direct solution of piecewise linear systems let s be a real n n matrix z c r n and z the componentwise modulus of z then the piecewise linear equation system z s z c is called an absolute value equation ave it has been proven to be equivalent to the general linear complementarity problem which means that it is np hard in general we will show that for several system classes in the sense of structural impositions on s the ave essentially retains the good natured solvability properties of regular linear systems i e it can be solved directly by a slightly modified gaussian elimination that we call the signed gaussian elimination for dense matrices s this algorithm has up to a term in o n the same operations count as the classical gaussian elimination with column pivoting for tridiagonal systems in n variables its computational cost is roughly that of sorting n floating point numbers the sharpness of the proposed restrictions on s will be established several system types of the so called absolute value equation can be solved directly solving dense systems costs roughly the same as solving dense linear systems solving tridiagonal systems in n variables has asymptotical cost of sorting n floats

a less conservative robust stability test for linear uncertain time delay systems this note concerns with the robust stability of linear uncertain systems with state delay the uncertainty is assumed to be of polytopic type a less conservative delay dependent linear matrix inequality lmi method is presented based on a new lyapunov krasovskii functional the present method incorporates a relaxed parameter dependent technique combined with a recently proposed idea of introducing free weighting matrices when confined to delay free case the present result is also less conservative than existing stability tests using parameter dependent methods numerical examples are given to show the less conservativeness of the results

decentralized finite time h filtering for interconnected markovian jump system with interval mode dependent delays this paper concerns with the problem of finite time h filtering for a class of interconnected markovian jump system with mode dependent delays in the interconnection sufficient conditions guaranteeing the interconnected markovian jump systems to be finite time bounded are established by constructing an augmented lyapunov krasovskii functional the obtained conditions are delay range dependent and mode dependent based on the results the decentralized filter is proposed to guarantee the finite time bounded and h performance of the resulting augmented system for admissible disturbances the desired filter parameters can be obtained via solving a group of linear matrix inequalities lmis finally a numerical example is employed to illustrate the effectiveness of the proposed methods

log periodic crashes revisited we revisit the finding that crashes can be deterministic and governed by log periodic formulas d sornette a johansen significance of log periodic precursors to financial crashes quant finance 1 2001 452 471 d sornette w x zhou the us 2000 2002 market descent how much longer and deeper quant finance 2 2002 468 481 one and two harmonic equations are usually employed to fit daily data during bubble episodes but a three harmonics has been shown to fit anti bubbles a johansen d sornette financial anti bubbles log periodicity in gold and nikkei collapses int j mod phys c 10 1999 563 575 here we show that the three harmonic formula can work for bubble episodes as well as anti bubbles this is illustrated with daily data from the brazilian real us dollar exchange rate and we also show that the three harmonics can fit an intraday data set from that foreign exchange rate

medium and small scale analysis of financial data abstract a stochastic analysis of financial data is presented in particular we investigate how the statistics of log returns change with different time delays the scale dependent behaviour of financial data can be divided into two regions the first time range the small timescale region in the range of seconds seems to be characterised by universal features the second time range the medium timescale range from several minutes upwards can be characterised by a cascade process which is given by a stochastic markov process in the scale a corresponding fokker planck equation can be extracted from given data and provides a non equilibrium thermodynamical description of the complexity of financial data

robust memoryless h controller design for linear time delay systems with norm bounded time varying uncertainty we consider the robust h control problem for linear time delay systems with norm bounded time varying uncertainty based on the riccati equation approach we present a method for designing a robust memoryless linear time invariant state feedback control law which stabilizes the system and reduces the effect of the disturbance input on the controlled output to a prescribed level for all admissible uncertainties

robust exponential h control for uncertain time varying delay systems with input saturation a markov jump model approach abstract this paper is concerned with the state feedback stabilization problem for uncertain time varying delay systems with input saturation based on the stochastic property of time varying delay the considered system can be transformed into a continuous markov jump system with stochastic delays where the growth trend and the maximum value of the time varying delay are limited the problem we address is to design a robust state feedback controller which can switch with time varying delay in terms of markov process such that the system is exponentially mean square stable with disturbance attenuation conditions for the existence of solutions to this problem are obtained in terms of linear matrix equalities lmis when these lmis are feasible the desired robust controller is given finally two examples are provided to demonstrate the effectiveness of the proposed approach

a reflective newton method for minimizing a quadratic function subject to bounds on some of the variables we propose a new algorithm a reflective newton method for the minimization of a quadratic function of many variables subject to upper and lower bounds on some of the variables this method applies to a general indefinite quadratic function for which a local minimizer subject to bounds is required and is particularly suitable for the large scale problem our new method exhibits strong convergence properties global and quadratic convergence and appears to have significant practical potential strictly feasible points are generated experimental results on moderately large and sparse problems support the claim of practicality for large scale problems

evidence of log periodicity in corporate bond spreads abstract in this paper we looked for evidence of log periodicity in recent us corporate bond spreads while we found evidence of log period behavior in both aaa and baa spreads the evidence supporting log periodicity in high yield hy spreads was found to be weak we conducted additional tests to confirm our results bivariate spectral analysis and surrogate data analysis and confirmed log periodicity in aaa and baa spreads but not in hy spreads we attempt to explain this variance using the recently developed market microstructure models of farmer sornette ausloos and others

discretized lyapunov functional for systems with distributed delay and piecewise constant coefficients the stability problem for systems with distributed delay is considered using discretized lyapunov functional the coefficients associated with the distributed delay are assumed to be piecewise constant and the discretization mesh may be non uniform the resulting stability criteria are written in the form of linear matrix inequality numerical examples are also provided to illustrate the effectiveness of the method the basic idea can be extended to a more general setting with more involved formulation

decentralized stabilization of large scale systems with multiple delays in the interconnections in this paper the problem of robust stabilization of a class of time varying large scale systems subject to external disturbances uncertain parameters and multiple time varying delays in the interconnections and non linear inputs is considered linear memory less controllers are developed to guarantee that all solutions of the class of systems considered are uniformly ultimately bounded also non linear memoryless controllers are synthesized to guarantee that the solutions are uniformly ultimately bounded with respect to a bound with any prespecified convergence rate towards it finally an example is included to illustrate the results developed in this paper

delay scheduled state feedback design for time delay systems with time varying delays a lpv approach abstract this paper is concerned with the synthesis of delay scheduled state feedback controllers which stabilize linear systems with time varying delays in this framework it is assumed that the delay is approximately known in real time and used in the controller in a scheduling fashion first a new model transformation turning a time delay system into an uncertain lpv system is introduced using this transformation a new delay dependent stability test based on the so called full block s procedure is developed and from this result a new delay dependent stabilization result is derived since the resulting lmi conditions depend polynomially on the parameters a relaxation result is then applied in order to obtain a tractable finite set of finite dimensional lmis the interest of the approach resides in 1 the synthesis of a new type of controller scheduled by the delay value which has a lower memory consumption than controllers with memory since it is not necessary to store past values of the state and 2 an easy consideration of uncertainties on the delay knowledge

can log periodic power law structures arise from random fluctuations abstract recent research has established log periodic power law lppl patterns prior to the detonation of the german stock index dax bubble in 1998 the purpose of this article is to explore whether a langevin equation extracted from real world data can generate synthetic time series with comparable lppl structures to this end we first estimate the stochastic process underlying the dax log returns during the period from mid 1997 until end 2003 the employed data set contains about 3 93 10 6 intraday dax quotes at a sampling rate of 15 s our results indicate that the dax log returns can be described as a markov process as a consequence a langevin equation is derived based on this model equation we run extensive simulations in order to generate 100 synthetic dax trajectories each covering 3000 trading days we find lppl behavior in ten artificial time series moreover we can establish a link between lppl patterns and ensuing bubble bursts in seven synthetic 600 week windows however the lppl components in most synthetic trajectories differ fundamentally from those lppl structures that have previously been detected in real financial time series summarized this paper demonstrates that lppl structures are not necessarily the signature of imitative behavior among investors but can also stem from noise even though the likelihood of this is extremely low thus our findings confirm with high statistical confidence that the lppl structures in the dax development are rooted deeper than only in the random fluctuations of the german stock market

improved approach to robust stability and h performance analysis for systems with an interval time varying delay abstract an improved delay and range dependent robust stability and h performance analysis criterion for systems with an interval time varying delay is investigated a novel lyapunov krasovskii functional containing triple integral terms is established and an extended free weighting matrix method double integral inequality method is subsequently proposed numerical examples validate the effectiveness of the proposed double integral inequality method and show that our approach is less conservative than existing methods

decentralized stabilization of interconnected systems with time varying delays this technical note establishes decentralized delay dependent stability and stabilization methods for two classes of interconnected continuous time systems the two classes cover the linear case and the lipschitz type nonlinear case in both cases the subsystems are subjected to convex bounded parametric uncertainties and time varying delays within the local subsystems and across the interconnections an appropriate lyapunov functional is constructed to exhibit the delay dependent dynamics at the subsystem level in both cases decentralized delay dependent stability analysis is performed to characterize linear matrix inequalities lmis based conditions under which every local subsystem of the linear interconnected delay system is robustly asymptotically stable with an gamma level l 2 gain then we design a decentralized state feedback stabilization scheme such that the family of closed loop feedback subsystems enjoys the delay dependent asymptotic stability with a prescribed gamma level l 2 gain for each subsystem the decentralized feedback gains are determined by convex optimization over lmis all the developed results are tested on a representative example

stability analysis of linear systems with two delays of overlapping ranges in this paper a delay dependent stability criterion is derived for linear time delay systems with two constant delays having overlapping ranges this overlapping feature of the delays is exploited in delay dependent analysis of the system using lyapunov krasovskii approach the developed treatment of the delays reduces conservatism in analysis compared to the approaches treating the delays individually numerical examples are used to demonstrate the less conservativeness of the derived criterion

adaptive feedback control of nonlinear time delay systems the lasalle razumikhin based approach this note presents a new method to design adaptive feedback controller for nonlinear time delay systems first by using the lasalle razumikhin theorem a sufficient condition is derived that ensures the convergence of a part of the solution with stability for a class of functional differential equations then using this condition the adaptive stabilization problem is solved for nonlinear time delay systems moreover it is shown that for a class of nonlinear time delay systems with triangular structure the adaptive stabilizing controller can be obtained by recursively constructing the lyapunov razumikhin function it will be shown that the provided recursive design approach which is obviously motivated by the typical backstepping method is not a trivial extension of the existing design method

decentralized stabilization of large scale interconnected systems with delays in this note we study the decentralized stabilization problem of linear time invariant large scale interconnected systems with delays without any assumption of system structure our main result here is the sufficient condition for the decentralized stabilization one application of the procedures to the decentralized observers is also presented

training a support vector machine in the primal most literature on support vector machines svms concentrates on the dual optimization problem in this letter we point out that the primal problem can also be solved efficiently for both linear and nonlinear svms and that there is no reason for ignoring this possibility on the contrary from the primal point of view new families of algorithms for large scale svm training can be investigated

an lmi approach to stability of systems with severe time delay this note describes the stability problems of uncertain systems with arbitrarily time varying and severe time delay using new lyapunov krasovskii functionals less conservative stability conditions are obtained for such systems the results are illustrated using the numerical examples based on simple linear matrix inequalities

technical communique improved delay range dependent stability criteria for linear systems with time varying delays this paper is concerned with the stability analysis of linear systems with time varying delays in a given range a new type of augmented lyapunov functional is proposed which contains some triple integral terms in the proposed lyapunov functional the information on the lower bound of the delay is fully exploited some new stability criteria are derived in terms of linear matrix inequalities without introducing any free weighting matrices numerical examples are given to illustrate the effectiveness of the proposed method

new results on stability of discrete time systems with time varying state delay this note is concerned with the stability analysis of discrete time systems with time varying state delay by defining new lyapunov functions and by making use of novel techniques to achieve delay dependence several new conditions are obtained for the asymptotic stability of these systems the merit of the proposed conditions lies in their less conservativeness which is achieved by circumventing the utilization of some bounding inequalities for cross products between two vectors and by paying careful attention to the subtle difference between the terms sigmam k dk k 1 middot and sigma m k dm k 1 middot which is largely ignored in the existing literature these conditions are shown via several examples to be much less conservative than some existing result

delay dependent robust stabilization of uncertain systems with multiple state delays this paper deals with the problem of robust stabilization for uncertain systems with multiple state delays the parameter uncertainties are time varying and unknown but are norm bounded and the delays are time varying a new method for achieving robust stabilization is presented for a class of uncertain time delay systems via linear memoryless state feedback control the results depend on the size of the delays and are given in terms of several linear matrix inequalities

brief paper delay dependent stability for discrete systems with large delay sequence based on switching techniques this paper considers the exponential stability problem for a class of discrete time varying delay systems with large delay sequences ldss a new method based on a switching technique is presented to solve this problem a switched delay system in which one of the discrete subsystems may be unstable is firstly employed to describe such a system and then some new concepts about ldss are introduced next using a novel piecewise lyapunov functional explicit delay dependent conditions are developed to show how long and how frequent the ldss can be and still maintain the system exponentially stable without ldss the criterion obtained in this paper includes the established one as a special case two numerical examples are given to show the effectiveness of the proposed method

technical communique improved delay dependent stability criteria for systems with a delay varying in a range this paper provides improved delay dependent stability criteria for systems with a delay varying in a range the criteria improve over some previous ones in that they have fewer matrix variables yet less conservatism which is established theoretically an example is given to show the advantages of the proposed results

nondegenerate piecewise linear systems a finite newton algorithm and applications in machine learning we investigate newton type optimization methods for solving piecewise linear systems plss with nondegenerate coefficient matrix such systems arise for example from the numerical solution of linear complementarity problem which is useful to model several learning and optimization problems in this letter we propose an effective damped newton method pls dn to find the exact up to machine precision solution of nondegenerate plss pls dn exhibits provable semiiterative property that is the algorithm converges globally to the exact solution in a finite number of iterations the rate of convergence is shown to be at least linear before termination we emphasize the applications of our method in modeling from a novel perspective of plss some statistical learning problems such as box constrained least squares elitist lasso kowalski torreesani 2008 and support vector machines cortes vapnik 1995 numerical results on synthetic and benchmark data sets are presented to demonstrate the effectiveness and efficiency of pls dn on these problems

decentralized adaptive tracking control of nonaffine nonlinear large scale systems with time delays this paper addresses the problem of decentralized tracking control of large scale systems with uncertain nonaffine nonlinear isolated subsystems and nonlinear interconnections with time varying delays based on lyapunov krasovskii functional approach and implicit function theorem a delay independent decentralized tracking controller is proposed due to functional approximation capability of fuzzy logic systems fls neither strict structure restrictions on the isolated subsystems nor a priori knowledge of the strong interconnections with time varying delays is required in our control design furthermore transient performance of the resulting closed loop system is also addressed under an analytical framework finally two numerical examples are provided to show the effectiveness of the proposed controller

delay dependent stabilization of linear systems with time varying state and input delays the integral inequality method is a new way of tackling the delay dependent stabilization problem for a linear system with time varying state and input delays email protected t ax t a 1x t h 1 t b 1u t b 2u t h 2 t in this paper a new integral inequality for quadratic terms is first established then it is used to obtain a new state and input delay dependent criterion that ensures the stability of the closed loop system with a memoryless state feedback controller finally some numerical examples are presented to demonstrate that control systems designed based on the criterion are effective even though neither a b 1 nor a a 1 b 1 is stabilizable

oscillations in the tsallis income distribution abstract oscillations in the complementary cumulative distribution function ccdf of individual income data have been found in the data of various countries studied by different authors at different time periods but the dynamical origins of this behavior are currently unknown although these datasets can be fitted by different functions at different income ranges the tsallis distribution has recently been found capable of fitting the whole distribution by means of only two parameters this procedure showed clearly such oscillatory feature in the entire income range feature but made it particularly visible at the tail of the distribution although log periodic functions fitted to the data are capable of describing this behavior a different approach to naturally disclose such oscillatory characteristics is to allow the tsallis q parameter to become complex in this paper we use this idea in order to describe the behavior of the ccdf of the brazilian personal income recently studied empirically by soares et al 2016 typical elements of periodic motion such as amplitude and angular frequency coupled to this income analysis were obtained by means of this approach a highly non linear function for the ccdf was obtained through this methodology and a numerical test showed it capable of recovering the main oscillatory feature of the original ccdf of the personal income data of brazil

improved stability criteria for linear systems with interval time varying delays this paper suggests first order and second order generalized zero equalities and constructs a new flexible lyapunov krasovskii functional with more state terms also by applying various zero equalities improved stability criteria of linear systems with interval time varying delays are developed using wirtinger based integral inequality jensen inequality and a lower bound lemma the time derivative of the lyapunov krasovskii functional is bounded by the combinations of various state terms including not only integral terms but also their interval normalized versions which contributes to make the stability criteria less conservative numerical examples show the improved performance of the criteria in terms of maximum delay bounds

how to quantify deterministic and random influences on the statistics of the foreign exchange market it is shown that price changes of the u s dollar german mark exchange rates upon different delay times can be regarded as a stochastic marcovian process furthermore we show how kramers moyal coefficients can be estimated from the empirical data finally we present an explicit fokker planck equation which models very precisely the empirical probability distributions in particular their non gaussian heavy tails

discretized lyapunov functional for uncertain systems with multiple time delay the stability of uncertain systems with multiple time delay is studied using a quadratic lyapunov functional by choosing piecewise linear parameters for the kernel of a quadratic expression the guaranteed stability condition is formulated in the form of linear matrix inequality the extent of conservatism depends on the grid size however numerical results show that even a very coarse discretization can produce quite satisfactory results the possibility of non uniform grid size and more general lyapunov functional is of interest even for a single delay system numerical examples are presented

log periodic self similarity an emerging financial law abstract a hypothesis that the financial log periodicity cascading self similarly through various time scales carries signatures of a law is pursued it is shown that the most significant historical financial events can be classified amazingly well using a single and unique value of the preferred scaling factor 2 which indicates that its real value should be close to this number this applies even to a declining decelerating log periodic phase crucial in this connection is identification of a super bubble bubble on bubble phenomenon identifying a potential universal preferred scaling factor as undertaken here may significantly improve the predictive power of the corresponding methodology several more specific related results include evidence that i the real end of the high technology bubble on the stock market started with a decelerating log periodic draw down in the beginning of september 2000 ii a parallel 2000 2002 decline seen in the standard poor s 500 from the log periodic perspective is already of the same significance as the one of the early 1930s and of the late 1970s iii all this points to a much more serious global crash in around 2025 of course from a level much higher at least one order of magnitude than in 2000

markov analysis and kramers moyal expansion of nonstationary stochastic processes with application to the fluctuations in the oil price we describe a general method for analyzing a nonstationary stochastic process x t which unlike many of the previous analysis methods does not require x t to have any scaling feature the method is used to study the fluctuations in the daily price of oil it is shown that the returns time series y t ln x t 1 x t is a stationary and markov process characterized by a markov time scale t m the coefficients of the kramers moyal expansion for the probability density function p y tmid r y 0 t 0 are computed p y tmid r y 0 t 0 satisfies a fokker planck equation which is equivalent to a langevin equation for y t that provides quantitative predictions for the oil price over times that are of the order of t m also studied is the average frequency of positive slope crossings nu alpha p y i alpha y i 1 alpha for the returns where t alpha 1nu alpha is the average waiting time for observing y t alpha again

convergence analysis of some algorithms for solving nonsmooth equations this paper presents convergence analysis of some algorithms for solving systems of nonlinear equations defined by locally lipschitzian functions for the directional derivative based and the generalized jacobian based newton methods both the iterates and the corresponding function values are locally superlinearly convergent globally a limiting point of the iterate sequence generated by the damped directional derivative based newton method is a zero of the system if and only if the iterate sequence converges to this point and the stepsize eventually becomes one provided that the system is strongly bd regular and semismooth at this point in this case the convergence is superlinear a general attraction theorem is presented which can be applied to two algorithms proposed by han pang and rangaraj a hybrid method which is both globally convergent in the sense of finding a stationary point of the norm function of the system and locally quadratically convergent is also presented

new stability criteria for linear discrete time systems with interval like time varying delays this technical note is concerned with stability of linear discrete time systems with interval like time varying delays two new stability criteria are derived by constructing a new lyapunov functional and utilizing two novel techniques for estimating the forward difference of the lyapunov functional the relationship between these stability criteria and some existing ones is established through the relationship it is clear that these stability criteria are less conservative than some existing ones which is confirmed by a numerical example

on h control for linear systems with interval time varying delay this paper deals with the problem of delay dependent robust h control for linear time delay systems with norm bounded and possibly time varying uncertainty 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 and no restriction on the derivative of the time varying delay is needed which allows the time delay to be a fast time varying function based on an integral inequality which is introduced in this paper and lyapunov krasovskii functional approach a delay dependent bounded real lemma brl is first established without using model transformation and bounding techniques on the related cross product terms then employing the obtained brl a delay dependent condition for the existence of a state feedback controller which ensures asymptotic stability and a prescribed h performance level of the closed loop systems for all admissible uncertainties is proposed in terms of a linear matrix inequality lmi a numerical example is also given to illustrate the effectiveness of the proposed method

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

investigating the effects of time delays on stochastic stability and designing l1 gain controllers for positive discrete time markov jump linear systems with time delay this paper is concerned with stochastic stability l1 gain performance analysis and positivity preserving l1 gain controller design for a positive discrete time markov jump linear system with time delay first necessary and sufficient conditions for stochastic stability of the system are derived by constructing a linear co positive stochastic lyapunov functional and establishing a system equation whose state variables consist of the mathematical expectation of the markovianized states and whose coefficient matrices depend on time delay and the transition probability it is revealed that stochastic stability of the positive discrete time markov jump linear system with time delay is influenced by the size of time delay and it is demonstrated by an example that the effect of time delay on stochastic stability can be either positive or negative second exact computation on an l1 gain index of a stochastically stable positive discrete time markov jump linear system with time delay is presented and a necessary and sufficient condition for the l1 gain performance is derived in the form of linear programming third an iterative algorithm is proposed to design a positivity preserving l1 gain controller and in single input case an optimal controller is obtained analytically such that the closed loop system achieves the minimal l1 gain performance then a modified pest s structured population dynamic model is developed to illustrate the effectiveness of the designed method

robust decentralized stabilization of a class of linear discrete time systems with non linear interactions this paper deals with robust stabilization of a class of linear discrete time systems under non linear perturbations via output feedback a bound on the non linear perturbations is maximized in the design it is shown that degree of freedoms by the introduction of instrumental variables employed in this paper lead to much flexibility in obtaining both a robust output feedback controller and a maximal allowable bound of the non linear perturbations an improved method involving linear matrix inequalities are suggested to solve the matrix inequalities characterizing a solution of the robust stabilization problem consequently the proposed method can yield a much less conservative result than that of earlier methods of major interest is an extension to a class of interconnected systems composed of linear subsystems with non linear interactions a robust decentralized controller is presented such that the closed loop systems are maximally tolerant to interconnected non linear couplings numerical examples i

improved estimation of fokker planck equations through optimization an improved method for the description of hierarchical complex systems by means of a fokker planck equation is presented in particular the limited memory broyden fletcher goldfarb shanno algorithm for constraint problems is used to minimize the distance between the numerical solutions of the fokker planck equation and the empirical probability density functions and thus to estimate properly the drift and diffusion term of the fokker planck equation the optimization routine is applied to a time series of velocity measurements obtained from a turbulent helium gas jet in order to demonstrate the benefits and to quantify the improvements of this optimization routine

iterative solution of piecewise linear systems and applications to flows in porous media the correct numerical modeling of free surface hydrodynamic problems often requires to have the solution of special linear systems whose coefficient matrix is a piecewise constant function of the solution itself in doing so one may fulfill relevant physical constraints the existence the uniqueness and two constructive iterative methods to solve a piecewise linear system of the form max boldsymbol l min boldsymbol u mathbf x t mathbf x mathbf b are analyzed the methods are shown to have a finite termination property i e they converge to an exact solution in a finite number of steps and actually they converge very quickly as confirmed by a few numerical tests which are derived from the mathematical modeling of flows in porous media

improved criteria on robust stability and h performance for linear systems with interval time varying delays via new triple integral functionals this paper analyzes delay dependent robust stability and h performance of linear systems with an interval time varying delay based on a new lyapunov krasovskii functional containing new triple integral terms the time derivative of the lyapunov krasovskii functional produces not only the strictly proper rational functions but also the non strictly proper rational functions of the time varying delays with first order denominators the combinations of the rational functions are directly handled via the jensen inequality lemma and the lower bound lemma for reciprocal convexity whereas such combinations were approximated in the literature the proposed criteria become less conservative with the significantly smaller number of decision variables than the existing criteria which will be demonstrated by some numerical examples

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

on finite termination of an iterative method for linear complementarity problems based on a well known reformulation of the linear complementarity problem lcp as a nondifferentiable system of nonlinear equations a newton type method will be described for the solution of lcps under certain assumptions it will be shown that this method has a finite termination property i e if an iterate is sufficiently close to a solution of lcp the method finds this solution in one step this result will be applied to a recently proposed algorithm by harker and pang in order to prove that their algorithm also has the finite termination property

on a semi smooth newton method and its globalization this paper addresses the globalization of the semi smooth newton method for non smooth equations f x 0 in mathbb r m with applications to complementarity and discretized l1 regularization problems assuming semi smoothness it is shown that super linearly convergent newton methods can be globalized if appropriate descent directions are used for the merit function f x 2 special attention is paid to directions obtained from the primal dual active set strategy

estimation of kramers moyal coefficients at low sampling rates an optimization procedure for the estimation of kramers moyal coefficients from stationary one dimensional markovian time series data is presented the method takes advantage of a recently reported approach that allows one to calculate exact finite sampling interval effects by solving the adjoint fokker planck equation therefore it is well suited for the analysis of sparsely sampled time series the optimization can be performed either by making a parametric ansatz for drift and diffusion functions or parameter free we demonstrate the power of the method in several numerical examples with synthetic time series

analysis of the real estate market in las vegas bubble seasonal patterns and prediction of the csw indices we analyze 27 house price indices of las vegas from june 1983 to march 2005 corresponding to 27 different zip codes these analyses confirm the existence of a real estate bubble defined as a price acceleration faster than exponential which is found however to be confined to a rather limited time interval in the recent past from approximately 2003 to mid 2004 and has progressively transformed into a more normal growth rate comparable to pre bubble levels in 2005 there has been no bubble till 2002 except for a medium sized surge in 1990 in addition we have identified a strong yearly periodicity which provides a good potential for fine tuned prediction from month to month a monthly monitoring using a model that we have developed could confirm by testing the intra year structure if indeed the market has returned to normal or if more turbulence is expected ahead we predict the evolution of the indices one year ahead which is validated with new data up to september 2006 the present analysis demonstrates the existence of very significant variations at the local scale in the sense that the bubble in las vegas seems to have preceded the more global usa bubble and has ended approximately two years earlier mid 2004 for las vegas compared with mid 2006 for the whole of the usa

h sub spl infin and positive real control for linear neutral delay systems this note is concerned with the h sub spl infin and positive real control problems for linear neutral delay systems the purpose of h sub spl infin control is the design of a memoryless state feedback controller which stabilizes the neutral delay system and reduces the h sub spl infin norm of the closed loop transfer function from the disturbance to the controlled output to a prescribed level while the purpose of positive real control is to design a memoryless state feedback controller such that the resulting closed loop system is stable and the closed loop transfer function is extended strictly positive real sufficient conditions for the existence of the desired controllers are given in terms of a linear matrix inequality lmi when this lmi is feasible the expected memoryless state feedback controllers can be easily constructed via convex optimization

new filter design for linear time delay systems abstract this paper develops new robust delay dependent filter design for a class of linear systems with time varying delays and convex bounded parameter uncertainties the design procedure hinges upon the constructive use of an appropriate lyapunov functional plus a free weighting matrices in order to exhibit the delay dependent dynamics the developed approach utilizes smaller number of lmi decision variables thereby leading to less conservative solutions to the delay dependent stability and filtering problems subsequently linear matrix inequalities lmis based conditions are characterized such that the linear delay system is robustly asymptotically stable with an level l 2 gain all the developed results are tested on representative examples

technical communique delay range dependent stability for systems with time varying delay this paper is concerned with the stability analysis for systems with time varying delay in a range an appropriate type of lyapunov functionals is proposed to investigate the delay range dependent stability problem the present results may improve the existing ones due to a method to estimate the upper bound of the derivative of lyapunov functional without ignoring some useful terms and the introduction of additional terms into the proposed lyapunov functional which take into account the range of delay numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method

semi implicit finite difference methods for the two dimensional shallow water equation abstract in this paper a semi implicit finite difference method for the 2 dimensional shallow water equations is derived and discussed a characteristic analysis of the governing equations is carried out first in order to determine those terms to be discretized implicitly so that the stability of the method will not depend upon the celerity such terms are the gradient of the water surface elevation in the momentum equations and the velocity divergence in the continuity equation the convective terms are discretized explicitly the simpler explicit discretization for the convective terms is the upwind discretization which is conditionally stable and introduces some artificial viscosity it is shown that the stability restriction is eliminated and the artificial viscosity is reduced when an eulerian lagrangian approach with large time steps is used to discretize the convective terms this method at each time step requires the solution of a linear symmetric 5 diagonal system such a system is diagonally dominant with positive elements on the main diagonal and negative ones elsewhere thus existence and uniqueness of the numerical solution is assured the resulting algorithm is mass conservative and fully vectorizable for an efficient implementation on modern vector computers the performance of this method is further improved when used in combination with an adi technique which results in two sets of simpler linear 3 diagonal systems and maintains all the properties described above

improved delay dependent robust stability criteria for uncertain time delay systems abstract this paper deals with the robust stability analysis for uncertain systems with time varying delay new delay dependent robust stability criteria of uncertain time delay systems are proposed by exploiting appropriate lyapunov functional candidate these developed results have advantages over some previous ones in that they have fewer matrix variables yet less conservatism due to the introduction of a method to estimate the upper bound of the derivative of lyapunov functional candidate without ignoring the additional useful terms numerical examples are given to demonstrate the effectiveness and the advantage of the proposed method

further improvement of free weighting matrices technique for systems with time varying delay a novel method is proposed in this note for stability analysis of systems with a time varying delay appropriate lyapunov functional and augmented lyapunov functional are introduced to establish some improved delay dependent stability criteria less conservative results are obtained by considering the additional useful terms which are ignored in previous methods when estimating the upper bound of the derivative of lyapunov functionals and introducing the new free weighting matrices the resulting criteria are extended to the stability analysis for uncertain systems with time varying structured uncertainties and polytopic type uncertainties numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method

evidence of markov properties of high frequency exchange rate data we present a stochastic analysis of a data set consisting of 106 quotes of the us dollar german mark exchange rate evidence is given that the price changes x upon different delay times can be described as a markov process evolving in thus the dependence of the probability density function pdf p x on the delay time can be described by a fokker planck equation a generalized diffusion equation for p x this equation is completely determined by two coefficients d1 x and d2 x drift and diffusion coefficient respectively we demonstrate how these coefficients can be estimated directly from the data without using any assumptions or models for the underlying stochastic process furthermore it is shown that the solutions of the resulting fokker planck equation describe the empirical pdfs correctly including the pronounced tails

passive control for singular time delay system with actuator saturation this paper considers the problem of passivity controller design for singular time delay system with actuator saturation and nonlinear disturbance firstly by tuning the wirtinger based integral inequality a sufficient condition is derived to guarantee that the nonlinear singular time delay system is regular impulse free asymptotically stable with the dissipation performance then based on the derived condition and applying linear matrix inequalities lmis techniques the passive state feedback controller is synthesized moreover the maximal estimate of the domain of attraction is proposed by an optimization problem finally some numerical examples are given to illustrate the effectiveness of the obtained theoretic results

renormalization group analysis of the 2000 2002 anti bubble in the us s p500 index explanation of the hierarchy of five crashes and prediction abstract we propose a straightforward extension of our previously proposed log periodic power law model of the anti bubble regime of the usa stock market since the summer of 2000 in terms of the renormalization group framework to model critical points using a previous work by gluzman and sornette phys rev e 65 2003 036142 on the classification of the class of weierstrass like functions we show that the five crashes that occurred since august 2000 can be accurately modeled by this approach in a fully consistent way with no additional parameters our theory suggests an overall consistent organization of the investors forming a collective network which interact to form the pessimistic bearish anti bubble regime with intermittent acceleration of the positive feedbacks of pessimistic sentiment leading to these crashes we develop retrospective predictions that confirm the existence of significant arbitrage opportunities for a trader using our model finally we offer a prediction for the unknown future of the us s p500 index extending over 2003 and 2004 that refines the previous prediction of sornette and zhou quant finance 2 2002 468

new results on h_ infty filtering for fuzzy time delay systems this paper is concerned with the h infin fuzzy filtering problem for a class of continuous time fuzzy systems with time varying delays the objective is to design a stable filter guaranteeing the asymptotic stability and a prescribed h infin performance of the filtering error system motivated by the parallel distributed compensation technique we design a new filter model in this paper filter parameter matrices can be obtained from the solution of a convex optimization problem in terms of linear matrix inequalities lmis when these lmis are feasible an explicit expression of a desired h infin fuzzy filter is given two numerical examples are provided to demonstrate the effectiveness and less conservativeness of the proposed design approach

on newton type approach for piecewise linear systems we investigate effective newton type methods for solving piecewise linear systems we prove that under certain relaxed conditions the proposed newton type methods converge monotonically and have a finite termination property moreover we give some conclusions on the existence of solution for the piecewise linear systems