measuring the strangeness of strange attractors we study the correlation exponent v introduced recently as a characteristic measure of strange attractors which allows one to distinguish between deterministic chaos and random noise the exponent v is closely related to the fractal dimension and the information dimension but its computation is considerably easier its usefulness in characterizing experimental data which stem from very high dimensional systems is stressed algorithms for extracting v from the time series of a single variable are proposed the relations between the various measures of strange attractors and between them and the lyapunov exponents are discussed it is shown that the conjecture of kaplan and yorke for the dimension gives an upper bound for v various examples of finite and infinite dimensional systems are treated both numerically and analytically

robust h control of t s fuzzy systems with input time varying delays a delay partitioning method abstract addressed in this paper is the robust h control issue of t s fuzzy systems with input time varying delays by means of the delay partitioning method the delay interval is partitioned into multiple unequal subintervals whose lengths satisfy a geometric sequence on this basis a modified lyapunov krasovskii functional is presented to analyze asymptotic stability of the open loop system then a state feedback controller that ensures a prescribed h performance level for the closed loop system is proposed in linear matrix inequality format finally two numerical examples are given to illustrate the effectiveness and advantages of the obtained results

improved linear matrix inequality approach to stability analysis of linear systems with interval time varying delays this paper investigates the problem of stability analysis for a class of linear systems with interval time varying delay in order to develop a less conservative stability condition a lyapunov krasovskii functional comprising novel integral terms is introduced convex combination idea is utilized to derive a stability criterion in terms of linear matrix inequalities lmis without any additional free weighting matrices which increase drastically the computational burden of the stability test numerical examples are presented to illustrate the superiority of the proposed approach compared to some existing ones in the literature

estimating the errors on measured entropy and mutual information abstract information entropy and the related quantity mutual information are used extensively as measures of complexity and to identify nonlinearity in dynamical systems expressions for the probability distribution of entropies and mutual informations calculated from finite amounts of data exist in the literature but the expressions have seldom been used in the field of nonlinear dynamics in this paper formulae for estimating the errors on observed information entropies and mutual informations are derived using the standard error analysis familiar to physicists their validity is demonstrated by numerical experiment for illustration the formulae are then used to evaluate the errors on the time lagged mutual information of the logistic map

stability and stabilization of t s fuzzy systems with time varying delays via augmented lyapunov krasovskii functionals this paper is concerned with the problem of stability and stabilization for takagi sugeno t s fuzzy systems with time varying delays by constructing a suitable lyapunov krasovskii functional sufficient conditions for ensuring the asymptotic stability and stabilization of the concerned fuzzy systems have been derived within the framework of linear matrix inequalities lmis the advantage and effectiveness of the proposed criteria will be shown through the comparison of maximum delay bounds with some results obtained by recently published papers via four numerical examples

fuzzy control turns 50 in 2015 we celebrate the 50th anniversary of fuzzy sets ten years after the main milestones regarding its applications in fuzzy control in their 40th birthday were reviewed in fss see 1 ten years is at the same time a long period and short time thinking to the inner dynamics of research this paper presented for these 50 years of fuzzy sets is taking into account both thoughts a first part presents a quick recap of the history of fuzzy control from model free design based on human reasoning to quasi lpv linear parameter varying model based control design via some milestones and key applications the second part shows where we arrived and what the improvements are since the milestone of the first 40 years a last part is devoted to discussion and possible future research topics

nonlinear analysis of river flow time sequences within the field of chaos theory several methods for the analysis of complex dynamical systems have recently been proposed in light of these ideas we study the dynamics which control the behavior over time of river flow investigating the existence of a low dimension deterministic component the present article follows the research undertaken in the work of porporato and ridolfi 1996a in which some clues as to the existence of chaos were collected particular emphasis is given here to the problem of noise and to nonlinear prediction with regard to the latter the benefits obtainable by means of the interpolation of the available time series are reported and the remarkable predictive results attained with this nonlinear method are shown

testing the assumptions of linear prediction analysis in normal vowels in this paper we develop an improved surrogate data test to show experimental evidence for all the simple vowels of u s english for both male and female speakers that gaussian linear prediction analysis a ubiquitous technique in current speech technologies cannot be used to extract all the dynamical structure of real speech time series the test provides robust evidence undermining the validity of these linear techniques supporting the assumptions of either dynamical nonlinearity and or non gaussianity common to more recent complex efforts at dynamical modeling speech time series however an additional finding is that the classical assumptions cannot be ruled out entirely and plausible evidence is given to explain the success of the linear gaussian theory as a weak approximation to the true nonlinear non gaussian dynamics this supports the use of appropriate hybrid linear nonlinear non gaussian modeling with a calibrated calculation of statistic and particular choice of experimental protocol some of the known systematic problems of the method of surrogate data testing are circumvented to obtain results to support the conclusions to a high level of significance

a novel identification method for takagi sugeno fuzzy model abstract based on the xie beni index and an improved particle swarm optimization algorithm a novel identification method for the takagi sugeno fuzzy model is proposed in this paper firstly xie beni indices with a fuzzy c means clustering algorithm are adopted to find the rule number of the takagi sugeno fuzzy model by utilizing the particle swarm optimization algorithm the initial membership function and the consequent parameters of the fuzzy model are obtained in addition through an improved fuzzy c regression model and orthogonal least square method the premise structure and consequent parameters can be obtained to establish the takagi sugeno fuzzy model some well known models are used to demonstrate that the proposed method outperforms some existing methods

stability analysis and performance design for fuzzy model based control system under imperfect premise matching this paper investigates the stability analysis and performance design of nonlinear systems to facilitate the stability analysis the takagi sugeno t s fuzzy model is employed to represent the nonlinear plant under the imperfect premise matching in which t s fuzzy model and fuzzy controller do not share the same membership functions a fuzzy controller with enhanced design flexibility and robustness property is proposed to control the nonlinear plant however the nice characteristic given by the perfect premise matching leading to conservative stability conditions vanishes in this paper under the imperfect premise matching information of membership functions of the fuzzy model and controller are considered in stability analysis with the introduction of slack matrices relaxed linear matrix inequality lmi based stability conditions are derived using lyapunov based approach furthermore lmi based performance conditions are provided to guarantee system performance simulation examples are given to illustrate the effectiveness of the proposed approach

information and entropy in strange attractors a technique for analyzing time series data from experiments is presented that provides estimates of four basic characteristics of a system 1 the measure theoretic entropy 2 the accuracy of the measurements 3 the number of measurements necessary to specify a system state and 4 the best delay time t to use in order to construct phase space portraits by the method of delays these characteristics are obtained by separating the entropy of measurements into a part due to noise and parts due to deterministic effects for the technique to work the noise associated with each measurement must be independent of the noise associated with all other measurements an algorithm for implementing the analysis is presented with three examples

network based output tracking control for t s fuzzy systems using an event triggered communication scheme this paper is concerned with network based output tracking control for a t s fuzzy system an event triggered communication scheme under which the threshold depends on the latest successfully transmitted sampled data is introduced to reduce network resource utilization taking the event triggered communication scheme and the asynchronous operation between the fuzzy system and the fuzzy controller the resulting system is modeled as an asynchronous threshold error dependent system with an interval time varying delay a new delay dependent criterion for l 2 gain tracking performance of the asynchronous system is derived by applying the deviation bounds of asynchronous normalized membership functions based on this performance criterion some criteria on the existence of the fuzzy tracking controller are established a co design algorithm is presented to obtain the control gains and the event triggering parameters simultaneously an example is given to illustrate the effectiveness of the proposed method

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

communication delay distribution dependent networked control for a class of t s fuzzy systems this paper investigates a robust networked control for a class of takagi sugeno t s fuzzy systems the controller design specifically takes probabilistic interval distribution of the communication delay into account a general framework of networked control is first proposed the two main features are 1 the zero order hold can choose the latest control input signal when the packets received are out of order and 2 as the result of 1 the models of the all kinds of uncertainties in networked signal transfer including network induced delay and data packet dropout are under a unified framework next if the probability distribution of communication delay is known or specified in a design process sufficient stability conditions for networked t s fuzzy systems are derived which are based on the lyapunov theory following this a stabilizing controller design method is developed which shows that the solvability of the design depends not only on the upper and lower bounds of the delay but on its probability distribution as well finally a numerical example is used to show the application of the theoretical results obtained in this paper

convergence of the k 2 entropy for random noises with power law spectra abstract we discuss a counter example to the traditional expectation that stochastic processes lead to a non convergence of the k 2 entropy in computed or measured time series we consider a simple class of colored random noises with power law spectra which have already been shown to generate finite and predictable values of the correlation dimension we show that the k 2 entropy of these random noises converges as well these results imply that the observation of a finite or null value of the k 2 entropy in the analysis of data is not enough to infer that the system is dominated by a deterministic process such as low dimensional chaos

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

delay range dependent robust stabilization for uncertain t s fuzzy control systems with interval time varying delays this paper is concerned with robust stabilization for a class of t s fuzzy control systems with interval time varying delays an approach is proposed to significantly improve the system performance while reducing the number of scalar decision variables in linear matrix inequalities the main points of the approach are i two coupling integral inequalities are proposed to deal with some integral items in the derivation of the stability criteria ii an appropriate lyapunov krasovskii functional is constructed by including both the lower and upper bounds of the interval time varying delays and iii neither model transformation nor free weighting matrices are employed in the theoretical result derivation as a result some improved sufficient stability criteria are derived and the maximum allowable delay bound and controller gains can be obtained simultaneously by solving an optimization problem numerical examples are given to demonstrate the effectiveness of the proposed approach

fundamental limitations for estimating dimensions and lyapunov exponents in dynamical systems we show that values of the correlation dimension estimated over a decade from the grassberger procaccia algorithm cannot exceed the value 2 log10n if n is the number of points in the time series when this bound is saturated it is thus not legitimate to conclude that low dimensional dynamics is present the estimation of lyapunov exponents is also discussed

research on the evolution of stock correlation based on maximal spanning trees abstract in this study we choose the daily closing price of 268 constituent stocks of the s p 500 index 221 stocks of london stock exchange 148 constituent stocks of the shanghai composite index and 152 constituent stocks of the hang seng index as the research objects and select the sample of all the stock markets from 2 january 2003 to 16 september 2013 for each stock market first using a moving window to scan through every stock return series and mutual information to measure the statistical interdependence between stock returns we construct a corresponding weighted network in every given window then we study the evolution of stock correlation by analyzing the average mutual information mutual information distribution and topology structure s variation of the maximal spanning tree extracting from every weighted network all the obtained results indicate that for all the stock markets both the average mutual information and the standard deviation of mutual information distribution first gradually increase and they reach a peak during the full outbreak periods and finally they decrease again in addition the topology structure of the maximal spanning tree also changes from compact star like to loose chain like first and then turns to compact star like once more all the facts tell us that the crisis does change the stock correlation and the stock correlation is from weak to strong first and then becomes weak again

products of similar matrices abstract given a nontrivial conjugacy class of gl v which is contained in sl v we want to find a minimal integer k such that every element of sl v is a product of at most k elements of the analogous question is studied when is replaced by 1 where is a nontrivial conjugacy class of gl v

constrained realization monte carlo method for hypothesis testing abstract we compare two theoretically distinct approaches to generate artificial or surrogate data for testing hypotheses about a given data set the first and more straightforward approach is to fit a single best model to the original data and then to generate surrogate data sets that are typical realizations of that model the second approach concentrates not on the model but directly on the original data it attempts to constrain the surrogate data sets so that they exactly agree with the original data for a specified set of sample statistics examples of these two approaches are provided for two simple cases a test for deviations from a gaussian distribution and a test for serial dependence in a time series additionally we consider test for nonlinearity in time series based on a fourier transform ft method and on more conventional autoregressive moving average arma fits to the data the comparative performance of hypothesis testing schemes based on these two approaches is found to depend on whether or not the discriminating statistic is pivotal a statistic is pivotal if its distribution is the same for all processes consistent with the null hypothesis the typical realization method requires that the discriminating statistic satisfy this property the constrained realization approach on the other hand does not share this requirement and can provide an accurate and powerful test without having to sacrifice flexibility in the choice of discriminating statistic

using surrogate data to detect nonlinearity in time series we address the issue of reliably discriminating between chaos and noise from a time series in particular we are interested in avoiding claims of chaos when simpler models such as linearly correlated noise can explain the data we take a statistical approach and use a form of bootstrapping to detect nonlinearity by showing that a given linear model is unlikely to have produced the data our method requires the careful statement of a null hypothesis which characterizes a candidate linear process the generation of an ensemble of surrogate data sets which are similar to the original time series but consistent with the null hypothesis and the computation of a discriminating statistic for the original and for each of the surrogate data sets the idea is to test the original time series against the null hypothesis by checking whether the discriminating statistic computed for the original time series differs significantly from the statistics computed for each of the surrogate sets we present algorithms for generating surrogate data under various null hypotheses and we show the results of numerical experiments on artificial data using correlation dimension lyapunov exponent and forecasting error as discriminating statistics finally we consider a number of experimental timemore series including sunspots electroencephalogram eeg signals and fluid convection and evaluate the statistical significance of the evidence for nonlinear structure in each case 52 refs 10 figs less

generalized redundancies for time series analysis abstract extensions to various information theoretic quantities such as entropy redundancy and mutual information are discussed in the context of their role in nonlinear time series analysis we also discuss linearized versions of these quantities and their use as benchmarks in tests for nonlinearity many of these quantities can be expressed in terms of the generalized correlation integral and this expression permits us to more clearly exhibit the relationships of these quantities to each other and to other commonly used nonlinear statistics such as the bds and green savit statistics further numerical estimation of these quantities is found to be more accurate and more efficient when the the correlation integral is employed in the computation finally we consider several local versions of these quantities including a local kolmogorov sinai entropy which gives an estimate of variability of the short term predictability

products of cyclic conjugacy classes in the groups psl n f abstract let g be the group psl n f where f is a field and n 3 if c is a conjugacy class of g denote c 1 c 1 c c the following is proved 1 if c1 c2 c3 are cyclic conjugacy classes of g then c1c2c3 g 1g 2 if f is algebraically closed and c1 c2 are cyclic conjugacy classes of g then c1c2 g if and only if c1 c 12 generalizations of these results concerning factorizations of a given nonscalar invertible matrix as a product of two or three cyclic matrices each lying in a prescribed conjugacy class of gl n f or sl n f are discussed

covering gl v and products of blockcyclic matrices let v be an n dimensional vector space over a field k where n n n 3 k 4 a linear transformation v v is called blockcyclic if the minimum rank satisfies n 2 we study products of blockcyclic conjugacy classes in gl v example if and are products of blockcyclic conjugacy classes in gl v then contains a cyclic transformation the results are used in our study on products of singular similarity classes knuppel and nielsen in press 8 a further application of our methods is the following theorem let k n n 1 a non central conjugacy class of gl v and gl v such that det det k then k a similar result was proved in lev s article lev 1996 10

conditional independence graph for nonlinear time series and its application to international financial markets abstract conditional independence graphs are proposed for describing the dependence structure of multivariate nonlinear time series which extend the graphical modeling approach based on partial correlation the vertexes represent the components of a multivariate time series and edges denote direct dependence between corresponding series the conditional independence relations between component series are tested efficiently and consistently using conditional mutual information statistics and a bootstrap procedure furthermore a method combining information theory with surrogate data is applied to test the linearity of the conditional dependence the efficiency of the methods is approved through simulation time series with different linear and nonlinear dependence relations finally we show how the method can be applied to international financial markets to investigate the nonlinear independence structure

testing for nonlinearity using redundancies quantitative and qualitative aspects abstract a method for testing nonlinearity in time series is described based on information theoretic functionals redundancies linear and nonlinear forms of which allow either qualitative or after incorporating the surrogate data technique quantitative evaluation of dynamical properties of scrutinized data an interplay of quantitative and qualitative testing on both the linear and nonlinear levels is analyzed and robustness of this combined approach against spurious nonlinearity detection is demonstrated evaluation of redundancies and redundancy based statistics as functions of time lag and embedding dimension can further enhance insight into dynamics of a system under study

stabilization of t s fuzzy system with time delay under sampled data control using a new looped functional this paper investigates the sampled data stabilization problem for a takagi sugeno t s fuzzy system with time delay by taking the information of states within the intervals from t k to t and t to t k 1 into account a new two side delay dependent looped functional is introduced which can not only relax the monotonic constraint of lyapunov krasovskii functional lkf but also make better use of the actual sampling pattern furthermore the sampled data fuzzy controller is designed to contain both the present and delayed state information thereby enhancing the control performance and design flexibility based on the novel augmented lkf and improved bounding technique less conservative stability criteria are derived in the form of linear matrix inequalities the superiority of proposed results is shown by two simulation examples

reciprocally convex approach to stability of systems with time varying delays whereas the upper bound lemma for matrix cross product introduced by park 1999 and modified by moon park kwon and lee 2001 plays a key role in guiding various delay dependent criteria for delayed systems the jensen inequality has become an alternative as a way of reducing the number of decision variables it directly relaxes the integral term of quadratic quantities into the quadratic term of the integral quantities resulting in a linear combination of positive functions weighted by the inverses of convex parameters this paper suggests the lower bound lemma for such a combination which achieves performance behavior identical to approaches based on the integral inequality lemma but with much less decision variables comparable to those based on the jensen inequality lemma

finite correlation dimension for stochastic systems with power law spectra abstract we discuss a counter example to the traditional view that stochastic processes lead to a non convergence of the correlation dimension in computed or measured time series specifically we show that a simple class of colored random noises characterized by a power law power spectrum have a finite and predictable value for the correlation dimension these results have implications on the experimental study of deterministic chaos as they indicate that the soie observation of a finite fractal dimension from the analysis of a time series is not sufficient to infer the presence of a strange attractor in the system dynamics we demonstrate that the types of random noises considered herein may be given an interpretation in terms of their fractal properties the consequent exploitation of the non gaussian behavior of these random noises leads us to the introduction of a new time series analysis method which we call multivariate scaling analysis we apply this approach to characterize several global properties of random noise

coarse grained embeddings of time series random walks gaussian random processes and deterministic chaos a new method for studying time series is described based on a statistic indicating the degree to which trajectories passing through a small region of an embedding space are parallel the method is particularly suited to time series with a significant correlation time analytic results are presented for brownian motion and gaussian random processes these are generally different from the results for chaotic systems allowing a test for deterministic dynamics in a time series a variety of examples are presented of the application of the method to low and high dimensional systems

robust h control for nonlinear systems over network a piecewise analysis method a piecewise analysis method pam is proposed to investigate the h performance analysis and h control design for nonlinear networked control systems nncss which are presented in the form of t s fuzzy model with time varying input delay different from the existing method in dealing with the time varying delay the whole variation interval of the delay is divided into two subintervals with equal length respecting for the delay belonging each subinterval new criteria on h performance analysis of the nncss are obtained by checking the variation of the derivative of the lyapunov functional in the two subintervals then criteria for the h controller design are obtained by using the convexity properties of the matrix inequality and some other new analysis techniques which are shown in terms of nonlinear matrix inequalities and can be solved by using a cone complementarity liberalization method as application of the derived results h controller design is carried out for the nonlinear mass spring system discussion shows that the proposed method is less conservative than the existing references

parameter dependent lyapunov functional for stability of time delay systems with polytopic type uncertainties this note concerns the problem of the robust stability of a linear system with a time varying delay and polytopic type uncertainties in order to construct a parameter dependent lyapunov functional for the system we first devised a new method of dealing with a time delay system without uncertainties in this method the derivative terms of the state which is in the derivative of the lyapunov functional are retained and some free weighting matrices are used to express the relationships among the system variables and among the terms in the leibniz newton formula as a result the lyapunov matrices are not involved in any product terms of the system matrices in the derivative of the lyapunov functional this method is then easily extended to a system with polytopic type uncertainties numerical examples demonstrate the validity of the proposed criteria

an improved result on the stability of uncertain t s fuzzy systems with interval time varying delay this paper is concerned with the stability of uncertain t s fuzzy systems with interval time varying delay by uniformly dividing the delay interval into multiple segments and constructing an appropriate augmented lyapunov krasovskii functional some less conservative stability criteria are obtained which include some existing results as special cases since a tighter bounding inequality is employed to deal with time varying delay dependent integral items then some sources of computational complexity such as the general convex combination and free weighting matrices are not necessary to be adopted in the derivation of our results as a result the developed criteria not only theoretically improve some existing results but also have higher computational efficiency numerical examples are given to demonstrate the effectiveness of the proposed method

new approach on robust delay dependent h _ infty control for uncertain t s fuzzy systems with interval time varying delay this paper investigates the robust h infin control for takagi sugeno t s fuzzy systems with interval time varying delay by employing a new and tighter integral inequality and constructing an appropriate type of lyapunov functional delay dependent stability criteria are derived for the control problem because neither any model transformation nor free weighting matrices are employed in our theoretical derivation the developed stability criteria significantly improve and simplify the existing stability conditions also the maximum allowable upper delay bound and controller feedback gains can be obtained simultaneously from the developed approach by solving a constrained convex optimization problem numerical examples are given to demonstrate the effectiveness of the proposed methods

strange attractors that are not chaotic abstract it is shown that in certain types of dynamical systems it is possible to have attractors which are strange but not chaotic here we use the word strange to refer to the geometry or shape of the attracting set while the word chaotic refers to the dynamics of orbits on the attractor in particular the exponential divergence of nearby trajectories we first give examples for which it can be demonstrated that there is a strange nonchaotic attractor these examples apply to a class of maps which model nonlinear oscillators continuous time which are externally driven at two incommensurate frequencies it is then shown that such attractore are persistent under perturbations which preserve the original system type i e there are two incommensurate external driving frequencies this suggests that for systems of the typw which we have considered nonchaotic strange attractors may be expected to occur for a finite interval of parameter values on the other hand when small perturbations which do not preserve the system type are numerically introduced the strange nonchaotic attractor is observed to be converted to a periodic or chaotic orbit thus we conjecture that in general continuous time systems flows which are not externally driven at two incommensurate frequencies should not be expected to have strange nonchaotic attractors except possibly on a set of measure zero in the parameter space

delay dependent h control for uncertain fuzzy systems with time varying delays this paper addresses the robust stabilization and robust h control problems of uncertain fuzzy delayed systems via a parallel distributed compensation pdc scheme the uncertainties are norm bounded and the delay may be either constant or time varying and either differentiable or non differentiable presented in this paper are some robust stabilization and robust h control criteria which are delay dependent in general and delay derivative dependent when the delay is differentiable these results enjoy much less conservatism and more computational simplicity compared with those in the existing literature and permit if the delay is differentiable the derivative to be larger than one some examples are given to illustrate the results in this paper

sampled data robust h control for t s fuzzy systems with time delay and uncertainties abstract this paper investigates sampled data robust h control for t s fuzzy systems with time delay and uncertainties by introducing the free weighting matrices to deal with the integral items and converting the coupling time varying matrix inequalities into a group of decoupling matrix inequalities an innovative delay dependent stabilization criterion is first presented then a sampled data h controller is designed to stabilize the t s fuzzy system to achieve the prescribed disturbance attenuation level which is dependent on both the size of state delay and upper bound of allowable sampling period since 1 the sawtooth structure of delay is fully considered 2 neither model transformation nor bounding techniques are employed in deriving the delay dependent results and 3 none of the integral items are arbitrarily ignored and magnified the less conservative results can be expected a practical application example is given to demonstrate the effectiveness of the proposed methods

the extended covering number of sln is n 1 abstract for a special linear group sln k k a field we want to find the minimal integer k extended covering number such that 1 c1 ck for arbitrary non central conjugacy classes ci of sln k using methods from chevalley groups length theorems on products of simple mappings and theorems on products of cyclic mappings we find that k n 1 provided n and the field are not too small

technical communique stability and robust stability for systems with a time varying delay to concern the stability and robust stability criteria for systems with time varying delays this note uses not only the time varying delayed state x t h t but also the delay upper bounded state x email protected to exploit all possible information for the relationship among a current state x t an exactly delayed state x t h t a marginally delayed state x email protected and the derivative of the state email protected t when constructing lyapunov krasovskii functionals and some appropriate integral inequalities originally suggested by park 1999 a delay dependent stability criterion for systems with uncertain time invariant delays ieee transactions on automatic control 44 4 876 877 two fundamental criteria are provided for the cases where no bound of delay derivative is assumed and where an upper bound of delay derivative is assumed examples show the resulting criteria outperform all existing ones in the literature

filtered noise can mimic low dimensional chaotic attractors this contribution presents four results first calculations indicate that when examined by the grassberger procaccia algorithm alone filtered noise can mimic low dimensional chaotic attractors given the ubiquity of signal filtering in experimental investigations this is potentially important second a criterion is derived which provides an estimate of the minimum data accuracy needed to resolve the dimension of an attractor third it is shown that a criterion derived by eckmann and ruelle physica d 56 185 1992 to estimate the minimum number of data points required in a grassberger procaccia calculation can be used to provide a further check on these dimension estimates fourth it is shown that surrogate data techniques recently published by theiler and his colleagues in nonlinear modeling and forecasting edited by m casdagli and s eubanks addison wesley reading ma 1992 can successfully distinguish between linearly correlated noise and nonlinear structure these results and most particularly the first indicate that grassberger procaccia results must be interpreted with far greater circumspection than has previously been the case and that the algorithm should be used in combination with additional procedures such as calculations with surrogate data when filtered signals are examined by this algorithm alone a finite noninteger value of mathit d 2 is consistent with low dimensional chaotic behavior but it is certainly not a definitive diagnostic of chaos

brief paper a discrete delay decomposition approach to stability of linear retarded and neutral systems this paper is concerned with stability of linear time delay systems of both retarded and neutral types by using some new simple quadratic lyapunov krasovskii functionals these lyapunov krasovskii functionals consist of two parts one part comes from some existing lyapunov krasovskii functionals employed in han q l 2005a absolute stability of time delay systems with sector bounded nonlinearity automatica 41 2171 2176 han q l 2005b a new delay dependent stability criterion for linear neutral systems with norm bounded uncertainties in all system matrices international journal of systems science 36 469 475 the other part is constructed by uniformly dividing the discrete delay interval into multiple segments and choosing proper functionals with different weighted matrices corresponding to different segments then using these new simple quadratic lyapunov krasovskii functionals some new discrete delay dependent stability criteria are derived for both retarded systems and neutral systems it is shown that these criteria for retarded systems and neutral systems are always less conservative than the ones in han 2005a and han 2005b cited above respectively numerical examples also show that the results obtained in this paper significantly improve the estimate of the discrete delay limit for stability over some other existing results

robust h_ infty control for uncertain takagi sugeno fuzzy systems with interval time varying delay this paper is concerned with the problem of robust hinfin control for a class of uncertain time delay fuzzy systems the time delay is assumed to be a time varying continuous function belonging to a given interval which means that the lower and upper bounds for the time varying delay are available no restriction on the derivative of the time varying delay is needed which allows the time delay to be a fast time varying function the takagi sugeno t s uncertain fuzzy model with interval time varying delay is adopted based on the lyapunov krasovskii functional approach some delay dependent conditions for the existence of robust hinfin controller are formulated in the form of linear matrix inequalities lmis when these lmis are feasible an hinfin controller is presented a numerical example is given to demonstrate the effectiveness of the proposed method

robust stability and stabilization for uncertain takagi sugeno fuzzy time delay systems in this paper we consider robust stability and stabilization of uncertain takagi sugeno fuzzy time delay systems where uncertainties come into the state and input matrices some stability conditions and robust stability conditions for fuzzy time delay systems have already been obtained in the literature however those conditions are rather conservative and do not guarantee the stability and robust stability for a wide class of fuzzy systems this is true in case of designing stabilizing controllers for fuzzy time delay systems we first consider robust stability conditions of uncertain fuzzy systems conditions we obtain here are delay dependent conditions that depend on the upper bound of time delay and are given in linear matrix inequalities lmis an appropriate selection of lyapunov krasovskii function and introduction of free weighting matrices generalize robust stability conditions next we consider the stabilization problem with memoryless and delayed feedback controllers based on our generalized robust stability conditions we obtain delay dependent sufficient conditions for the closed loop system to be robustly stable and give a design method of robustly stabilizing controllers finally we give two examples that illustrate our results we compare our conditions with other stability conditions and show our conditions are rather generalized

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

surrogate time series before we apply nonlinear techniques e g those inspired by chaos theory to dynamical phenomena occurring in nature it is necessary to first ask if the use of such advanced techniques is justified by the data while many processes in nature seem very unlikely a priori to be linear the possible nonlinear nature might not be evident in specific aspects of their dynamics the method of surrogate data has become a very popular tool to address such a question however while it was meant to provide a statistically rigorous foolproof framework some limitations and caveats have shown up in its practical use in this paper recent efforts to understand the caveats avoid the pitfalls and to overcome some of the limitations are reviewed and augmented by new material in particular we will discuss specific as well as more general approaches to constrained randomisation providing a full range of examples new algorithms will be introduced for unevenly sampled and multivariate data and for surrogate spike trains the main limitation which lies in the interpretability of the test results will be illustrated through instructive case studies we will also discuss some implementational aspects of the realisation of these methods in the tisean software package

a tight upper bound on the gain of linear and nonlinear predictors for stationary stochastic processes one of the striking questions in prediction theory is this is there a chance to predict future values of a given signal usually we design a predictor for a special signal or problem and then measure the resulting prediction quality if there is no a priori knowledge on the optimal predictor the achieved prediction gain will depend strongly of the prediction model used to cope with this lack of knowledge a theorem on the maximum achievable prediction gain of stationary signals is presented this theorem provides the foundation for estimating a quality goal for the predictor design independent of a special predictor implementation linear or nonlinear as usual the prediction gain is based on the mean square error mse of the predicted signal the achievable maximum of the prediction gain is calculated using an information theoretic quantity known as the mutual information in order to obtain the gain we use a nonparametric approach to estimate the maximum prediction gain based on the observation of one specific signal we illustrate this by means of well known example signals and show an application to load forecasting an estimation algorithm for the prediction gain has been implemented and used in the experimental part of the paper

fuzzy robust dynamic output feedback control of nonlinear systems with linear fractional parametric uncertainties in this paper the problem of robust dynamic output feedback control for a class of discrete time nonlinear systems with parametric uncertainties is studied the parametric uncertainties are assumed to be of a linear fractional form first the takagi sugeno t s fuzzy model is employed to represent the nonlinear system then novel approaches are developed to design the dynamic output feedback controller and sufficient conditions for robust stabilization are obtained in the form of linear matrix inequalities lmis the proposed approaches not only have abilities to effectively handle the parametric uncertainties but also are suitable for the fuzzy system with immeasurable premise variables simulation examples are presented to illustrate the design procedures and the effectiveness of the proposed methods

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

technical communique a delay partitioning approach to the stability analysis of discrete time systems this paper revisits the problem of stability analysis for linear discrete time systems with time varying delay in the state by utilizing the delay partitioning idea new stability criteria are proposed in terms of linear matrix inequalities lmis these conditions are developed based on a novel lyapunov functional in addition to delay dependence the obtained conditions are also dependent on the partitioning size we have also established that the conservatism of the conditions is a non increasing function of the number of partitions numerical examples are given to illustrate the effectiveness and advantage of the proposed methods

reconstructing attractors from scalar time series a comparison of singular system and redundancy criteria abstract a delay vector phase space reconstruction in which the delay time satisfiesa minimum redundancy criterion is compared with a reconstruction obtained using a singular system approach minimum redundancy produces the better reconstruction the reconstructions are compared using a distortion functional d which measures how well the location of a point in the original phase space can be determined on the basis of its image under the reconstruction process the superiority of the redundancy analysis over the singular system analysis is found to arise from the former s foundation on the notion of general independence as opposed to the latter s foundation on the notion of linear independence