches respectively each proposed observer design technique is formulated into the optimal problems with the linear matrix inequalities finally several simulation examples show the validity and superiority of the proposed observer design techniques by comparing with the conventional techniques

decentralized sampled data h fuzzy filter for nonlinear large scale systems this paper presents a decentralized sampled data h fuzzy filter design method for nonlinear large scale systems which are represented by a takagi sugeno t s fuzzy model based on the t s fuzzy model the error system between the nonlinear large scale system and the filter is obtained the discretization process of the error system is accomplished with the exact discrete time approach to eliminate the exact approximate mismatch by using the discrete time lyapunov sense the sufficient condition of the asymptotic stability for the error system is given and a prescribed level of the h norm is ensured to guarantee the h fuzzy filter performance finally numerical examples are given to show the effectiveness of the proposed methods

sampled data fuzzy stabilization of nonlinear systems under nonuniform sampling this paper investigates the sampled data fuzzy stabilization problem for a class of nonlinear systems that is exactly modeled in takagi sugeno fuzzy form at least locally a new method for designing parallel distribution compensation fuzzy controller is proposed which just requires that the nonlinear function is locally lipschitz by considering the sample and hold behavior of the system and using jensen s integral inequality an inequality constrain condition is derived from the locally lipschitz property further by defining a time dependent lyapunov krasovskii functional term a new technique instead of the use of s procedure is developed and stabilization conditions for state feedback and observer based output feedback under nonuniform sampling are obtained compared with the existing ones the new design method not only avoids the difficulty of finding exact upper bounds of asynchronous errors of mismatch membership functions but contains less conservatism and less numerical complexity as well finally some illustrative examples are given to show the effectiveness of the proposed design method and the significant improvement over the existing results

radial positive solutions of elliptic systems with neumann boundary conditions abstract we consider radial solutions of elliptic systems of the form u u a x f u v in b r v v b x g u v in b r u v 0 on b r where essentially a b are assumed to be radially nondecreasing weights and f g are nondecreasing in each component with few assumptions on the nonlinearities we prove the existence of at least one couple of nondecreasing nontrivial radial solutions we emphasize that we do not assume any variational structure nor subcritical growth on the nonlinearities our result covers systems with supercritical as well as asymptotically linear nonlinearities

technical communique further studies on lmi based relaxed stabilization conditions for nonlinear systems in takagi sugeno s form this paper further studies stabilization of nonlinear systems represented by a takagi sugeno t s discrete fuzzy model by extending a nonquadratic lyapunov function and applying a nonparallel distributed compensation non pdc law a new stabilization conclusion is presented that is a generalization of some previous results in the literature the new conclusion under a special situation is also suitable for a pdc law which presents to be more relaxed than some existing results an example is provided to demonstrate the effectiveness of the new conclusions

fuzzy regulators and fuzzy observers relaxed stability conditions and lmi based designs this paper presents new relaxed stability conditions and lmi linear matrix inequality based designs for both continuous and discrete fuzzy control systems they are applied to design problems of fuzzy regulators and fuzzy observers first takagi and sugeno s fuzzy models and some stability results are recalled to design fuzzy regulators and fuzzy observers nonlinear systems are represented by takagi sugeno s ts fuzzy models the concept of parallel distributed compensation is employed to design fuzzy regulators and fuzzy observers from the ts fuzzy models new stability conditions are obtained by relaxing the stability conditions derived in previous papers lmi based design procedures for fuzzy regulators and fuzzy observers are constructed using the parallel distributed compensation and the relaxed stability conditions other lmi s with respect to decay rate and constraints on control input and output are also derived and utilized in the design procedures design examples for nonlinear systems demonstrate the utility of the relaxed stability conditions and the lmi based design procedures

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

global structure of radial positive solutions for a prescribed mean curvature problem in a ball abstract in this paper we are concerned with the global structure of radial positive solutions of boundary value problem div n v f x v 0 in b r v 0 on b r where n y y 1 y 2 y r n is a positive parameter b r x r n x r and denotes the euclidean norm in r n all results depending on the behavior of nonlinear term f near 0 are obtained by using global bifurcation techniques

new approaches to relaxed quadratic stability condition of fuzzy control systems this paper deals with the quadratic stability conditions of fuzzy control systems that relax the existing conditions reported in the previous literatures two new conditions are proposed and shown to be useful in analyzing and designing fuzzy control systems the first one employs the s procedure to utilize information regarding the premise parts of the fuzzy systems the next one enlarges the class of fuzzy control systems whose stability is ensured by representing the interactions among the fuzzy subsystems in a single matrix and solving it by linear matrix inequality the relationships between the suggested stability conditions and the conventional well known stability conditions reported in the previous literatures are also discussed and it is shown in a rigorous manner that the second condition of this paper includes the conventional conditions finally some examples and simulation results are presented to illustrate the effectiveness of the stability conditions

existence and multiplicity results for some nonlinear problems with singular phi laplacian using leray schauder degree theory we obtain various existence and multiplicity results for nonlinear boundary value problems phi u f t u u l u u 0 where l u u 0 denotes the dirichlet periodic or neumann boundary conditions on 0 t phi a a r is an increasing homeomorphism phi 0 0 the difichlet problem is always solvable for neumann or periodic boundary conditions we obtain in particular existence conditions for nonlinearities which satisfy some sign conditions upper and lower solutions theorems ambrosetti prodi type results we prove lazer solimini type results for singular nonlinearities and periodic boundary conditions c 2007 elsevier inc all rights reserved

observer based robust fuzzy control of nonlinear systems with parametric uncertainties this paper addresses the robust fuzzy control problem for nonlinear systems in the presence of parametric uncertainties and the state variables unavailable for measurement the takagi sugeno t s fuzzy model system with parametric uncertainties is adopted for modeling the nonlinear system and establishing fuzzy state observer sufficient conditions are derived for robust stabilization in the sense of lyapunov asymptotic stability and are formulated in the format of linear matrix inequalities lmis the effectiveness of the proposed fuzzy controller and fuzzy observer design methodology is finally demonstrated through numerical simulations on an inverted pendulum system

the log term of the szego kernel in this paper we study the relations between the log term of the szego kernel of the unit circle bundle of the dual line bundle of an ample line bundle over a compact kahler manifold we prove a local rigidity theorem the result is related to the classical ramadanov conjecture

stabilization of nonlinear systems under variable sampling a fuzzy control approach this paper investigates the problem of stabilization for a takagi sugeno t s fuzzy system with nonuniform uncertain sampling the sampling is not required to be periodic and the only assumption is that the distance between any two consecutive sampling instants is less than a given bound by using the input delay approach the t s fuzzy system with variable uncertain sampling is transformed into a continuous time t s fuzzy system with a delay in the state though the resulting closed loop state delayed t s fuzzy system takes a standard form the existing results on delay t s fuzzy systems cannot be used for our purpose due to their restrictive assumptions on the derivative of state delay a new condition guaranteeing asymptotic stability of the closed loop sampled data system is derived by a lyapunov approach plus the free weighting matrix technique based on this stability condition two procedures for designing state feedback control laws are given one casts the controller design into a convex optimization by introducing some over design and the other utilizes the cone complementarity linearization idea to cast the controller design into a sequential minimization problem subject to linear matrix inequality constraints which can be readily solved using standard numerical software an illustrative example is provided to show the applicability and effectiveness of the proposed controller design methodology

on the decomposition of global conformal invariants ii abstract this paper is a continuation of s alexakis the decomposition of global conformal invariants i submitted for publication see also math dg 0509571 where we complete our partial proof of the deser schwimmer conjecture on the structure of global conformal invariants our theorem deals with such invariants p g n that locally depend only on the curvature tensor r i j k l without covariant derivatives in s alexakis the decomposition of global conformal invariants i ann of math in press we developed a powerful tool the super divergence formula which applies to any riemannian operator that always integrates to zero on compact manifolds in particular it applies to the operator i g n that measures the non conformally invariant part of p g n this paper resolves the problem of using this information we have obtained on the structure of i g n to understand the structure of p g n

technical communique theoretical justification of approximate norm minimization method for intelligent digital redesign this paper investigates the theoretical justification of intelligent digital redesign idr methods based on the approximate discrete time models its main purpose is to design the digital fuzzy controller achieving the minimum norm distance between the trajectories of the approximate closed loop systems under the analog and the digital controls it is verified that if there exist the digital gains such that the approximate norm distance is sufficiently small the redesigned controller makes the trajectories of the exact closed loop systems close or at least asymptotically stabilizes the plant

digitalizing a fuzzy observer based output feedback control intelligent digital redesign approach this paper concerns an intelligent digital redesign idr technique for a takagi sugeno fuzzy observer based output feedback control fobofc system the term idr involves converting an existing analog control into an equivalent digital counterpart in the sense of state matching the idr problem is herein viewed as a minimization problem of the norm distances between nonlinearly interpolated linear operators to be matched its constructive condition with global rather than local state matching is formulated in terms of bilinear matrix inequalities the main features of the proposed method are that the state estimation error in the plant dynamics is considered in the idr condition that plays a crucial role in the performance improvement the stability property is preserved by the proposed idr algorithm the separation principle is shown when the premise variables are measurable finally the idr condition for a more general fobofc an estimated premise variable case is conducted a numerical example is demonstrated to visualize the feasibility of the developed methodology

a closed formula for the asymptotic expansion of the bergman kernel we prove a graph theoretic closed formula for coefficients in the tian yau zelditch asymptotic expansion of the bergman kernel the formula is expressed in terms of the characteristic polynomial of the directed graphs representing weyl invariants the proof relies on a combinatorial interpretation of a recursive formula due to m englis and a loi

intelligent digital redesign revisited approximate discretization and stability limitation this paper sharpens the recently developed intelligent digital redesign idr technique in regard of stability a major assumption in the previous result was that the firing strength of each fuzzy rule is approximated as its sampled value during a sampling period for efficient discretization of the takagi sugeno t s fuzzy system by which some unexpected stability might be experienced for certain sampling period as large as the assumption is unrealistic to clarify results for that case we refine the idr condition and prove that the uniformly semiglobal practical asymptotic stability of the sampled data t s fuzzy control system by the intelligently redesigned digital fuzzy controller rather than the global exponential stability shown in the previous result

a new discrete time robust stability condition a new robust stability condition for uncertain discrete time systems with convex polytopic uncertainty is given it enables to check stability using parameter dependent lyapunov functions which are derived from lmi conditions it is shown that this new condition provides better results than the classical quadratic stability besides the use of a parameter dependent lyapunov function this condition exhibits a kind of decoupling between the lyapunov and the system matrices which may be explored for control synthesis purposes a numerical example illustrates the results

spacelike hypersurfaces with prescribed boundary values and mean curvature we consider the boundary value problem for the mean curvature operator in minkowski space and give necessary and sufficient conditions for the existence of smooth strictly spacelike solutions our main results hold for non constant mean curvature and make no assumptions about the smoothness of the boundary or boundary data

the variation of the de rham zeta function calcul de la variation des valeurs speciales de la fonction zeta de de rham par rapport a la variation de la metrique etablissement de l equation d euler lagrange pour les variations conformes

semiclassical yang mills theory i instantons the partition functions of quantum yang mills theory have an expansion in powers of the coupling constant the leading order term in this expansion is called the semiclassical approximation we study the semiclassical approximation for yang mills theory on a compact riemannian 4 manifold using geometric techniques and do explicit calculations for the case when the manifold is the 4 sphere this involves calculating the riemannian measure and certain functional determinants on the moduli space of self dual connections the main result is that the contribution to the semiclassical partition functions coming from thek 1 connections on the 4 sphere isfinite andcalculable we also discuss a renormalization procedure in which the radius of the 4 sphere is allowed to tend to infinity

lmi based relaxed nonquadratic stabilization conditions for nonlinear systems in the takagi sugeno s form this paper presents the stabilization analysis for a class of nonlinear systems that are represented by a takagi and sugeno ts discrete fuzzy model takagi and sugeno ieee trans systems man cybern 15 1 1985 116 the main result given here concerns their stabilization using new control laws and new nonquadratic lyapunov functions new relaxed conditions and linear matrix inequality based design are proposed that allow outperforming previous results found in the literature two examples are also provided to demonstrate the efficiency of the approaches

ground state solution for a problem with mean curvature operator in minkowski space abstract in this paper we prove the existence of a radial ground state solution for a quasilinear problem involving the mean curvature operator in minkowski space

a new intelligent digital redesign for t s fuzzy systems global approach this paper proposes a novel and efficient global intelligent digital redesign technique for a takagi sugeno t s fuzzy system the term of intelligent digital redesign involves converting an existing analog fuzzy model based controller into an equivalent digital counterpart in the sense of state matching the proposed method should be notably discriminated from the previous works in that it allows us to globally match the states of the overall closed loop t s fuzzy system with the predesigned analog fuzzy model based controller and those with the digitally redesigned fuzzy model based controller and further to examine the stabilizability by the redesigned controller in the sense of lyapunov the key idea is that the global intelligent digital redesign problem is viewed as a convex minimization problem of the norm distance between nonlinearly interpolated linear operators to be matched sufficient conditions for the global state matching and the stability of the digitally controlled system are formulated in terms of linear matrix inequalities lmis a complex nonlinear system duffing like chaotic oscillator is simulated and demonstrated to validate the feasibility and effectiveness of the proposed digital redesign technique which implies the safe applicability to the digital control system