stability analysis and synthesis of nonlinear time delay systems via linear takagi sugeno fuzzy models abstract this paper concerns with the stability analysis and synthesis of nonlinear retarded systems via linear takagi sugeno ts fuzzy model approach first the ts fuzzy models with time delay are present and the stability conditions are derived using lyapunov razumikhin functional approach then a stabilization approach for nonlinear retarded systems through fuzzy state feedback and fuzzy observer based controller is proposed it shows that the analysis results provide an efficient technique for the design of fuzzy controllers sufficient conditions for the existence of fuzzy state feedback gain and fuzzy observer gain of the time delay systems are derived through the numerical solution of a set of coupled linear matrix inequalities

fine structure of spectral properties for random correlation matrices an application to financial markets we study some properties of eigenvalue spectra of financial correlation matrices in particular we investigate the nature of the large eigenvalue bulks which are observed empirically and which have often been regarded as a consequence of the supposedly large amount of noise contained in financial data we challenge this common knowledge by acting on the empirical correlation matrices of two data sets with a filtering procedure which highlights some of the cluster structure they contain and we analyze the consequences of such filtering on eigenvalue spectra we show that empirically observed eigenvalue bulks emerge as superpositions of smaller structures which in turn emerge as a consequence of cross correlations between stocks we interpret and corroborate these findings in terms of factor models and we compare empirical spectra to those predicted by random matrix theory for such models

factorization of the dissipative wave equation and inverse scattering a decomposition of the solution of the dissipative wave equation into incoming and outgoing components across a smooth surface in a homogeneous region is presented the proof of the decomposition is given only for the plane surface this is then applied to the factorization of the dissipative wave equation into incoming and outgoing components in a planar stratified medium the ricatti integral differential equation for the reflection operator that relates the two components is obtained it is shown how the zeroth and second moments with respect to the transverse variable in a planar stratified medium of the reflection kernel can be used in the inverse problem to recover the velocity and dissipation coefficient from knowledge of the scattered field

t s fuzzy model based piecewise h output feedback controller design for networked nonlinear systems with medium access constraint abstract this paper investigates the problem of h output feedback control for a class of networked nonlinear systems subject to medium access constraint where the nonlinear systems are represented by takagi sugeno t s fuzzy models with norm bounded uncertainties the communication constraint concerned is that only one sensor node and one actuator node can access the shared network which is the case in network environment the accessibility of sensor nodes and or actuator nodes is determined by medium access control with a prescribed probability the attention is focused on the design of a piecewise static output feedback controller such that the closed loop control system is stochastically stable with a guaranteed h performance based on piecewise quadratic lyapunov functions together with some matrix inequality convexifying techniques an approach to the design of h output feedback controller is proposed in terms of linear matrix inequalities finally two simulation examples are provided to illustrate the effectiveness of the proposed methods

robust stability and stabilisation of 2d discrete state delayed systems abstract in this paper we first present sufficient stability and robust stability conditions for discrete linear state delayed 2d systems in terms of linear matrix inequalities all results are obtained with fornasini marchesini delay model but appropriate transformation to the corresponding roesser form is provided as well generalisation to the multiple state delayed case is also given then the stabilisation and robust stabilisation using static state feedback are studied stabilising feedback gain matrices are constructed based on the solutions of certain linear matrix inequalities an numerical example is used to illustrate the effectiveness of the approach

the electromagnetic scattering problem in the time domain for a dissipative slab and a point source using invariant imbedding a vertical magnetic dipole source above an inhomogeneous slab is considered where the permittivity e e z and conductivity z vary with the depth z using the axial symmetry of the problem a hankel transform is introduced besides physical scattering kernels nonphysical scattering kernels are introduced and the direct and inverse transformed problem is solved by means of wave splitting in an invariant imbedding approach the imbedding equations for the nonphysical scattering kernels are simpler than the corresponding equations for the physical kernels and they are solved using existing techniques for the imbedding equations for normally incident plane waves the solution for the physical kernels is obtained by establishing relations between the two sets of kernels these relations are given by volterra equations of the second kind and thus are very easy to solve numerically some applications and extensions of the results derived in the paper are discussed

random matrix theory and fund of funds portfolio optimisation abstract the proprietary nature of hedge fund investing means that it is common practise for managers to release minimal information about their returns the construction of a fund of hedge funds portfolio requires a correlation matrix which often has to be estimated using a relatively small sample of monthly returns data which induces noise in this paper random matrix theory rmt is applied to a cross correlation matrix c constructed using hedge fund returns data the analysis reveals a number of eigenvalues that deviate from the spectrum suggested by rmt the components of the deviating eigenvectors are found to correspond to distinct groups of strategies that are applied by hedge fund managers the inverse participation ratio is used to quantify the number of components that participate in each eigenvector finally the correlation matrix is cleaned by separating the noisy part from the non noisy part of c this technique is found to greatly reduce the difference between the predicted and realised risk of a portfolio leading to an improved risk profile for a fund of hedge funds

wave splitting and the reflection operator for the wave equation in r3 the problem of wave splitting in a nonhomogeneous medium in r3 is considered previous results for wave splitting in a planar stratified medium can be generalized to a general nonhomogeneous medium with sufficiently smooth velocity the wave equation is factorized into an up and down going wave system using certain integral and integral differential operators the equation for the reflection operator which relates the up going wave to a down going wave is then obtained and certain properties of the reflection operator are deduced

noise dressing of financial correlation matrices we show that results from the theory of random matrices are potentially of great interest to understand the statistical structure of the empirical correlation matrices appearing in the study of multivariate time series the central result of the present study which focuses on the case of financial price fluctuations is the remarkable agreement between the theoretical prediction based on the assumption that the correlation matrix is random and empirical data concerning the density of eigenvalues associated to the time series of the different stocks of the s 500 or other major markets in particular the present study raises serious doubts on the blind use of empirical correlation matrices for risk management

stability analysis and stabilization of 2 d switched systems under arbitrary and restricted switchings in this paper the problems of stability analysis and stabilization are investigated for discrete time two dimensional 2 d switched systems which are formulated by the well known fornasini marchesini local state space model firstly by using the switched quadratic lyapunov function approach a sufficient stability condition is established for such systems under arbitrary switching signal then the extended average dwell time technique combining with the piecewise lyapunov function approach is developed and it is utilized for the stability analysis of the 2 d switched systems for the restricted switching case based on the stability analysis results sufficient conditions are presented to stabilize the 2 d switched systems finally two examples are provided to illustrate the effectiveness of the proposed new design techniques

h_ infty fuzzy control with randomly occurring infinite distributed delays and channel fadings in this paper the h output feedback control problem is investigated for a class of discrete time fuzzy systems with randomly occurring infinite distributed delays and channel fadings a random variable obeying the bernoulli distribution is introduced to account for the probabilistic infinite distributed delays the stochastic rice fading model is employed to simultaneously describe the phenomena of random time delays and channel fadings via setting different values of the channel coefficients the aim of this paper is to design an h output feedback fuzzy controller such that the closed loop takagi sugeno t s fuzzy control system is exponentially mean square stable and the disturbance rejection attenuation is constrained to a given level by means of the h performance index intensive analysis is carried out to obtain sufficient conditions for the existence of desired output feedback controllers ensuring both the exponential mean square stability and the prescribed h performance the cone complementarity linearization algorithm is utilized to cast the controller design problem into a sequential minimization one that is solvable by the semi definite programming method a simulation result is exploited to illustrate the usefulness and effectiveness of the proposed design technique

cluster structure in the correlation coefficient matrix can be characterized by abnormal eigenvalues abstract in a large number of previous studies the researchers found that some of the eigenvalues of the financial correlation matrix were greater than the predicted values of the random matrix theory r m t here we call these eigenvalues as abnormal eigenvalues in order to reveal the hidden meaning of these abnormal eigenvalues we study the toy model with cluster structure and find that these eigenvalues are related to the cluster structure of the correlation coefficient matrix in this paper model based experiments show that in most cases the number of abnormal eigenvalues of the correlation matrix is equal to the number of clusters in addition empirical studies show that the sum of the abnormal eigenvalues is related to the clarity of the cluster structure and is negatively correlated with the correlation dimension

factorization of the wave equation in higher dimensions the factorization of the wave equation into a coupled system involving up and down going wave components is obtained for the case where the field quantities are multivariate functions of spatial variables but the velocity c is a function of the z variable only the form of the reflection operator is derived and the quadratic differential integral equation satisfied by its kernel is obtained

positive filtering for positive takagi sugeno fuzzy systems under l 1 performance in this paper the positive filtering problem is addressed for positive takagi sugeno t s fuzzy systems under the 1 induced performance to estimate the output of positive t s fuzzy systems error bounding positive filters are constructed a new performance characterization is first established to guarantee the asymptotic stability of the filtering error system with the 1 induced performance moreover sufficient conditions expressed by linear programming problems are derived to design the required filters finally a numerical example is presented to show the effectiveness of the derived theoretical results

universal and nonuniversal properties of cross correlations in financial time series we use methods of random matrix theory to analyze the cross correlation matrix c of stock price changes of the largest 1000 u s companies for the 2 year period 1994 1995 we find that the statistics of most of the eigenvalues in the spectrum of c agree with the predictions of random matrix theory but there are deviations for a few of the largest eigenvalues we find that c has the universal properties of the gaussian orthogonal ensemble of random matrices furthermore we analyze the eigenvectors of c through their inverse participation ratio and find eigenvectors with large ratios at both edges of the eigenvalue spectrum a situation reminiscent of localization theory results

topological properties of stock networks based on minimal spanning tree and random matrix theory in financial time series abstract we investigated the topological properties of stock networks constructed by a minimal spanning tree we compared the original stock network with the estimated network the original network is obtained by the actual stock returns while the estimated network is the correlation matrix created by random matrix theory we found that the consistency between the two networks increases as more eigenvalues are considered in addition we suggested that the largest eigenvalue has a significant influence on the formation of stock networks

transient wave propagation in reciprocal bi isotropic media at oblique incidence in this paper a new wave splitting is suggested that simplifies the analysis of wave propagation in reciprocal bi isotropic media two different methods to solve the scattering problem are analyzed the invariant imbedding and the green function approach the medium is modeled by constitutive relations in the time domain time convolutions and the slab is assumed to be inhomogeneous with respect to the depth it is shown that the cross polarized contribution to the reflected field at normal incidence is zero for the general reciprocal inhomogeneous slab moreover the rotation and the attenuation of the wave front are calculated explicitly in the general inhomogeneous slab case special attention is paid to normal incidence and to the homogeneous semi infinite medium

a wave splitting approach to time dependent inverse scattering for the stratified cylinder this paper examines the inverse problem for the stratified inhomogeneous cylinder in which the unknown velocity function is recovered from reflection data the analysis is based on weston s theoretical wave splitting for stratified three dimensional media j math phys 28 1987 pp 1061 1068 j math phys 29 1988 pp 36 45 the forms of the splitting operators are presented and the inverse problem is solved numerically by means of the r equation an integro differential equation that characterizes the scattering medium independently of the wave field although the r equation is singular at one round trip time corresponding to a caustic when a radially incoming cylindrical wave reaches the z axis several numerical examples indicate that the velocity function can be reconstructed quite accurately

analysis of the green s function approach to one dimensional inverse problems i one parameter reconstruction an analysis of a green s function approach based on wave splitting to the one dimensional electromagnetic inverse problem is given the green s functions refer to split components of the fundamental solution the linear system of equations for the green s functions is shown to be well posed for the inverse problem and stability estimates theorems on existence uniqueness local correctness and convergence are given

delay dependent stability for 2d systems with time varying delay subject to state saturation in the roesser model this paper addresses the problem of delay dependent stability of 2d systems with time varying delay subject to state saturation in the roesser model by introducing diagonally dominant matrices new delay dependent conditions are obtained in terms of linear matrix inequalities lmis where the lower and upper delay bounds along horizontal and vertical directions respectively are known numerical examples are provided to demonstrate the proposed results

layer stripping solutions of multidimensional inverse scattering problems a layer stripping procedure for solving three dimensional schrodinger equation inverse scattering problems is developed this method operates by recursively reconstructing the potential from the jump in the scattered field at the wave front and then using the reconstructed potential to propagate the wave front and the scattered field further into the inhomogeneous region it is thus a generalization of algorithms that have been developed for one dimensional inverse scattering problems although the procedure has not yet been numerically tested the corresponding one dimensional algorithms have performed well on synthetic data the procedure is applied to a two dimensional inverse seismic problem connections between simplifications of this method and born approximation inverse scattering methods are also noted

correlation and network analysis of global financial indices random matrix theory rmt and network methods are applied to investigate the correlation and network properties of 20 financial indices the results are compared before and during the financial crisis of 2008 in the rmt method the components of eigenvectors corresponding to the second largest eigenvalue form two clusters of indices in the positive and negative directions the components of these two clusters switch in opposite directions during the crisis the network analysis uses the fruchterman reingold layout to find clusters in the network of indices at different thresholds at a threshold of 0 6 before the crisis financial indices corresponding to the americas europe and asia pacific form separate clusters on the other hand during the crisis at the same threshold the american and european indices combine together to form a strongly linked cluster while the asia pacific indices form a separate weakly linked cluster if the value of the threshold is further increased to 0 9 then the european indices france germany and the united kingdom are found to be the most tightly linked indices the structure of the minimum spanning tree of financial indices is more starlike before the crisis and it changes to become more chainlike during the crisis the average linkage hierarchical clustering algorithm is used to find a clearer cluster structure in the network of financial indices the cophenetic correlation coefficients are calculated and found to increase significantly which indicates that the hierarchy increases during the financial crisis these results show that there is substantial change in the structure of the organization of financial indices during a financial crisis

stability analysis and synthesis for switched takagi sugeno fuzzy positive systems described by the roesser model abstract this article focuses on stability analysis and controller synthesis of a class of roesser type switched takagi sugeno fuzzy systems with delays first sufficient conditions derived by use of the co positive lyapunov function and the average dwell time method are presented to guarantee the proposed system is positive and exponentially stable then via a state feedback fuzzy controller criteria are also given under which not only the resulting closed loop system is positive and exponentially stable but also the desired controller gain matrices can be designed by solving a set of coupled matrix inequalities finally two illustrative examples are provided to show the effectiveness of the approach outlined in this article

stability analysis and h controller synthesis of discrete time switched systems with time delay abstract this paper studies the problems of stability analysis and h controller synthesis of switched systems with time varying delay based on an input output approach the attention is focused on developing a new method to further reduce the conservatism of the existing results the system under consideration is transformed into an interconnection system and the scaled small gain condition for the interconnection systems is introduced based on the system transformation and the scaled small gain theorem an improved delay dependent stability criterion is proposed such that the interconnection system is asymptotically stable which is also proved to guarantee the asymptotic stability of the system based on the direct lyapunov method in another perspective the proposed stability condition is demonstrated to be less conservative than most existing results moreover an admissible controller which solves the problem of h controller synthesis is formulated into a convex optimization problem illustrative examples are provided to show the advantage and the effectiveness of the proposed method

correlation dimension of financial market abstract in this paper correlation dimension is applied to financial data analysis we calculate the correlation dimensions of some real market data and find that the dimensions are significantly smaller than those of the simulation data based on geometric brownian motion based on the analysis of the chinese and us stock market data the main results are as follows first by calculating three data sets for the chinese and us market we find that large market volatility leads to a significant decrease in the dimensions second based on 5 min stock price data we find that the chinese market dimension is significantly larger than the us market this shows a significant difference between the two markets for high frequency data third we randomly extract stocks from a stock set and calculate the correlation dimensions and find that the average value of these dimensions is close to the dimension of the original set in addition we analyse the intuitional meaning of the relevant dimensions used in this paper which are directly related to the average degree of the financial threshold network the dimension measures the speed of the average degree that varies with the threshold value a smaller dimension means that the rate of change is slower

spectral density of the correlation matrix of factor models a random matrix theory approach we studied the eigenvalue spectral density of the correlation matrix of factor models of multivariate time series by making use of the random matrix theory we analytically quantified the effect of statistical uncertainty on the spectral density due to the finiteness of the sample we considered a broad range of models ranging from one factor models to hierarchical multifactor models

random matrix theory for portfolio optimization a stability approach we apply random matrix theory rmt to an empirically measured financial correlation matrix c and show that this matrix contains a large amount of noise in order to determine the sensitivity of the spectral properties of a random matrix to noise we simulate a set of data and add different volumes of random noise having ascertained that the eigenspectrum is independent of the standard deviation of added noise we use rmt to determine the noise percentage in a correlation matrix based on real data from s p500 eigenvalue and eigenvector analyses are applied and the experimental results for each of them are presented to identify qualitatively and quantitatively different spectral properties of the empirical correlation matrix to a random counterpart finally we attempt to separate the noisy part from the non noisy part of c we apply an existing technique to cleaning c and then discuss its associated problems we propose a technique of filtering c that has many advantages from the stability point of view over the existing method of cleaning

characterization of strange attractors a new measure of strange attractors is introduced which offers a practical algorithm to determine their character from the time series of a single observable the relation of this new measure to fractal dimension and information theoretic entropy is discussed

higher order parabolic approximations to time independent wave equations a sequence of numerically tractable higher order parabolic approximations is derived for the reduced wave equation in an inhomogeneous medium the derivation is motivated by a definition of waves propagating in a distinguished direction for a homogeneous medium these definitions are exact and yield uncoupled infinite order parabolic equations which are equivalent to the wave equation the difficulty of obtaining higher order parabolic approximations for the elastic wave equation in an inhomogeneous medium is also discussed