on simple scheme of finite fixed time control design control laws are designed for stabilisation of a chain of integrators of arbitrary degree in finite and fixed time presented control laws are obtained with use of lyapunov function method and homo

on the alternating series 1 12 13 14 abstract it is shown that the best constants a and b such that inequalities 1 2n a k n 1 1 k 1 1 k 1 2n b hold for every n 1 are a 1 1 log 2 2 1 258891 and b 1

numerical methods for the estimation of multifractal singularity spectra on sampled data physical variables in scale invariant systems often show chaotic turbulent like behavior commonly associated to the existence of an underlying fractal or multifractal structure however the assessment of multifractality over experimental discretized data requires of appropriate methods and to establish criteria to measure the confidence degree on the estimates in this paper we have evaluated the quality of different techniques used for multifractal analysis we have tested four different techniques the moment m method the wavelet transform modulus maxima wtmm method the gradient modulus wavelet projection gmwp method and the gradient histogram gh method which are used to estimate the singularity spectra of multifractal signals the test consists in analyzing synthetic multifractal 1d signals with given multifractal spectrum we have compared the results studying the sensibility of each method to the length of the series size of the ensemble and type of spectrum our results show that gmwp method is the one attaining the best performance providing reliable estimates which can be improved when the statistics is increased all the other methods are affected by problems such as the linearization of the right tail of the spectrum and some of them are very demanding in data

nonlinear feedback design for fixed time stabilization of linear control systems two types of nonlinear control algorithms are presented for uncertain linear plants controllers of the first type are stabilizing polynomial feedbacks that allow to adjust a guaranteed convergence time of system trajectories into a prespecified neighborhood of the origin independently on initial conditions the control design procedure uses block control principles and finite time attractivity properties of polynomial feedbacks controllers of the second type are modifications of the second order sliding mode control algorithms they provide global finite time stability of the closed loop system and allow to adjust a guaranteed settling time independently on initial conditions control algorithms are presented for both single input and multi input systems theoretical results are supported by numerical simulations

finite time stability conditions for non autonomous continuous systems finite time stability is defined for continuous non autonomous systems starting with a result from haimo 1986 we then extend this result to n dimensional non autonomous systems through the use of smooth and non smooth lyapunov functions as in perruquetti and drakunov 2000 one obtains two different sufficient conditions and a necessary one for finite time stability of continuous non autonomous systems

multifractal analysis of chinese stock volatilities based on the partition function approach abstract we have performed a detailed multifractal analysis on the 1 min volatility of two indexes and 1139 stocks in the chinese stock markets based on the partition function approach the partition function q s scales as a power law with respect to the box size s the scaling exponents q form a nonlinear function of q statistical tests based on bootstrapping show that the extracted multifractal nature is significant at the 1 significance level the individual securities can be well modeled by the p model in turbulence with p 0 40 0 02 based on the idea of ensemble averaging including quenched and annealed average we treat each stock exchange as a whole and confirm the existence of multifractal nature in the chinese stock markets

universal stabilization of a class of nonlinear systems with homogeneous vector fields abstract under relative degree one and minimum phase assumptions it is well known that the class l of finite dimensional linear single input u single output y systems a b c is universally stabilized by the feedback strategy u y y 2 where is a function of nussbaum type the terminology universal stabilization being used in the sense of rendering s 0 s a global attractor for each member of the underlying class whilst assuring boundedness of the function a natural generalization of this result to a class h k of nonlinear control systems a b c with positively homogeneous of degree k 1 drift vector field a is described specifically under the relative degree one cb 0 and minimum phase hypotheses the latter being interpreted as that of asymptotic stability of the equilibrium of the zero dynamics it is shown that the strategy u vby vb k 1 y dot vby vb k 1 assures h k universal stabilization more generally the strategy u exp vby vb y dot exp vby vb y 2 assures h universal stabilization where h k 1 h k

scaling in currency exchange we study the scaling behavior in currency exchange rates our results suggest that they satisfy scaling with an exponent close to 0 5 but that it differs qualitatively from that of a simple random walk indeed price variations cannot be considered as independent variables and subtle correlations are present furthermore we introduce a novel statistical analysis for economic data which makes the physical properties of a signal more evident and eliminates the systematic effects of time periodicity

multifractal behavior of the korean stock market index kospi abstract we investigate multifractality in the korean stock market index kospi the generalized qth order height height correlation function shows multiscaling properties there are two scaling regimes with a crossover time around t c 40 min we consider the original data sets and the modified data sets obtained by removing the daily jumps which occur due to the difference between the closing index and the opening index to clarify the origin of the multifractality we also smooth the data through convolution with a gaussian function after convolution we observe that the multifractality disappears in the short time scaling regime t t c but remains in the long time scaling regime t t c regardless of whether or not the daily jumps are removed we suggest that multifractality in the short time scaling regime is caused by the local fluctuations of the stock index but the multifractality in the long time scaling regime appears to be due to the intrinsic trading properties such as herding behavior information outside the market the long memory of the volatility and the nonlinear dynamics of the stock market

on an output feedback finite time stabilization problem studies the problem of finite time output feedback stabilization for the double integrator system a class of output feedback controllers that can achieve global finite time stability for the double integrator system are constructed based on a finite time separation principle furthermore it is shown that the closed loop system resulting from our control law can maintain its local finite time stability regardless of some nonlinear perturbations thus our control law actually applies to a large class of nonlinear second order systems

continuous finite time stabilization of the translational and rotational double integrators a class of bounded continuous time invariant finite time stabilizing feedback laws is given for the double integrator lyapunov theory is used to prove finite time convergence for the rotational double integrator these controllers are modified to obtain finite time stabilizing feedback that avoid unwinding

stabilizability does not imply homogeneous stabilizability for controllable homogeneous systems this paper presents an example of a homogeneous planar controllable system which is stabilizable while not stabilizable by homogeneous feedback addition of an integrator to the system provides a three dimensional it affine system with the same properties

on leibniz series defined by convex functions abstract it is shown that for every 0 we have k n 1 1 k 1 k 1 2 n n for some strictly decreasing sequence n n 1 such that 1 2 n 1 2 1 1 2 n 1 1 hence with lim n n 1 2 this is only a particular case of more general new results on leibniz series defined by convex functions

homogeneous approximation recursive observer design and output feedback we introduce two new tools that can be useful in nonlinear observer and output feedback design the first one is a simple extension of the notion of homogeneous approximation to make it valid both at the origin and at infinity homogeneity in the bi limit exploiting this extension we give several results concerning stability and robustness for a homogeneous in the bi limit vector field the second tool is a new recursive observer design procedure for a chain of integrator combining these two tools we propose a new global asymptotic stabilization result by output feedback for feedback and feedforward systems

half integer approximations for the partial sums of the harmonic series abstract let s n denote the n th partial sum of the harmonic series an asymptotic approximation for s n is obtained in terms of the half integer variable n 1 2 including bounds for the remainder improved estimates of the comtet function for the harmonic series are obtained as a consequence

scale invariant distribution and multifractality of volatility multipliers in stock markets abstract the statistical properties of the multipliers of the absolute returns are investigated using 1 min high frequency data of financial time series the multiplier distribution is found to be independent of the box size s when s is larger than some crossover scale providing direct evidence of the existence of scale invariance in financial data the multipliers with base a 2 are well approximated by a normal distribution and the most probable multiplier scales as a power law with respect to the base a we unravel that the volatility multipliers possess multifractal nature which is independent of construction of the multipliers that is the values of s and a

scaling characteristics in the taiwan stock market some statistical tools including histogram spectral analysis and fractal theory were used on the daily taiwan stock price index tspi from 1987 to 2002 to examine the possible scale invariant behavior and the clustering characteristics in taiwan stock market it was found that the tspi data exhibited the characteristic of right skewed frequency distribution the long term memory and the possibility of scale invariance were roughly identified through the analysis of autocorrelation and power spectrum respectively the monofractal analysis was then performed by the box counting method scale invariance was clearly found in the time series and the box dimension was shown to be a decreasing function of the threshold index level implying multifractal characteristics i e the low and high regions scale differently to test this hypothesis the time series were transferred into a useful compact form through the multifractal formalism namely the q q and f plots the analysis confirmed the existence of multifractal characteristics in the investigated time series the origin of multifractal phenomena in taiwan stock market might be interpreted in terms of the multiplicative cascade process of stock market information

free electron gas in the apollonian network multifractal energy spectrum and its thermodynamic fingerprints we study the free electron gas in an apollonian network within the tight binding framework the scale free and small world character of the underlying lattice is known to result in a quite structured energy spectrum with deltalike singularities gaps and minibands after an exact numerical diagonalization of the corresponding adjacency matrix of the network with a finite number of generations we employ a scaling analysis of the moments of the density of states to characterize its multifractality and report the associated singularity spectrum the fractal nature of the energy spectrum is also shown to be reflected in the thermodynamic behavior by logarithmic modulations on the temperature dependence of the specific heat the absence of chiral symmetry of the apollonian network leads to distinct thermodynamic behaviors due to electrons and holes thermal excitations

verification of iss iiss and ioss properties applying weighted homogeneity several conditions are proposed to check different robustness properties iss iiss ioss and oss for generic nonlinear systems applying the weighted homogeneity concept global or local the advantages of this result are that under some mild conditions the system robustness can be established as a function of the degree of homogeneity

homogeneous lyapunov function for homogeneous continuous vector field the goal of this article is to provide a construction of a homogeneous lyapunov function p associated with a system of differential equations j f x x r n 1 under the hypotheses 1 f c r n vanishes at x 0 and is homogeneous 2 the zero solution of this system is locally asymptotically stable moreover the lyapunov function v x tends to infinity with 1 x i and belongs to c r 0 r n cp with p e as large as wanted as application to the theory of homogeneous systems we present two well known results of robustness in a slightly extended form and with simpler proofs

statistical properties of the volatility of price fluctuations we study the statistical properties of volatility measured by locally averaging over a time window t the absolute value of price changes over a short time interval ensuremath delta t we analyze the s 500 stock index for the 13 year period jan 1984 to dec 1996 we find that the cumulative distribution of the volatility is consistent with a power law asymptotic behavior characterized by an exponent ensuremath mu ensuremath approx 3 similar to what is found for the distribution of price changes the volatility distribution retains the same functional form for a range of values of t further we study the volatility correlations by using the power spectrum analysis both methods support a power law decay of the correlation function and give consistent estimates of the relevant scaling exponents also both methods show the presence of a crossover at approximately 1 5 days in addition we extend these results to the volatility of individual companies by analyzing a data base comprising all trades for the largest 500 u s companies over the two year period jan 1994 to dec 1995

nilpotent approximations of control systems and distributions a constructive method is given to approximate the vector fields in a nonlinear control system which is linear in the controls by a system of similar form and on the same state space with the describing vector fields of the approximating system generating a lie algebra which has a certain relevant sub algebra nilpotent given a k dimensional distribution on r n say locally defined near zero the method leads to an approximating k distribution which has nilpotent basis agrees with the original distribution at zero and each derived distribution of the approximating distribution and original distribution also agree at zero

coarse graining and self similarity of price fluctuations abstract we propose a new approach for analyzing price fluctuations in their strongly correlated regime ranging from minutes to months this is done by employing a self similarity assumption for the magnitude of coarse grained price fluctuation or volatility the existence of a cramer function the characteristic function for self similarity is confirmed by analyzing real price data from a stock market we also discuss the close interrelation among our approach the scaling of moments method and the multifractal approach for price fluctuations

finite time controllers continuous finite time differential equations are introduced as fast accurate controllers for dynamical systems these have qualities superior to controllers which are currently in use in such appl

technical communique finite time output stabilization with second order sliding modes in this note a class of discontinuous feedback laws that switch over branches of parabolas in the auxiliary state plane is analyzed conditions are provided under which controllers belonging to this class are second order sliding mode algorithms they ensure uniform global finite time output stability for uncertain systems of relative degree two

homogeneity approach to high order sliding mode design it is shown that a general uncertain single input single output regulation problem is solvable only by means of discontinuous control laws giving rise to the so called high order sliding modes the homogeneity properties of the corresponding controllers yield a number of practically important features in particular finite time convergence is proved and asymptotic accuracy is calculated in a very general way in the presence of input noises discrete measurements and switching delays a robust homogeneous differentiator is included in the control structure thus yielding robust output feedback controllers with finite time convergence it is demonstrated that homogeneity features significantly simplify the design and investigation of a new family of high order sliding mode controllers finally simulation results are presented

power law of quiet time distribution in the korean stock market abstract we report the quiet time probability distribution of the absolute return in the korean stock market index we define the quiet time as a time interval during the absolute return of the stock index that are above a threshold r c through an exponential bin plot we observe that the quiet time distribution qtd shows power law behavior p f t t for a range of threshold values the quiet time distribution has two scaling regimes separated by the crossover time t c 200 min the power law exponents of the quiet time distribution decrease when the return time t increases in the late time regime t t c the power law exponents are independent of the threshold within the error bars for the fixed return time the scaled qtd is characterized by a scaling function such as p f t 1 t f t t where the scaling function f x x 2 and t is the average quiet time the scaling exponents 2 depend on the return time t and are independent of the threshold r c the average quiet time follows the power law such as t r c where the exponents depend on the return time t

scaling and correlation in financial time series we discuss the results of three recent phenomenological studies focussed on understanding the distinctive statistical properties of nancial time series i the probability distribution of stock price uctuations stock price uctuations occur in all magnitudes in analogy to earthquakes from tiny uctuations to very drastic events such as the crash of 19 october 1987 sometimes referred to as black monday the distribution of price uctuations decays with a power law tail well outside the levy stable regime and describes uctuations that dier by as much as 8 orders of magnitude in addition this distribution preserves its functional form for uctuations on time scales that dier by 3 orders of magnitude from 1 min up to approximately 10 days ii correlations in nancial time series while price uctuations themselves have rapidly decaying correlations the magnitude of uctuations measured by either the absolute value or the square of the price uctuations has correlations that decay as a power law persisting for several months iii volatility and trading activity we quantify the relation between trading activity measured by the number of transactions nt and the price change gt for a given stock over a time interval t t t we nd that nt displays long range power law correlations in time which leads to the interpretation that the long range correlations previously found for jgtj are connected to those of nt c 2000 elsevier science b v all rights reserved

an algorithm for the characterization of time series based on local regularity abstract the pointwise holder exponent describes the local regularity of a function this description is particularly applicable to complex time series representing natural phenomena that exhibit statistical self similarity where the scaling exponent fluctuates from point to point in this work an algorithm is proposed for the estimation of both global and local scaling exponents of time series the technique is based on scaled window variance method and its practical implementation relies on the convolution operation the proposed algorithm is an attractive alternative to existing techniques because of its simplicity and computational efficiency the accuracy of the algorithm is verified by application on synthetic signals with a prescribed time evolution of holder exponents case studies are presented in the fields of fluid dynamics room acoustics and machinery diagnostics

probability distribution function and multiscaling properties in the korean stock market abstract we consider the probability distribution function pdf and the multiscaling properties of the index and the traded volume in the korean stock market we observed the power law of the pdf at the fat tail region for the return volatility the traded volume and changes of the traded volume we also investigate the multifractality in the korean stock market we consider the multifractality by the detrended fluctuation analysis mfdfa we observed the multiscaling behaviors for index return traded volume and the changes of the traded volume we apply mfdfa method for the randomly shuffled time series to observe the effects of the autocorrelations the multifractality is strongly originated from the long time correlations of the time series

cesaro s theorems for complex sequences abstract the classical cesaro s theorems apply to ratios of real valued sequences like n g n where g n monotonically or n 0 and g n 0 monotonically here such results are generalized to complex valued sequences and at the same time the restriction of monotonicity on g n is removed in the real case such a condition is replaced with a more general property that does not require the ordering of the range an application to the asymptotics of linear difference equations is presented

multifractality in stock indexes fact or fiction abstract multifractal analysis and extensive statistical tests are performed upon intraday minutely data within individual trading days for four stock market indexes including hsi szsc s p 500 and nasdaq to check whether the indexes instead of the returns possess multifractality we find that the mass exponent q is linear and the singularity q is close to 1 for all trading days and all indexes furthermore we find strong evidence showing that the scaling behaviors of the original data sets cannot be distinguished from those of shuffled time series hence the so called multifractality in the intraday stock market indexes is merely an illusion

universal single input single output siso sliding mode controllers with finite time convergence an universal controller is constructed formulated in input output terms only which causes the output of any uncertain smooth single input single output siso minimum phase dynamic system with known relative degree to vanish in finite time this allows exact tracking of arbitrary real time smooth signals only one parameter is to be adjusted since the approach is based on higher order finite time convergence sliding modes the control can be made arbitrarily smooth providing for the arbitrarily high tracking accuracy order with respect to the sampling step

on the asymptotic stability of switched homogeneous systems abstract the stability of switched systems generated by the family of autonomous subsystems with homogeneous right hand sides is investigated it is assumed that for each subsystem the proper homogeneous lyapunov function is constructed the sufficient conditions of the existence of the common lyapunov function providing global asymptotic stability of the zero solution for any admissible switching law are obtained in the case where we can not guarantee the existence of a common lyapunov function the classes of switching signals are determined under which the zero solution is locally or globally asymptotically stable it is proved that for any given neighborhood of the origin one can choose a number l 0 dwell time such that if intervals between consecutive switching times are not smaller than l then any solution of the considered system enters this neighborhood in finite time and remains within it thereafter

global finite time stabilisation by output feedback for a class of uncertain nonlinear systems this article considers the problem of global finite time stabilisation by output feedback for a class of nonlinear systems comprised of a chain of power integrators perturbed by an uncertain vector field to solve the problem we first construct a homogeneous observer and controller in a recursive way for the nominal system without the perturbing nonlinearities then using the homogeneous domination approach we scale the homogeneous observer and controller with an appropriate choice of gain to render the uncertain nonlinear system globally finite time stable due to the use of a reduced order observer the proposed output feedback controller is applicable to those systems with unknown gains associated with the power integrators

integral estimates for convergent positive series abstract it is shown that for every 1 we have k n 1 1 k 1 1 n n 1 for some strictly decreasing sequence n n 1 such that 1 2 n 1 4 1 1 1 2 n 1 hence with lim n n 1 2 this is only a particular case of more general new results on series defined by convex functions

global finite time stabilization by output feedback for planar systems without observable linearization this note considers the problem of global finite time stabilization by output feedback for a class of planar systems without controllable observable linearization a sufficient condition for the solvability of the problem is established by developing a nonsmooth observer and modifying the adding a power integrator technique we show that an output feedback controller can be explicitly constructed to globally stabilize the systems in finite time as a direct application of the main result global output feedback finite time stabilization is achieved for the double linear integrator systems perturbed by some nonlinear functions which are not necessarily homogeneous

microcanonical multifractal formalism a geometrical approach to multifractal systems part i singularity analysis multifractal formalism in the microcanonical framework has proved to be a valuable approach to understand and analyze complex signals typically associated with natural phenomena in scale invariant systems in this paper we discuss the multifractal microcanonical formalism in a comprehensive unified way including new theoretical proofs and validation tests on real signals so completing some known gaps in the foundations of this theory we also review the latest advances and describe the present perspectives in this field some technical details on the implementation of involved algorithms and relevant open issues are also discussed

application of the microcanonical multifractal formalism to monofractal systems the design of appropriate multifractal analysis algorithms able to correctly characterize the scaling properties of multifractal systems from experimental discretized data is a major challenge in the study of such scale invariant systems in the recent years a growing interest for the application of the microcanonical formalism has taken place as it allows a precise localization of the fractal components as well as a statistical characterization of the system in this paper we deal with the specific problems arising when systems that are strictly monofractal are analyzed using some standard microcanonical multifractal methods we discuss the adaptations of these methods needed to give an appropriate treatment of monofractal systems

h control stabilization and input output stability of nonlinear systems with homogeneous properties new relations are established between h control and stabilization and between input output stability and lyapunov stability of nonlinear systems with homogeneous properties these results can be applied to h controller design and stability analysis

stabilisation of perturbed chains of integrators using lyapunov based homogeneous controllers abstractin this paper we present a lyapunov based homogeneous controller for the stabilisation of a perturbed chain of integrators of arbitrary order r 1 the proposed controller is based on homogeneous controller for stabilisation of pure chain of integrators the control of homogeneity degree is also introduced and various controllers are designed using this concept namely a bounded controller with minimum amplitude of discontinuous control and a controller with globally fixed time convergence the performance of the controller is validated through simulations

the multifractal structure of contrast changes in natural images from sharp edges to textures we present a formalism that leads naturally to a hierarchical description of the different contrast structures in images providing precise definitions of sharp edges and other texture components within this formalism we achieve a decomposition of pixels of the image in sets the fractal components of the image such that each set contains only points characterized by a fixed strength of the singularity of the contrast gradient in its neighborhood a crucial role in this description of images is played by the behavior of contrast differences under changes in scale contrary to naive scaling ideas where the image is thought to have uniform transformation properties field 1987 each of these fractal components has its own transformation law and scaling exponents a conjecture on their biological relevance is also given

convergence acceleration for observers by gain commutation increasing convergence rates of observers and differentiators for a class of nonli near systems in the output canonical form under presence of bounded matched disturbances lipschitz uncertainties and measurement noises is investigated a supervisory algorithm is designed that switches among different values of observer gains to accelerate the estimation in the noise free case the presented switched gain observer ensures global uniform time of convergence of the estimation error to the origin in the presence of noise the goals of overshoot reducing for the initial phase acceleration of convergence and improvement of asymptotic precision of estimation are achieved efficiency of the proposed switching gain observer is demonstrated by numerical comparison with a sliding mode and linear high gain observers

output feedback finite time stabilization of disturbed feedback linearizable nonlinear systems a novel methodology for designing multivariable high order sliding mode hosm controllers for disturbed feedback linearizable nonlinear systems is introduced it provides for the finite time stabilization of the origin of the state space by using output feedback only the additional assumptions of algebraic strong observability and smooth enough matched disturbances are required the control problem is solved in two consecutive steps firstly designing an observer based on the measured output and secondly designing of a full state controller computed from a new virtual output with vector relative degree the introduced notion of algebraic strong observability allows recovering the state of the system using the measured output and its derivatives by estimating the required derivatives through the hosm differentiator a finite time convergent observer is constructed

finite time output feedback position and attitude tracking of a rigid body the position and attitude tracking of a rigid body without velocity measurements is addressed dual quaternions are used to describe the coupled rotational and translational motions of the rigid body yielding compact forms of the kinematics and dynamics suitable for control law synthesis an output feedback pose position and attitude tracking controller is then designed by integrating techniques from passivity and homogeneity more precisely a passivity enabling auxiliary system is proposed to provide necessary damping instead of velocity feedback and a homogeneous method is used to ensure finite time convergence the proposed controller guarantees uniform almost global finite time stability of the closed loop system and produces a well defined vector field on the attitude configuration manifold thus avoiding the unwinding phenomenon moreover it can be split to obtain velocity free controllers with finite time convergence for the cases of translation only or rotation only control numerical examples verify the effectiveness of the proposed method

reconstructing images from their most singular fractal manifold real world images are complex objects difficult to describe but at the same time possessing a high degree of redundancy a previous on the statistical properties of natural images reveals that natural images can be viewed through different partitions which are essentially fractal in nature one particular fractal component related to the most singular sharpest transitions in the image seems to be highly informative about the whole scene we show how to decompose the image into their fractal components we see that the most singular component is related to but not coincident with the edges of the objects present in the scenes we propose a new simple method to reconstruct the image with information contained in that most informative component we see that the quality of the reconstruction is strongly dependent on the capability to extract the relevant edges in the determination of the most singular set we discuss the results from the perspective of coding proposing this method as a starting point for future developments

a random process for the construction of multiaffine fields abstract we define a random process for the construction of multiaffine fields given the scaling exponents for the structure functions the difference with analogous processes for positive defined multifractal measures is stressed in particular our methods can be used for the study of the scaling laws exhibited by the velocity field in three dimensional fully developed turbulence we also discuss the probability distribution functions for the increments of the signal in the scaling range

a note on delay robustness for homogeneous systems with negative degree robustness with respect to delays is discussed for homogeneous systems with negative degree it is shown that if homogeneous system with negative degree is globally asymptotically stable at the origin in the delay free case then the system is globally asymptotically stable with respect to a compact set containing the origin independently of delay the possibility of applying the result for local analysis of stability for not necessary homogeneous systems is analyzed the theoretical results are supported by numerical examples

homogeneous high order sliding mode design a lyapunov approach abstract we provide a lyapunov based design of high order sliding mode hosm control of arbitrary order for a class of single input single output uncertain nonlinear systems first we provide a general method to design degree 0 homogeneous controllers based on a homogeneous control lyapunov function clf then for a perturbed chain of integrators we construct a smooth and homogeneous clf and use it to design a family of homogeneous and discontinuous control laws the controller drives in finite time the trajectories of the system to a sliding surface of arbitrary relative degree and keeps the trajectories on this manifold despite persistently acting matched perturbations so that a sliding mode is established we obtain a large and simply parametrized family of usual discontinuous and quasi continuous hosm controllers of nested and polynomial type that share the robustness and accuracy properties of the existing ones

finite time stability and robust control synthesis of uncertain switched systems stability analysis is developed for uncertain nonlinear switched systems while being asymptotically stable and homogeneous of degree q 0 these systems are shown to approach the equilibrium point in finite time restricted to second order systems this feature is additionally demonstrated to persist regardless of inhomogeneous perturbations based on this fundamental property switched control algorithms are then developed to globally stabilize uncertain minimum phase systems of uniform m vector relative degree 2 2 t the controllers constructed do not rely on the generation of sliding motions while providing robustness features similar to those possessed by their sliding mode counterparts the proposed synthesis procedure is illustrated via application to a friction servo motor

robust exact uniformly convergent arbitrary order differentiator an arbitrary order differentiator that in the absence of noise converges to the true derivatives of the signal after a finite time independent of the initial differentiator error is presented the only assumption on a signal to be differentiated n 1 times is that its n th derivative is uniformly bounded by a known constant the proposed differentiator switches from a newly designed uniform differentiator to the classical high order sliding mode hosm differentiator the uniform part drives the differentiation error trajectories into a compact neighborhood of the origin in a time that is independent of the initial differentiation error then the hosm differentiator is used to bring the differentiation error to zero in finite time

weighted homogeneity for time delay systems finite time and independent of delay stability global delay independent stability is analyzed for nonlinear time delay systems by applying homogeneity theory it is shown that finite time stability can be encountered in this class of systems under uniformity of the convergence time with respect to delay some additional tools for stability analysis of time delay systems using homogeneity are also presented in particular it is shown that if a time delay system is homogeneous with nonzero degree and it is globally asymptotically stable for some delay then this property is preserved for any delay value which is known as the independent of delay stability

empirical evidences of a common multifractal signature in economic biological and physical systems abstract recent developments in microcanonical multifractal formalism have lead to a sensible improvement in the numerical techniques for the determination of the multifractal characteristics of real signals with the aid of these techniques we have found empirical evidence of a common multifractal signature in six very different systems ranging from stock market time series to sea surface temperature records these systems are not only found to be multifractal but their singularity spectra are coincident we propose an explanation of this striking coincidence in terms of a cascade process and analyze its consequences

long term correlations and multifractal nature in the intertrade durations of a liquid chinese stock and its warrant abstract the intertrade duration of equities is an important financial measure characterizing trading activities it is defined as the waiting time between successive trades of an equity using the ultrahigh frequency data of a liquid chinese stock and its associated warrant we perform a comparative investigation of the statistical properties of their intertrade duration time series the distributions of the two equities can be better described by the shifted power law form than the weibull form and their scaled distributions do not collapse onto a single curve although the intertrade durations of the two equities have very different magnitude their intraday patterns exhibit very similar shapes both detrended fluctuation analysis dfa and detrending moving average analysis dma show that the 1 min intertrade duration time series of the two equities are strongly correlated in addition both multifractal detrended fluctuation analysis mfdfa and multifractal detrending moving average analysis mfdma unveil that the 1 min intertrade durations possess multifractal nature however the difference between the two singularity spectra of the two equities obtained from the mfdma is much smaller than that from the mfdfa

finite time stabilization of nonlinear systems with parametric and dynamic uncertainties in this note non smooth finite time stabilization of nonlinear systems with parametric and dynamic uncertainties is investigated to solve this problem the input to state stability property is used to characterize unmeasured dynamic uncertainties a constructive partial state control design is proposed on the basis of involved combined use of lyapunov backstepping and input to state stability techniques under small gain type local conditions a solution for the finite time regulation of a class of uncertain nonlinear systems is obtained

multifractal detrended cross correlation analysis of foreign exchange and sensex fluctuation in indian perspective abstract the manuscript studies autocorrelation and cross correlation of sensex fluctuations and forex exchange rate in respect to indian scenario multifractal detrended fluctuation analysis mfdfa and multifractal detrended cross correlation analysis mfdxa were employed to study the correlation between the two series it was observed that the two series are strongly cross correlated the change of degree of cross correlation with time was studied and the results are interpreted qualitatively

technical communique input output finite time stabilization of linear systems bounded input bounded output bibo stability is usually studied when only the input output behavior of a dynamical system is of concern the present paper investigates the analogous concept in the framework of finite time stability fts namely the input output fts io fts fts has been already investigated in several papers in terms of state boundedness whereas in this work we deal with the characterization of the input output behavior sufficient conditions are given concerning the class of l 2 and l input signals for the analysis of io fts and for the design of a static state feedback controller guaranteeing io fts of the closed loop system the effectiveness of the proposed results is eventually illustrated by means of some numerical examples

generalized hurst exponent and multifractal function of original and translated texts mapped into frequency and length time series a nonlinear dynamics approach can be used in order to quantify complexity in written texts as a first step a one dimensional system is examined two written texts by one author lewis carroll are considered together with one translation into an artificial language i e esperanto are mapped into time series their corresponding shuffled versions are used for obtaining a baseline two different one dimensional time series are used here one based on word lengths lts the other on word frequencies fts it is shown that the generalized hurst exponent h q and the derived f curves of the original and translated texts show marked differences the original texts are far from giving a parabolic f function in contrast to the shuffled texts moreover the esperanto text has more extreme values this suggests cascade model like with multiscale time asymmetric features as finally written texts a discussion of the difference and complementarity of mapping into a lts or fts is presented the fts f curves are more opened than the lts ones

robust finite time output feedback control of perturbed double integrator this paper addresses the problem of finite time output feedback stabilization for the perturbed double integrator system a simple output feedback proportional derivative pd controller is proposed global finite time stability is proven based on lyapunov stability theory and geometric homogeneity technique furthermore it is proven that the proposed controller can maintain local finite time stability regardless of some nonlinear perturbations thus the proposed controller actually can be applied to a large class of uncertain second order nonlinear systems simulations demonstrate the effectiveness of the proposed approach

homogeneous feedback controls for homogeneous systems let x x j 2n aj x xj be a real analytic n dimensional vector field with x 0 0 which is homogeneous of degree m 0 with respect to a dilation erx er1x1 ernxn and y xj we show that control system x x x uy admits a continuous asymptotically stabilizing feedback control u x then a one dimensional dynamic extension of the system admits a homogeneous asymptotically stabilizing dynamic feedback control u x such that the vector field w x 1 m u x 1 j 2aj x xj describing the extended controlled system is homogeneous of degree m with respect to the extended dilation er x e er1x1 ernxn

finite time stabilization of a perturbed double integrator part i continuous sliding mode based output feedback synthesis the twisting and supertwisting algorithms generating important classes of second order sliding modes sosms are well recognized for their finite time stability and robustness properties in the present paper a continuous modification of the twisting algorithm and an inhomogeneous perturbation of the supertwisting algorithm are introduced to extend the class of sosm s that present the afore mentioned attractive features thus modified the twisting and supertwisting algorithms are utilized in the state feedback synthesis and respectively velocity observer design made for the finite time stabilization of a double integrator if only output measurements are available performance and robustness issues of the resulting output feedback synthesis are illustrated by means of numerical simulations

multifractal geometry in stock market time series it has been recently noticed that time series of returns in stock markets are of multifractal multiscaling character in that context multifractality has been always evidenced by its statistical signature i e the scaling exponents associated to a related variable however a direct geometrical framework much more revealing about the underlying dynamics is possible in this paper we present the techniques allowing the multifractal decomposition we will show that there exists a particular fractal component the most singular manifold msm which contains the relevant information about the dynamics of the series it is possible to reconstruct the series at a given precision from the msm we analyze the dynamics of the msm which shows revealing features about the evolution of this type of series