normalization and stabilization for rectangular singular fractional order t s fuzzy systems abstract this paper considers the normalization and stabilization of rectangular singular fractional order takagi sugeno t s fuzzy systems with order 0 1 by using the proportional and derivative type dynamic compensator the rectangular singular fractional order t s fuzzy systems are transformed into an augmented square singular fractional order t s fuzzy systems and the admissibility of the augmented square singular fractional order t s fuzzy systems can guarantee the normalization and stabilization of the rectangular singular fractional order t s fuzzy systems two sufficient conditions are expressed in terms of a set of bilinear matrix inequalities which can be efficiently solved by an iterative lmi algorithm a numerical example is given to verify the effectiveness of the results proposed

robust stability of uncertain discrete time singular fuzzy systems this paper considers the problem of robust stability analysis of uncertain discrete time singular fuzzy systems described by a class of extended takagi sugeno fuzzy dynamic models with time varying norm bounded parameter uncertainties a sufficient condition ensuring a discrete singular fuzzy system to be regular causal and stable is proposed in terms of a set of linear matrix inequalities based on this a robust stability condition is obtained both of these conditions can be checked by using recently developed algorithms in solving lmis examples are provided to demonstrate the reduced conservatism and effectiveness of the proposed conditions

modeling the effects of anesthesia on the electroencephalogram changes to the electroencephalogram eeg observed during general anesthesia are modeled with a physiological mean field theory of electrocortical activity to this end a parametrization of the postsynaptic impulse response is introduced which takes into account pharmacological effects of anesthetic agents on neuronal ligand gated ionic channels parameter sets for this improved theory are then identified which respect known anatomical constraints and predict mean firing rates and power spectra typically encountered in human subjects through parallelized simulations of the eight nonlinear two dimensional partial differential equations on a grid representing an entire human cortex it is demonstrated that linear approximations are sufficient for the prediction of a range of quantitative eeg variables more than 70 000 plausible parameter sets are finally selected and subjected to a simulated induction with the stereotypical inhaled general anesthetic isoflurane thereby 86 parameter sets are identified that exhibit a strong biphasic rise in total power a feature often observed in experiments a sensitivity study suggests that this biphasic behavior is distinguishable even at low agent concentrations finally our results are briefly compared with previous work by other groups and an outlook on future fits to experimental data is provided

alternating convex projection methods for covariance control design the problem of designing a static state feedback or full order dynamic controller is formulated as a problem of designing an appropriate plant state covariance matrix we show that closed loop stability and multiple output norm constraints imply that the plant state covariance matrix lies at the intersection of some specified closed convex sets in the space of symmetric matrices we address the covariance feasibility problem to determine the existence and compute a covariance matrix to satisfy assignability and output norm performance constraints we address the covariance optimization problem to construct an assignable covariance matrix which satisfies output performance constraints and is as close as possible to a given desired covariance we also treat inconsistent constraints where we look for an assignable covariance matrix which best approximates desired but non achievable output performance objectives we call this the infeasible covariance optimization problem all these problems are of a conve

paper low order control design for lmi problems using alternating projection methods computational techniques based on alternating projections are proposed to solve control design problems described by linear matrix inequalities lmis in particular we concentrate on the stabilization and the suboptimal h output feedback control design problems these problems can be described by a pair of lmis and an additional coupling condition this coupling condition is convex for the full order control design problem but convexity is lost for the control problem of order strictly less than the plant order we formulate these problems as feasibility problems with matrix constraint sets of simple geometry and we utilize this geometry to obtain analytical expressions for the orthogonal projection operators onto these sets full order and low order controllers are designed using alternating projection methods for the full order controller case global convergence of the alternating projection methods to a feasible solution is guaranteed however for the low order control case only local convergence is guaranteed an example is provided to illustrate the use of these methods for the full order and the low order controller design

entropy based algorithms for best basis selection adapted waveform analysis uses a library of orthonormal bases and an efficiency functional to match a basis to a given signal or family of signals it permits efficient compression of a variety of signals such as sound and images the predefined libraries of modulated waveforms include orthogonal wavelet packets and localized trigonometric functions and have reasonably well controlled time frequency localization properties the idea is to build out of the library functions an orthonormal basis relative to which the given signal or collection of signals has the lowest information cost the method relies heavily on the remarkable orthogonality properties of the new libraries all expansions in a given library conserve energy and are thus comparable several cost functionals are useful one of the most attractive is shannon entropy which has a geometric interpretation in this context

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

propagation and stability of waves of electrical activity in the cerebral cortex nonlinear equations are introduced to model the behavior of the waves of cortical electrical activity that are responsible for signals observed in electroencephalography these equations incorporate nonlinearities axonal and dendritic lags excitatory and inhibitory neuronal populations and the two dimensional nature of the cortex while rendering nonlinear features far more tractable than previous formulations both analytically and numerically the model equations are first used to calculate steady state levels of cortical activity for various levels of stimulation dispersion equations for linear waves are then derived analytically and an analytic expression is found for the linear stability boundary beyond which a seizure will occur the effects of boundary conditions in determining global eigenmodes are also studied in various geometries and the corresponding eigenfrequencies are found numerical results confirm the analytic ones which are also found to reproduce existing results in the relevant limits thereby elucidating the limits of validity of previous approximations

minimum norm regularization of descriptor systems by mixed output feedback we study the regularization problem for linear constant coefficient descriptor systems ex ax bu y1 cx y2 x by proportional and derivative mixed output feedback necessary and sufficient conditions are given which guarantee that there exist output feedbacks such that the closed loop system is regular has index at most one and e bg has a desired rank i e there is a desired number of differential and algebraic equations to resolve the freedom in the choice of the feedback matrices we then discuss how to obtain the desired regularizing feedback of minimum norm and show that this approach leads to useful results in the sense of robustness only if the rank of e is decreased numerical procedures are derived to construct the desired feedback gains these numerical procedures are based on orthogonal matrix transformations which can be implemented in a numerically stable way

analysis and design of fuzzy controller and fuzzy observer this paper addresses the analysis and design of a fuzzy controller and a fuzzy observer on the basis of the takagi sugeno t s fuzzy model the main contribution of the paper is the development of the separation property that is the fuzzy controller and the fuzzy observer can be independently designed a numerical simulation and an experiment on an inverted pendulum system are described to illustrate the performance of the fuzzy controller and the fuzzy observer

computing a nearest symmetric positive semidefinite matrix the nearest symmetric positive semidefinite matrix in the frobenius norm to an arbitrary real matrix a is shown to be b h 2 where h is the symmetric polar factor of b a at 2 in the 2 norm a nearest symmetric positive semidefinite matrix and its distance 2 a from a are given by a computationally challenging formula due to halmos we show how the bisection method can be applied to this formula to compute upper and lower bounds for 2 a differing by no more than a given amount a key ingredient is a stable and efficient test for positive definiteness based on an attempted choleski decomposition for accurate computation of 2 a we formulate the problem as one of zero finding and apply a hybrid newton bisection algorithm some numerical difficulties are discussed and illustrated by example

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

stability analysis and design of fuzzy control systems abstract the stability analysis and the design technique of fuzzy control systems using fuzzy block diagrams are discussed first we show the concept of fuzzy blocks and consider the connection problems of fuzzy blocks diagrams we derive some theorems and corollaries with respect to two basic types of connections of fuzzy blocks in order to preserve some properties in a connection of fuzzy blocks continuous piecewise polynomial membership functions are defined secondly a sufficient condition which guarantees the stability of fuzzy systems is obtained in terms of lyapunov s direct method we give an important fact based on this condition thirdly we propose a new design technique of a fuzzy controller the fuzzy block diagrams and the stability analysis are applied to the design problems of a model based fuzzy controller

permutation entropy analysis based on gini simpson index for financial time series abstract in this paper a new coefficient is proposed with the objective of quantifying the level of complexity for financial time series for researching complexity measures from the view of entropy we propose a new permutation entropy based on gini simpson index gpe logistic map is applied to simulate time series to show the accuracy of the gpe method and expound the extreme robustness of our gpe by the results of simulated time series meanwhile we compare the effect of the different order of gpe and then we employ it to us and european and chinese stock markets in order to reveal the inner mechanism hidden in the original financial time series after comparison of these results of stock indexes it can be concluded that the relevance of different stock markets are obvious to study the complexity features and properties of financial time series it can provide valuable information for understanding the inner mechanism of financial markets

feedback control of nonlinear systems by extended linearization for single input multiple output nonlinear systems we consider a design method based on the family of linearizations of the system parameterized by constant operating points nonlinear state feedback control laws and observer state feedback control laws are designed such that the eigenvalues of the family of linearized closed loop systems are placed at specified values that are locally invariant with respect to the closed loop operating point the method is illustrated by application to the problem of automatically balancing an inverted pendulum

fuzzy descriptor systems and nonlinear model following control this paper defines a fuzzy descriptor system by extending the ordinary takagi sugeno t s fuzzy model several kinds of stability conditions for the fuzzy descriptor system are derived and represented in terms of linear matrix inequalities lmis we illustrate an example of defining the fuzzy descriptor system instead of the ordinary t s fuzzy model an lmi design approach is employed to find stable feedback gains and a common lyapunov function in addition this paper presents a nonlinear model following control for the fuzzy descriptor system a new parallel distributed compensation the so called twin parallel distributed compensations tpdc to realize the nonlinear model following control is proposed we present a design technique based on the tpdc the proposed method is a unified approach to nonlinear model following control it contains the regulation and servo control problems as special cases

image restoration by the method of convex projections part 1ߞtheory a projection operator onto a closed convex set in hilbert space is one of the few examples of a nonlinear map that can be defined in simple abstract terms moreover it minimizes distance and is nonexpansive and therefore shares two of the more important properties of ordinary linear orthogonal projections onto closed linear manifolds in this paper we exploit the properties of these operators to develop several iterative algorithms for image restoration from partial data which permit any number of nonlinear constraints of a certain type to be subsumed automatically their common conceptual basis is as follows every known property of an original image f is envisaged as restricting it to lie in a well defined closed convex set thus m such properties place f in the intersection e0 ei of the corresponding closed convex sets e1 e2 em given only the projection operators pi onto the individual ei s i 1 m we restore f by recursive means clearly in this approach the realization of the pi s in a hilbert space setting is one of the major synthesis problems section i describes the geometrical significance of the three main theorems in considerable detail and most of the underlying ideas are illustrated with the aid of simple diagrams section ii presents rules for the numerical implementation of 11 specific projection operators which are found to occur frequently in many signal processing applications and the appendix contains proofs of all the major results

technical communique stabilization of discrete time singular systems a matrix inequalities approach this paper is concerned with the state feedback stabilization problem of discrete time singular systems the singular system under consideration is not assumed to be regular the problem we address is to design state feedback controllers such that the resulting closed loop system is regular causal and stable conditions for the existence of solutions to this problem are obtained expressed in terms of certain matrix inequalities when these conditions are satisfied the explicit formula of desired state feedback controllers is also given without resorting to decomposing the system matrices

delay dependent stability and h control for a class of fuzzy descriptor systems with time delay this paper addresses issues of stability analysis and h control for a class of fuzzy time delay descriptor systems described by an extended takagi sugeno t s fuzzy model a delay dependent stability criterion is first presented and a h control synthesis approach is then developed both the stability criterion and the h controller synthesis are based on the solutions of linear matrix inequalities lmis finally two examples are given to illustrate the effectiveness of the approaches proposed in this paper

testing for nonlinearity in time series the method of surrogate data we describe a statistical approach for identifying nonlinearity in time series the method first specifies some linear process as a null hypothesis then generates surrogate data sets which are consistent with this null hypothesis and finally computes a discriminating statistic for the original and for each of the surrogate data sets if the value computed for the original data is significantly different than the ensemble of values computed for the surrogate data then the null hypothesis is rejected and nonlinearity is detected we discuss various null hypotheses and discriminating statistics the method is demonstrated for numerical data generated by known chaotic systems and applied to a number of experimental time series which arise in the measurement of superfluids brain waves and sunspots we evaluate the statistical significance of the evidence for nonlinear structure in each case and illustrate aspects of the data which this approach identifies

chaos and generalised multistability in a mesoscopic model of the electroencephalogram abstract we present evidence for chaos and generalised multistability in a mesoscopic model of the electroencephalogram eeg two limit cycle attractors and one chaotic attractor were found to coexist in a two dimensional plane of the ten dimensional volume of initial conditions the chaotic attractor was found to have a moderate value of the largest lyapunov exponent 3 4 s 1 base e with an associated kaplan yorke lyapunov dimension of 2 086 there are two different limit cycles appearing in conjunction with this particular chaotic attractor one multiperiodic low amplitude limit cycle whose largest spectral peak is within the alpha band 8 13 hz of the eeg and another multiperiodic large amplitude limit cycle which may correspond to epilepsy the cause of the coexistence of these structures is explained with a one parameter bifurcation analysis each attractor has a basin of differing complexity the large amplitude limit cycle has a basin relatively uncomplicated in its structure while the small amplitude limit cycle and chaotic attractor each have much more finely structured basins of attraction but none of the basin boundaries appear to be fractal the basins of attraction for the chaotic and small amplitude limit cycle dynamics apparently reside within each other we briefly discuss the implications of these findings in the context of theoretical attempts to understand the dynamics of brain function and behaviour

a new metric for probability distributions we introduce a metric for probability distributions which is bounded information theoretically motivated and has a natural bayesian interpretation the square root of the well known spl chi sup 2 distance is an asymptotic approximation to it moreover it is a close relative of the capacitory discrimination and jensen shannon divergence

stability analysis of discrete singular fuzzy systems abstract this work mainly develops a discrete singular fuzzy model and discusses its stability the standard discrete t s model is generalized into the so called discrete singular takagi sugeno dst s model which can represent a larger class of nonlinear systems and the stability criteria of this system are then investigated these criteria are described by non strict linear matrix inequalities and we thus involve the projection method for ensuring stability based on some derived projection operators a projection algorithm is proposed for solving a feasible solution an illustrating example demonstrates the validity and effectiveness of the proposed method

metabifurcation analysis of a mean field model of the cortex mean field models mfms of cortical tissue incorporate salient average features of neural masses in order to model activity at the population level thereby linking microscopic physiology to macroscopic observations e g with the electroencephalogram eeg one of the common aspects of mfm descriptions is the presence of a high dimensional parameter space capturing neurobiological attributes deemed relevant to the brain dynamics of interest we study the physiological parameter space of a mfm of electrocortical activity and discover robust correlations between physiological attributes of the model cortex and its dynamical features these correlations are revealed by the study of bifurcation plots which show that the model responses to changes in inhibition belong to two archetypal categories or families after investigating and characterizing them in depth we discuss their essential differences in terms of four important aspects power responses with respect to the modeled action of anesthetics reaction to exogenous stimuli such as thalamic input and distributions of model parameters and oscillatory repertoires when inhibition is enhanced furthermore while the complexity of sustained periodic orbits differs significantly between families we are able to show how metamorphoses between the families can be brought about by exogenous stimuli we here unveil links between measurable physiological attributes of the brain and dynamical patterns that are not accessible by linear methods they instead emerge when the nonlinear structure of parameter space is partitioned according to bifurcation responses we call this general method metabifurcation analysis the partitioning cannot be achieved by the investigation of only a small number of parameter sets and is instead the result of an automated bifurcation analysis of a representative sample of 73 454 physiologically admissible parameter sets our approach generalizes straightforwardly and is well suited to probing the dynamics of other models with large and complex parameter spaces

stability analysis and systematic design of fuzzy control systems abstract a method of the stability analysis and systematic design of fuzzy control systems is presented in this paper the fuzzy control system is formulated by a set of local takagi sugeno fuzzy models t s fuzzy model with aggregation the controller is designed by state feedback for each local model separately it is shown that under some conditions the controller designed can guarantee the global stability of the closed loop fuzzy system the stability of the whole closed loop fuzzy system is also proved via the piecewise lyapunov function the simulation results for the fuzzy control of a nonlinear system the ball and beam system bb system show that this method is effective

quantifying the dynamical complexity of chaotic time series a powerful approach is proposed for the characterization of chaotic signals it is based on the combined use of two classes of indicators i the probability of suitable symbolic sequences obtained from the ordinal patterns of the corresponding time series ii the width of the corresponding cylinder sets this way much information can be extracted and used to quantify the complexity of a given signal as an example of the potentiality of the method i introduce a modified permutation entropy which allows for quantitative estimates of the kolmogorov sinai entropy in hyperchaotic models where other methods would be unpractical as a by product estimates of the fractal dimension of the underlying attractors are possible as well