generation of converging regge pole bounds a new formulation of complex rotation quantization we propose an unprecedented bounding theory which generates converging bounds to the regge poles of rational fraction scattering potentials this is made possible by the recent work of handy 2001 j phys a math gen 34 l271 and handy and wang 2001 j phys a math gen 34 8297 which transforms the schrodinger equation into an equivalent fourth order linear differential equation for the probability density this new representation is better suited for numerical considerations since the rapid oscillations of the regge pole wavefunction are factored out more importantly the moments of the probability density can be constrained and thereby the underlying complex angular momentum parameter of the effective potential function through appropriate moment problem theorems as incorporated within the eigenvalue moment method of handy and bessis 1985 phys rev lett 55 931 and handy et al 1988 phys rev lett 60 253

three dimensional vibrations of thick circular and annular plates abstract the ritz method is applied in a three dimensional 3 d analysis to obtain accurate frequencies for thick circular and annular plates the method is formulated in a manner which allows one to have any combination of free or fixed plate boundaries admissible functions for the three displacement components are chosen as trigonometric functions in the circumferential co ordinate and algebraic polynomials in the radial and axial co ordinates upper bound convergence of the non dimensional frequencies to at least four significant figures is demonstrated comparisons of results are made with ones obtained by others using 2 d mindlin thick plate theory and with other 3 d solutions extensive and accurate four significant figure frequencies are presented for completely free circular plates having thickness to diameter ratios of 0 2 0 3 0 4 and 0 5 for poisson s ratios 0 0 3 and 0 499 frequencies are also given for thick annular plates having a thickness to outer diameter of 0 2 inside to outside diameter ratios of 0 1 0 5 and 0 9 and 0 3 all 3 d modes are included in the analyses e g flexural thickness shear in plane stretching and torsional the circular and annular plate frequency data given is exact to at least four digits thus being benchmark data against which results from 2 d thick plate theories or other approximate methods e g finite elements may be compared

technical communique improvement on observer based h control for t s fuzzy systems this paper provides an improved result over that in liu and zhang 2003 new approaches to h controller designs based on fuzzy observers for t s fuzzy systems via lmi automatica 39 1571 1582 for the problem of observer based h control for nonlinear systems in takagi sugeno t s fuzzy model it contributes in three aspects i the present result is less conservative than that in liu and zhang 2003 new approaches to h controller designs based on fuzzy observers for t s fuzzy systems via lmi automatica 39 1571 1582 ii the present strict lmi method is a single step approach which overcomes the drawback of a two step approach in liu and zhang 2003 new approaches to h controller designs based on fuzzy observers for t s fuzzy systems via lmi automatica 39 1571 1582 iii the matrix dimensions are largely reduced compared with the corresponding ones in liu and zhang 2003 new approaches to h controller designs based on fuzzy observers for t s fuzzy systems via lmi automatica 39 1571 1582

fault detection for uncertain fuzzy systems an lmi approach this paper studies the problem of designing a robust fault detection system for uncertain takagi sugeno fuzzy models the worst case fault sensitivity measure is formulated in terms of linear matrix inequalities the existence of a robust fault detection system that guarantees i the l2 gain from a fault signal to a residual signal greater than a prescribed value and ii the l2 gain from an exogenous input to a residual signal less than a prescribed value is given in terms of the solvability of linear matrix inequalities numerical examples are used to illustrate the effectiveness of the proposed design techniques

h output feedback control design for uncertain fuzzy singularly perturbed systems an lmi approach this paper examines the problem of designing a robust h output feedback controller for a class of singularly perturbed systems described by a takagi sugeno fuzzy model based on a linear matrix inequality lmi approach lmi based sufficient conditions for the uncertain singularly perturbed nonlinear systems to have an h performance are derived to eliminate the ill conditioning caused by the interaction of slow and fast dynamic modes solutions to the problem are presented in terms of lmis which are independent of the singular perturbation the proposed approach does not involve the separation of states into slow and fast ones and it can be applied not only to standard but also to nonstandard singularly perturbed nonlinear systems a numerical example is provided to illustrate the design developed in this paper

parity space based fault detection for linear discrete time varying systems with unknown input in this paper a new approach to parity space based fault detection fd is put forward for linear discrete time varying ldtv systems the focus of our study is on solving the problem with heavy online computational burden the main contributions are two folds firstly the problem of parity space based fd is formulated as finding a minimum of quadratic form of unknown input secondly by applying projection in krein space a solution of optimal parity space based fd is obtained via recursively computing innovations it is shown that the reduction of computation cost is achievable especially with the increase of parity space order finally a numerical example is given to demonstrate the application of the proposed method

3d symplectic expansion for piezoelectric media the symplectic series expansion method is extended to three dimensional problem for transversely isotropic piezoelectric media the governing equations are first derived in hamiltonian form and symplectic eigensolutions are directly obtained through analytical method all solutions of the problem are reduced to finding eigenvalues and eigensolutions the classical st venant solutions are described by zero eigensolutions and the localized solutions are depicted by non zero eigensolutions symplectic relationships of the ortho normalization are used end conditions are rewritten by eigensolutions and a numerical scheme is formed analytically some numerical examples are given copyright 2007 john wiley sons ltd

fuzzy filter design for ito stochastic systems with application to sensor fault detection the paper deals with the robust fault detection problem for takagi sugeno t s fuzzy ito stochastic systems our aim is to develop a robust fault detection approach to the t s fuzzy systems with brownian motion by using a general observer based fault detection filter as a residual generator the robust fault detection is formulated as a filtering problem attention is focused on the design of both the fuzzy rule independent and the fuzzy rule dependent fault detection filters guaranteeing a prescribed noise attenuation level in an hinfin sense sufficient conditions are proposed to guarantee the mean square asymptotic stability with an hinfin performance for the fault detection system the corresponding solvability conditions for the desired fuzzy rule independent and fuzzy rule dependent fault detection filters are also established finally a numerical example is provided to illustrate the effectiveness of the proposed theory

generating converging bounds to the complex discrete states of the p2 ix3 iαx hamiltonian the eigenvalue moment method emm is applied to the h p2 ix3 i x hamiltonian enabling the algebraic numerical generation of converging bounds to the complex energies of the l2 states as argued through asymptotic methods by delabaere and trinh the robustness of the formalism and its computational implementation suggest that the present non negativity formulation implicitly contains the key algebraic relations by which to prove bessis conjecture that the eigenenergies of the h0 hamiltonian are real the required algebraic analysis of the emm procedure pertaining to this problem will be presented in a forthcoming paper

adaptive reliable h_ infty filtering against sensor failures this paper is concerned with the adaptive reliable hinfin filtering problem against sensor failures for continuous time linear systems an adaptive hinfin performance index is defined to describe the disturbance attenuation performance of systems with time varying parameter estimations by combining the linear matrix inequality lmi approach for hinfin filter design and adaptive method a method of designing adaptive reliable hinfin filters is proposed where the filter parameter matrices are updated automatically to compensate the sensor failures effects on systems based on the online estimations of eventual faults it is shown that the design condition for the newly proposed adaptive hinfin filtering is more relaxed than that for the traditional fixed gain filter design based on lmi approach an illustrative example and its simulation results are given to illustrate the effectiveness of the proposed design method

an improved input delay approach to stabilization of fuzzy systems under variable sampling in this paper we investigate the problem of stabilization for sampled data fuzzy systems under variable sampling a novel lyapunov krasovskii functional lkf is defined to capture the characteristic of sampled data systems and an improved input delay approach is proposed by the use of an appropriate enlargement scheme new stability and stabilization criteria are obtained in terms of linear matrix inequalities lmis compared with the existing results the newly obtained ones contain less conservatism some illustrative examples are given to show the effectiveness of the proposed method and the significant improvement on the existing results

the finite element analysis of the vibration characteristics of piezoelectric discs abstract finite element methods and modal analysis techniques have been used to predict the vibration characteristics of piezoelectric discs with finite diameter to thickness d t ratios the finite element method for piezoelectric materials is formulated in generalized variables and co ordinates and the eigenvalue problem is solved directly by treating the electrical term effectively as an extra mechanical degree of freedom this not only avoids the fully populated stiffness matrix likely to be caused by the condensation technique but also enables the problem to be solved by a standard finite element package the mechanical response function for constant voltage excitation and the electrical impedance characteristic functions are also formed numerical results are presented for piezoelectric discs with d t ratios of 20 and 10 five types of mode are identified according to their mode shape characteristics these are radial edge thickness shear thickness extensional and high frequency radial modes however no mode has been predicted having the piston like motion assumed in one dimensional theory the most strongly excited modes of the disc are the thickness extensional modes which are in the frequency range of the first through thickness mode predicted by a one dimensional model the finite element results have been checked experimentally excellent agreement being obtained

three dimensional static analysis of multi layered piezoelectric hollow spheres via the state space method a general non axisymmetric exact analysis of the statics of a laminated piezoelectric hollow sphere is presented in the paper by using a state space method to select a proper set of state variables three displacement functions and two stress functions are introduced it is found that the basic equations of a spherically isotropic piezoelectric medium are eventually turned to two separated state equations with constant coefficients the solutions of which are then obtained by virtue of matrix theory the continuity conditions at each interface are then used to derive two relationships between respective boundary variables at the inner and outer spherical surfaces no matter how many layers the sphere contains the orders of the final solving equations remain unaltered

a robust deconvolution scheme for fault detection and isolation of uncertain linear systems an lmi approach optimal h deconvolution filter theory is exploited for the design of robust fault detection and isolation fdi units for uncertain polytopic linear systems such a filter is synthesized under frequency domain conditions which ensure guaranteed levels of disturbance attenuation residual decoupling and deconvolution performance in prescribed frequency ranges by means of the projection lemma a quasi convex formulation of the problem is obtained via lmis a fdi logic based on adaptive thresholds is also proposed for reducing the generation of false alarms the effectiveness of the design technique is illustrated via a numerical example

fault detection for t s fuzzy systems with unknown membership functions this paper is concerned with the fault detection fd problem for takagi sugeno t s fuzzy systems with unknown membership functions if the membership functions are unknown the linear fd filter designs with fixed gains have been considered in the literature to reduce the conservatism of the existing results a switching mechanism that depends on the lower and upper bounds of the unknown membership functions is provided to construct an fd filter with varying gains it is shown that the switching type fd filter with varying gains can achieve a better fd performance than the linear fd filter with fixed gains in addition based on some time domain inequalities a novel weighting matrix design approach is introduced to transform the fault sensitivity specification into an h constraint finally two examples are given to show the advantages of the proposed fd method

fault detection for fuzzy systems with intermittent measurements this paper investigates the problem of fault detection for takagi sugeno t s fuzzy systems with intermittent measurements the communication links between the plant and the fault detection filter are assumed to be imperfect i e data packet dropouts occur intermittently which appear typically in a network environment and a stochastic variable satisfying the bernoulli random binary distribution is utilized to model the unreliable communication links the aim is to design a fuzzy fault detection filter such that for all data missing conditions the residual system is stochastically stable and preserves a guaranteed performance the problem is solved through a basis dependent lyapunov function method which is less conservative than the quadratic approach the results are also extended to t s fuzzy systems with time varying parameter uncertainties all the results are formulated in the form of linear matrix inequalities which can be readily solved via standard numerical software two examples are provided to illustrate the usefulness and applicability of the developed theoretical results

the transient responses of a special non homogeneous magneto electro elastic hollow cylinder for axisymmetric plane strain problem by virtue of the introduction of new dependent variable and the separation of variables technique the transient responses of a special non homogeneous magneto electro elastic hollow cylinder are transformed to two volterra integral equations of the second kind of about two functions with respect to time these integral equations can be solved successfully by means of the interpolation method then the complete solutions of displacements stresses electric potential electric displacements magnetic potential and magnetic inductions are obtained the present method is suitable for a magneto electro elastic hollow cylinder with an arbitrary thickness subjected to arbitrary axisymmetric mechanical and electromagnetic loads numerical results are finally presented

transient response of a hollow cylinder with radial and axial material inhomogeneity the transient response of a hollow finite cylinder with radial and axial material inhomogeneity to a pulse of short duration is analyzed the problem is solved in two steps radial inhomogeneity is treated first by dividing the cylinder into coaxial segments each with a constant modulus e which is allowed to vary from segment to segment transfer matrices relating variables at the two radial interfaces of a segment combine to satisfy continuity of stress and displacement at these interfaces the galerkin method is then utilized to treat the general case with both radial and axial inhomogeneity adopting the eigenfunctions of the radially inhomogeneous cylinder as trial functions features of both static and transient responses resemble that for a weakening material along the axis displacement increases and stress reduces in proportion to the reduction in modulus spatial attenuation of transient stress cannot be replicated when geometric dimensionality is reduced from 3 d axisymmetric to 2 d plane strain

free vibration of laminated circular piezoelectric plates and discs the free vibration characteristics of laminated circular piezoelectric plates and discs are considered using a discrete layer model of the weak form of the equations of periodic motion through thickness approximations are used for the three displacement components and the electrostatic potential resulting in an accurate representation of the discontinuity in gradients of these quantities from the mismatch in material properties at a dissimilar interface in the radial and circumferential co ordinates several different approximation functions are used that depend upon the type of problem being considered specifically the boundary conditions at the outer edge of the solid representative cases are studied both for thin plates and for thick discs excellent agreement is found with results of previous studies and several new results are presented

dynamic solution of a multilayered orthotropic piezoelectric hollow cylinder for axisymmetric plane strain problems the dynamic solution of a multilayered orthotropic piezoelectric infinite hollow cylinder in the state of axisymmetric plane strain is obtained by the method of superposition the solution is divided into two parts one is quasi static and the other is dynamic the quasi static part is derived by the state space method and the dynamic part is obtained by the separation of variables method coupled with the initial parameter method as well as the orthogonal expansion technique by using the obtained quasi static and dynamic parts and the electric boundary conditions as well as the electric continuity conditions a volterra integral equation of the second kind with respect to a function of time is derived which can be solved successfully by means of the interpolation method the displacements stresses and electric potentials are finally obtained the present method is suitable for a multilayered orthotropic piezoelectric infinite hollow cylinder consisting of arbitrary layers and subjected to arbitrary axisymmetric dynamic loads numerical results are finally presented and discussed

asynchronous output feedback control of networked nonlinear systems with multiple packet dropouts t s fuzzy affine model based approach this paper investigates the problem of robust output feedback control for a class of networked nonlinear systems with multiple packet dropouts the nonlinear plant is represented by takagi sugeno t s fuzzy affine dynamic models with norm bounded uncertainties and stochastic variables that satisfy the bernoulli random binary distribution are adopted to characterize the data missing phenomenon the objective is to design an admissible output feedback controller that guarantees the stochastic stability of the resulting closed loop system with a prescribed disturbance attenuation level it is assumed that the plant premise variables which are often the state variables or their functions are not measurable so that the controller implementation with state space partition may not be synchronous with the state trajectories of the plant based on a piecewise quadratic lyapunov function combined with an s procedure and some matrix inequality convexifying techniques two different approaches to robust output feedback controller design are developed for the underlying t s fuzzy affine systems with unreliable communication links the solutions to the problem are formulated in the form of linear matrix inequalities lmis finally simulation examples are provided to illustrate the effectiveness of the proposed approaches

free vibrations of functionally graded piezoceramic hollow spheres with radial polarization by introducing displacement functions as well as stress functions two independent state equations with variable coefficients are established from the three dimensional equations of a radially inhomogeneous spherically isotropic piezoelastic medium by virtue of the laminated approximation method the state equations are then transformed into the ones with constant variables in each layer and the state variable solutions are presented based on the solutions linear algebraic equations about the state variables only at the inner and outer spherical surfaces are derived by utilizing the continuity conditions at each interface frequency equations corresponding to two independent classes of vibrations are finally obtained from the free surface conditions numerical calculations are presented and the effect of the material gradient index on natural frequencies is discussed

comments on robust stabilization of a class of uncertain nonlinear systems via fuzzy control quadratic stabilizability h sup spl infin control theory and linear matrix inequalities this paper presents stability analysis for a class of uncertain nonlinear systems and a method for designing robust fuzzy controllers to stabilize the uncertain nonlinear systems first a stability condition for takagi and sugeno s fuzzy model is given in terms of lyapunov stability theory next new stability conditions for a generalized class of uncertain systems are derived from robust control techniques such as quadratic stabilization h sup spl infin control theory and linear matrix inequalities the derived stability conditions are used to analyze the stability of takagi and sugeno s fuzzy control systems with uncertainty which can be regarded as a generalized class of uncertain nonlinear systems the design method employs the so called parallel distributed compensation important issues for the stability analysis and design are remarked finally three design examples of fuzzy controllers for stabilizing nonlinear systems and uncertain nonlinear systems are presented

extension of a spectral bounding method to complex rotated hamiltonians with application to p2 i x3 we show that a recently developed method for generating bounds for the discrete energy states of the non hermitian ix3 potential handy c r 2001 j phys a math gen 34 l271 is applicable to complex rotated versions of the hamiltonian this has important implications for extension of the method in the analysis of resonant states regge poles and general bound states in the complex plane bender and boettcher 1998 phys rev lett 80 5243

beyond the wkb approximation in pt symmetric quantum mechanics the mergings of energy levels associated with the breaking of symmetry in the model of bender and boettcher and in its generalization to incorporate a centrifugal term are analysed in detail even though conventional wkb techniques fail it is shown how the ode im correspondence can be used to obtain a systematic approximation scheme which captures all previously observed features nonperturbative effects turn out to play a crucial role governing the behaviour of almost all levels once the symmetry breaking transition has been passed in addition a novel treatment of the radial schrodinger equation is used to recover the values of local and non local conserved charges in the related integrable quantum field theories without any need for resummation even when the angular momentum is nonzero

fault detection and isolation for a class of uncertain state feedback fuzzy control systems this paper investigates the fault detection and isolation fdi problem for a class of nonlinear state feedback control systems with parameter uncertainties first the considered nonlinear systems are described by multiple t s fuzzy models with uncertain grades of membership and local nonlinear parts in normal case and faulty cases then a switching technique is introduced to address the uncertain grades of membership external disturbances local nonlinear parts faults and the coupling of them in a multiple model scheme a bank of fdi observers are constructed each of which is based on the t s model that describes the system in the presence of a particular fault such that one of them can track the current system state and the corresponding observer estimate error can converge exponentially to zero finally two examples are given to illustrate the effectiveness and advantages of the new results

fault detection for t s fuzzy systems with partly unmeasurable premise variables abstract this paper studies the fault detection problem for t s fuzzy systems with partly unmeasurable premise variables by using measurable premise variables and estimations of unmeasurable premise variables of fuzzy models as the premise variables of observers a novel fuzzy fault detection observer scheme is constructed and the corresponding design condition is proposed via a set theoretic description different from the conventional fault detection observer schemes where all premise variables of the observer are the estimations of the premise variables in the fuzzy systems the proposed method can take full advantage of the partly measurable premise variables for achieving a better fault detection performance a numerical example is given to illustrate the effectiveness of the proposed method

generating converging eigenenergy bounds for the discrete states of the ix3 non hermitian potential recent investigations by bender and boettcher and by mezincescu have argued that the discrete spectrum of the non hermitian potential v x ix3 should be real we give further evidence for this through a novel formulation which transforms the general one dimensional schrodinger equation with complex potential into a fourth order linear differential equation for x 2 this permits the application of the eigenvalue moment method developed by handy bessis and coworkers yielding rapidly converging lower and upper bounds to the low lying discrete state energies we adapt this formalism to the pure imaginary cubic potential generating tight bounds for the first five discrete state energy levels

orthogonal polynomial projection quantization a new hill determinant method accurate energy eigenvalues are obtained by simply projecting the unknown bound state wave function on essentially arbitrary sets of orthogonal polynomials and setting a subset of these to zero the projection integrals are represented in terms of the power moments of the wave function obtained recursively by transforming schr dinger s equation into a moment equation because unbounded wave functions do not have power moments all solutions are guaranteed to be l2 resulting in a more robust rapidly converging and stable method when compared with configuration space hill determinant methods more importantly our approach permits the use of arbitrary nonanalytic positive reference functions including those that manifest the true asymptotic behavior of the discrete states these advantages are not usually possible with the standard hill approach the formulation presented here can be applied to any problem for which schr dinger s equation can be transformed into a moment equation in this regard it is related to the l2 quantization prescription developed by tymczak et al 1998 phys rev lett 80 3674 1998 phys rev a 58 2708 corresponding to the hill determinant method in momentum space and to the eigenvalue moment method handy and bessis 1985 phys rev lett 55 931 handy et al 1988 phys rev lett 60 253 the first use of semidefinite programming related analysis in quantum physics the latter method can be used to generate the ground state whose orthogonal polynomials can serve to generate even more rapidly converging estimates for the excited discrete state energies we demonstrate the power of this new approach on the sextic and quartic anharmonic oscillators as well as on recently studied one and two dimensional pseudo hermitian hamiltonians

magneto thermo electro elastic transient response in a piezoelectric hollow cylinder subjected to complex loadings abstract the article presents an analytical solution for magneto thermo electro elastic problems of a piezoelectric hollow cylinder placed in an axial magnetic field subjected to arbitrary thermal shock mechanical load and transient electric excitation using an interpolation method solves the volterra integral equation of the second kind caused by interaction among magnetic thermal electric and mechanical fields the electric displacement is determined thus the exact expressions for the transient responses of displacement stresses electric displacement electric potential and perturbation of the magnetic field vector in the piezoelectric hollow cylinder are obtained by means of hankel transforms laplace transforms and inverse laplace transforms from sample numerical calculations it is seen that the present method is suitable for a piezoelectric hollow cylinder subjected to arbitrary thermal shock mechanical load and transient electric excitation and the result carried out may be used as a reference to solve other transient coupled problems of magneto thermo electro elasticity

fuzzy filter design for nonlinear systems in finite frequency domain this paper is concerned with the problem of fuzzy filter design for discrete time nonlinear systems in the takagi sugeno t s form different from existing fuzzy filters the proposed ones are designed in finite frequency domain first a so called finite frequency l2 gain is defined that extends the standard l2 gain then a sufficient condition for the filtering error system with a finite frequency l2 gain is derived based on the obtained condition three fuzzy filters are designed to deal with noises in the low middle and high frequency domain respectively the proposed fuzzy filtering method can get a better noise attenuation performance when frequency ranges of noises are known beforehand an example about a tunnel diode circuit is given to illustrate its effectiveness

the transient responses of piezoelectric hollow cylinders for axisymmetric plane strain problems by virtue of the separation of variables technique the axisymmetric plane strain electroelastic dynamic problem of hollow cylinder is transferred to an integral equation about a function with respect to time which can be solved successfully by means of the interpolation method then the solution of the displacements stresses electric displacements and electric potentials are finally obtained the present method is suitable for the hollow cylinder with arbitrary thickness subjected to arbitrary mechanical and electrical loads numerical results are also presented

free vibrations of piezoelectric cylindrical shells filled with compressible fluid abstract three displacement functions are introduced to represent each mechanical displacement according to the three dimensional theory after expanding these functions and the electric potential with orthogonal series the free vibration equation of piezoelectric cylindrical shells satisfying ss3 edge conditions can be obtained the equation was solved by utilizing bessel functions with complex arguments the effects of compressible fluid on shells are considered and some new phenomena which are exclusive for piezoelectric cylindrical shells are reported results of empty infinite piezoelectric cylindrical shells are compared to those presented in relative references some lowest frequencies that were missed by paul and venkatesan paul h s and venkatesan m 1987 vibrations of hollow circular cylinder of piezoelectric ceramics journal of the acoustic society of america82 852 856 were discovered

on local h switched controller design for uncertain t s fuzzy systems subject to actuator saturation with unknown membership functions abstract this manuscript proposes a local h switched controller design for a class of uncertain nonlinear plants described by takagi sugeno t s fuzzy models with unknown membership functions the control design requires only the lower and upper bounds of the system nonlinearities and of the system linear parameters which can depend on uncertain parameters the switched control law chooses a state feedback controller gain which belongs to a given set of gains that minimizes the time derivative of a quadratic lyapunov function this procedure eliminates the necessity of finding the membership function expressions to implement the control law guarantees an h performance and ensures that the state trajectory remains within a region in which the t s fuzzy model is valid due to the h control design that frequently results in very large control inputs it is considered that the switched control law is subject to actuator saturation finally two examples are presented the first example studies the control of a chaotic lorenz system it shows that for disturbances with large magnitude the proposed procedures provided better results than the obtained with another recent method found in the literature that considers full access to the membership functions in the second example a practical implementation of an active nonlinear suspension control system considering an uncertain bounded mass and a fault in the actuator confirms the effectiveness of the proposed approach

generation of converging regge pole bounds for arbitrary rational fraction scattering potentials we expand upon the regge pole bounding formalism previously presented by handy and msezane 2001 j phys a math gen 34 l531 by analysing in greater detail several important singular potentials including the v r 2 r3 potential the polarization potential v r 2 r4 and the lennard jones class v r 2 rm 2 rn for m n 6 4 12 6 with respect to the polarization potential our bounds enable one to assess the accuracy of the turning point based asymptotic formula of avdonina et al avdonina n b belov s felfli z msezane a z and naboko s n 2001 cau preprint 2002 phys rev a 65 at press we also extend the method to the non singular coulomb case veff r 1 r l l 1 r2 which represents a more challenging class of problems within the present bounding formalism due to the nature of the underlying boundary conditions

nonsynchronized state estimation of multichannel networked nonlinear systems with multiple packet dropouts via t s fuzzy affine dynamic models this paper investigates the problem of robust h state estimation for a class of multichannel networked nonlinear systems with multiple packet dropouts the nonlinear plant is represented by takagi sugeno t s fuzzy affine dynamic models with norm bounded uncertainties and stochastic variables with general probability distributions are adopted to characterize the data missing phenomenon in output channels the objective is to design an admissible state estimator guaranteeing the stochastic stability of the resulting estimation error system with a prescribed h disturbance attenuation level it is assumed that the plant premise variables which are often the state variables or their functions are not measurable so that the estimator implementation with state space partition may not be synchronized with the state trajectories of the plant based on a piecewise quadratic lyapunov function combined with s procedure and some matrix inequality convexifying techniques two different approaches are developed to robust filtering design for the underlying t s fuzzy affine systems with unreliable communication links all the solutions to the problem are formulated in the form of linear matrix inequalities lmis finally simulation examples are provided to illustrate the effectiveness of the proposed approaches

h_ infty observer design for fuzzy system with immeasurable state variables via a new lyapunov function this paper is concerned with the design of h infty observers for fuzzy system with immeasurable state variables via a new lyapunov function by decomposing the space of premise variables into crisp regions and fuzzy regions piecewise fuzzy h infty observers are established at different instants to cope with the challenges caused by the mismatch of the premise variables and exogenous disturbances based on the proposed new lyapunov functions that depend on the different regions where the premise variables are located sufficient conditions in terms of linear matrix inequalities are obtained to guarantee the stability and desired performance of the error systems finally a simulation example is provided to show that the new design technology proposed in this paper achieves better h infty performance than the existing design methods

dynamic responses of piezoelectric hollow cylinders in an axial magnetic field abstract this paper presents an analytical solution for the interaction of electric potentials electric displacements elastic deformations and mechanical loads and describes electromagnetoelastic responses and perturbation of the magnetic field vector in a piezoelectric hollow cylinder subjected to sudden mechanical load and electric potential an interpolation method is applied to solve the volterra integral equation of the second kind caused by interactions between different physical fields by means of finite integral transforms laplace transforms and their inverse transforms the exact expressions for the dynamic responses of stresses electric displacements electric potentials and perturbation response of an axial magnetic field vector in the piezoelectric hollow cylinders are obtained the present method is suitable for piezoelectric hollow cylinders in an axial magnetic field subjected to arbitrary mechanical loads and electrical potential shocks finally numerical results are carried out and discussed

spectral bounds for the pt breaking hamiltonian p2 x4 iax the non hermitian hamiltonian p2 x4 iax which spontaneously breaks pt symmetry and the subject of a recent study by bender et al 2001 j phys a math gen 34 l31 is amenable to a positivity representation facilitating the generation of converging bounds to the complex eigenenergies of the pt breaking states this system is much easier i e fewer variational parameters than the previously studied case of the hamiltonian p2 ix3 iax 2001 handy j phys a math gen 34 5065 handy et al 2001 j phys a math gen 34 5593 as first proposed by delabaere and trinh 2000 j phys a math gen 33 8771 enabling the generation of low order algebraic spectral bounds i e in addition to high order numerically generated converging bounds to the discrete states we examine both approaches here

a note on the static behavior of simply supported laminated piezoelectric cylinders an exact three dimensional solution of the equations of linear piezoelectricity is given for the static response of a finite laminated piezoelectric cylinder with its ends simply supported the equilibrium equations and the conservation of charge equation are constructed in cylindrical coordinates the three displacement components and the electrostatic potential are expressed in terms of fourier series in the axial and circumferential directions leading to a coupled system of four ordinary differential equations in the radial coordinate the frobenious method is used to obtain the elastic and electric fields for each layer of the laminate which are a function of eight constants enforcing the boundary and continuity conditions across each interface yields the required number of equations to solve for these constants several examples are presented to study the fundamental behavior of these solids

revisitation of the localized excitations of the 2 1 dimensional kdv equation in a previous paper lou s y 1995 j phys a math gen 28 7227 a generalized dromion structure was revealed for the 2 1 dimensional kdv equation which was first derived by boiti et al boiti m leon j j p manna m and pempinelli f 1986 inverse problems 2 271 using the idea of the weak lax pair in this paper using a backlund transformation and the variable separation approach we find there exist much more abundant localized structures for the 2 1 dimensional kdv equation the abundance of the localized structures of the model is introduced by the entrance of an arbitrary function of the seed solution some special types of dromion solution lumps breathers instantons and the ring type of soliton are discussed by selecting the arbitrary functions appropriately the dromion solutions can be driven by sets of straight line and curved line ghost solitons the dromion solutions may be located not only at the cross points of the lines but also at the closed points of the curves the breathers may breathe both in amplitude and in shape

spectral analysis of the complex cubic oscillator using the exact semiclassical analysis we study the spectrum of a one parameter family of complex cubic oscillators the invariance property of the complex hamiltonians and the reality property of the spectrum are discussed analytic continuations of the spectrum in the complex parameter and their connections with the resonance problem for the real cubic oscillator are investigated the global analytic structure of the spectrum yields a branch point structure similar to the multivalued analytic structure discovered by bender and wu for the quartic oscillator

complex wkb analysis of energy level degeneracies of non hermitian hamiltonians the hamiltonian h p 2 x 4 iax where a is a real parameter is investigated the spectrum of h is discrete and entirely real and positive for a 3 169 as a increases past this point adjacent pairs of energy levels coalesce and then become complex starting with the lowest lying energy levels for large energies the values of a at which this merging occurs scale as the three quarters power of the energy that is as a and e at the points of coalescence the ratio a a e 3 4 approaches a constant whose numerical value is acrit 1 1838363072914 conventional wkb theory determines the high lying energy levels but cannot be used to calculate acrit this critical value is predicted exactly by complex wkb theory

fault detection in finite frequency domain for t s fuzzy systems with partly unmeasurable premise variables abstract this paper is concerned with the problem of finite frequency fault detection fd for a class of t s fuzzy systems with partly unmeasurable premise variables to fully use the available information of the considered t s fuzzy system an fd observer whose premise variables consist of the measurable premise variables and the estimations of unmeasurable ones of the fuzzy model is designed however the membership functions of the fuzzy model and the observer to be designed are unsynchronized such that the existing fd methods based on parallel distribute compensation pdc strategy may be infeasible to overcome this difficulty a novel non pdc h h unknown input observer is designed to achieve the purpose of fault detection and provide less conservative results finally two simulation examples are given to illustrate the validity and merits of the presented fd scheme

on the equivalence of moment quantization and continuous wavelet transform analysis the space of polynomials maps onto itself under affine transformations this suggests that a moment reformulation of continuous wavelet transform cwt theory the affine convolution of a signal or wavefunction should lead to significant simplifications in its implementation we present a comprehensive formalism with numerical examples that inextricably links moment quantization mq and cwt theory for rational fraction potential problems and mother wavelets of the form q x an appropriate polynomial mq permits a more efficient and accurate in a pointwise convergent sense cwt implementation whereas cwt broadens the scope of applicability for mq methods and is its natural extension when a more global approximation is desired our formalism also gives one justification for the empirical superiority manifested by previous mq studies as compared with dyadic wavelet reconstruction methods we implement our formalism in the context of the quartic sextic and octic anharmonic oscillator potentials and demonstrate the flexibility of the method by treating both the mexican hat wavelet transform as well as that based on the mother wavelet

general solutions for coupled equations for piezoelectric media abstract three general solutions are obtained for the coupled dynamic equations for a transversely isotropic piezoelectric medium these solutions are expressed in terms of the two functions and f where satisfies a second degree partial differential equation and f a sixth degree partial differential equation respectively if the terms concerning the derivatives of time are removed the results become three general solutions for the corresponding equilibrium equations in which the function f can be represented by functions fi i 1 2 3 each of which satisfies a second degree partial differential equation by utilizing a generalized almansi theorem and the solution wang and zheng int j solids structures32 105 115 1995 obtained is proved to be consistent with one case of one of the three general solutions when the constants e15 e31 e33 0 the piezo electric coupling is absent then two of the solutions reduce to the elasticity general solutions for a transversely isotropie medium one of which is the result hu acta scientia sin 2 2 145 151 1953 obtained the other one has not been published last the solution in the limiting explicit form for the problem for a half space with concentrated loads at the boundary is obtained by utilizing the general solutions

the exact elasto electric field of a rotating piezoceramic spherical shell with a functionally graded property a displacement separation technique is employed to simplify the basic equations of a piezoceramic body with radial inhomogeneity it is shown that the controlling equations are finally reduced to an uncoupled second order ordinary differential equation and a coupled system of three second order ordinary differential equations solutions to these differential equations are given for the case that material constants are of power functions of the radial coordinate the static analysis of a steadily rotating spherical shell is then presented

simultaneous fault detection and control for switched linear systems with mode dependent average dwell time this paper investigates the problem of the simultaneous fault detection and control sfdc for switched linear systems to meet the control and detection objectives the time dependent detection filters and dynamic output feedback controllers are presented in sfdc under a mixed h h framework a mode dependent average dwell time mdadt approach which means that each subsystem has its own average dwell time is adopted in this paper to reduce the conservativeness of the average dwell time method and the discretized lyapunov function dlf technique is first used to relax the mdadt constraints in sfdc some sufficient conditions for designing filters controllers which satisfy the h h performance are given in terms of linear matrix inequalities lmis what s more a two step algorithm to solve the sfdc problem is proposed the effectiveness of the proposed method is illustrated through two simulation examples

moment quantization and a adic discrete continuous wavelet transform theory we establish how moment quantization directly leads to a complete a adic discrete continuous wavelet transform theory in contrast to the approximate reconstruction methods published earlier 1996 phys rev a 54 3754 1997 j phys a math gen 30 4709

comment on a recent paper by mezincescu it has been conjectured that for 0 the entire spectrum of the non hermitian symmetric hamiltonian hn p2 x2 ix where n 2 is real strong evidence for this conjecture for the special case n 3 was provided in a recent paper by mezincescu mezincescu g a 2000 j phys a math gen 33 4911 in which the spectral zeta function z3 1 for the hamiltonian h3 p2 ix3 was calculated exactly here the calculation of mezincescu is generalized from the special case n 3 to the region of all n 2 0 and the exact spectral zeta function zn 1 for hn is obtained using zn 1 it is shown that to extremely high precision about three parts in 1018 the spectrum of hn for other values of n such as n 4 is entirely real

on piezoelastic contact problem for a smooth punch this paper firstly conducts a systematic three dimensional investigation of the problem of a rigid smooth punch bonded to a transversely isotropic piezoelectric half space the potential theory method is employed and generalized to take into account the effect of the electric field in contrast to pure elasticity two potentials are introduced for an arbitrarily shaped punch two governing equations are derived which can be solved using numerical methods particularly a closed form exact solution is obtained for a flat centrally loaded circular punch which is maintained at a constant electric potential

fault detection for t s fuzzy systems with past output measurements abstract this paper is concerned with the fault detection fd filter design problem for the discrete time nonlinear systems with past output measurements and sensor saturation the considered discrete time nonlinear systems are described by t s fuzzy models a decomposition method is used to deal with the characteristics of sensor saturation a new fd filter with past output measurements is firstly proposed by using the lyapunov functional method subsequently the design conditions are given in terms of convex problems constrained by linear matrix inequalities lmi moreover it is shown that the fd filter with past output measurements can achieve better fd performances than the existing ones with current output measurements finally some simulation results are given to illustrate the advantages of the proposed design method

on the eigenproblems of pt symmetric oscillators we consider the non hermitian hamiltonian h d2 dx2 p x2 ix 2n 1 on the real line where p x is a polynomial of degree at most n 1 with all non negative real coefficients possibly p 0 it is proved that the eigenvalues must be in the sector arg 2n 3 also for the cubic case h d2 dx2 ix 3 we establish a zero free region of the eigenfunction u and its derivative u and we find some other interesting properties of eigenfunctions

radial vibration of piezoelectric magnetostrictive composite hollow sphere the radial vibration of a multilayered piezoelectric magnetostrictive composite hollow sphere is investigated in terms of the gaussian equations two unknown time functions are first introduced to complete the solution of electric displacement and magnetic induction the solution for mechanical field involving two unknown time functions is obtained by means of the superposition method the state space method as well as the separation of variables method by means of the electric and magnetic boundary conditions and continuity conditions two volterra integral equations of the second kind with respect to two time functions are derived the interpolation method is employed to solve the volterra integral equations the present solution is suitable for analyzing the transient responses of composite hollow sphere composed of piezoelectric and magnetostrictive layers with arbitrary composite sequence numerical results are presented and discussed

brief an lmi approach to design robust fault detection filter for uncertain lti systems in this paper the robust fault detection filter design problem for uncertain linear time invariant lti systems with both unknown inputs and modelling errors is studied the basic idea of our study is to use an optimal residual generator assuming no modelling errors as the reference residual model of the robust fault detection filter design for uncertain lti systems with modelling errors and based on it to formulate the robust fault detection filter design as an h model matching problem by using some recent results of h optimization a solution of the optimization problem is then presented via a linear matrix inequality lmi formulation the main results include the development of an optimal reference residual model the formulation of robust fault detection filter design problem the derivation of a sufficient condition for the existence of a robust fault detection filter and a construction of it based on the lmi solution parameters the determination of adaptive threshold for fault detection an illustrative design example is employed to demonstrate the effectiveness of the proposed approach

extension of a spectral bounding method to the pt invariant states of the ix n non hermitian potential the eigenvalue moment method emm developed by handy j phys a math gen 2001 34 l271 j phys a math gen 2001 34 5065 handy et al j phys a math gen 2001 34 5593 and handy and xiao qian wang j phys a math gen 2001 34 8297 which generates converging lower and upper bounds to the complex discrete state energies is extended to the case of discrete states with non real support in particular bender and boettcher phys rev lett 1998 80 5243 have argued on the reality of the discrete state spectrum for the ix n potential for n integer 4 such pt invariant solutions can only exist on appropriate complex contours we develop and apply the necessary emm formalism to such cases in particular the restriction of emm to the anti stokes angles significantly increases the convergence rate of the bounds

robust and reduced order filtering new lmi based characterizations and methods this paper addresses several challenging problems of robust filtering we derive new linear matrix inequality lmi characterizations of minimum variance or h sub 2 performance and demonstrate that they allow the use of parameter dependent lyapunov functions while preserving tractability of the problem the resulting conditions are less conservative than earlier techniques which are restricted to fixed not parameter dependent lyapunov functions the remainder of the paper discusses reduced order filter problems new lmi based nonconvex optimization formulations are introduced for the existence of reduced order filters and several efficient optimization algorithms of local and global optimization are proposed nontrivial and less conservative relaxation techniques are presented as well the viability and efficiency of the proposed approaches are then illustrated through computational experiments and comparisons with existing methods