multiscale analysis of financial time series by renyi distribution entropy abstract it is of great interests to analyze the complexity or dependence of time series of the daily stock closing price in different regions entropy is typically a fundamental technique to explore the complexity of time series the well studied irregularity measure sample entropy sampen and a more recently proposed complexity measure distribution entropy disten are treated as classification features in our study based on renyi entropy which has been recently suggested as a measure of complexity in nonlinear systems we propose multiscale renyi distribution entropy mrde to research the complexity of nonlinear time series over multiple time scales considering the validity and accuracy renyi entropy obtains more information than the shannon entropy for time series mingled with much noise like financial time series which is mainly reflected in the choice of parameters for frequent events and rare events both the simulated signals logistic map and gaussian noise and the financial time series with three different stock markets are calculated and compared using an innovative method in different situations for different stock markets the entropy decreases as the scale factor increases except when the parameter is the maximum in the special case meanwhile we illustrate the necessity and advantage of renyi distribution entropy rde method by comparing rde results with the sampen results about stability and consistency on synthetic data and financial time series it is applied to measure the dependence by detecting the length of the time series and special algorithm parameters

design of robust controllers for time delay systems the problem of stabilizing linear dynamical time delay systems subject to bounded uncertainties is investigated two memoryless feedback controllers are considered it is established that when the matching conditions are met and certain bounding relations are satisfied then the linear controller renders the zero response of the system asymptotically stable saturation type controllers are shown to guarantee that all system responses are uniformly ultimately bounded

stabilization of highly nonlinear hybrid systems by feedback control based on discrete time state observations given an unstable hybrid stochastic differential equation sde can we design a feedback control based on the discrete time observations of the state at times 0 tau 2 tau ldots so that the controlled hybrid sde becomes asymptotically stable it has been proved that this is possible if the drift and diffusion coefficients of the given hybrid sde satisfy the linear growth condition however many hybrid sdes in the real world do not satisfy this condition namely they are highly nonlinear and there is no answer to the question yet if the given sde is highly nonlinear the aim of this paper is to tackle the stabilization problem for a class of highly nonlinear hybrid sdes under some reasonable conditions on the drift and diffusion coefficients we show how to design the feedback control function and give an explicit bound on tau the time duration between two consecutive state observations whence the new theory established in this paper is implementable

stabilization of hybrid stochastic differential equations by feedback control based on discrete time state observations recently mao 2013 discusses the mean square exponential stabilization of continuous time hybrid stochastic differential equations by feedback controls based on discrete time state observations mao 2013 also obtains an upper bound on the duration between two consecutive state observations however it is due to the general technique used there that the bound on is not very sharp in this paper we will consider a couple of important classes of hybrid sdes making full use of their special features we will be able to establish a better bound on our new theory enables us to observe the system state less frequently so costs less but still to be able to design the feedback control based on the discrete time state observations to stabilize the given hybrid sdes in the sense of mean square exponential stability

inequalities similar to certain extensions of hilbert s inequality in the present paper we establish some new inequalities similar to certain extensions of hilbert s inequality by using a fairly elementary analysis

comment on multiscale entropy analysis of complex physiologic time series a comment on the letter by madalena costa ary l goldberger and c k peng phys rev lett 89 068102 2002 the authors of the letter offer a reply

robust h control for a class of nonlinear discrete time delay stochastic systems with missing measurements this paper is concerned with the problem of robust h output feedback control for a class of uncertain discrete time delayed nonlinear stochastic systems with missing measurements the parameter uncertainties enter into all the system matrices the time varying delay is unknown with given low and upper bounds the nonlinearities satisfy the sector conditions and the missing measurements are described by a binary switching sequence that obeys a conditional probability distribution the problem addressed is the design of an output feedback controller such that for all admissible uncertainties the resulting closed loop system is exponentially stable in the mean square for the zero disturbance input and also achieves a prescribed h performance level by using the lyapunov method and stochastic analysis techniques sufficient conditions are first derived to guarantee the existence of the desired controllers and then the controller parameters are characterized in terms of linear matrix inequalities lmis a numerical example is exploited to show the usefulness of the results obtained

control of markovian jump discrete time systems with norm bounded uncertainty and unknown delay this paper studies the problem of control for discrete time delay linear systems with markovian jump parameters the system under consideration is subjected to both time varying norm bounded parameter uncertainty and unknown time delay in the state and markovian jump parameters in all system matrices we address the problem of robust state feedback control in which both robust stochastic stability and a prescribed h sub spl infin performance are required to be achieved irrespective of the uncertainty and time delay it is shown that the above problem can be solved if a set of coupled linear matrix inequalities has a solution

stochastic stability properties of jump linear systems jump linear systems are defined as a family of linear systems with randomly jumping parameters usually governed by a markov jump process and are used to model systems subject to failures or changes in structure the authors study stochastic stability properties in jump linear systems and the relationship among various moment and sample path stability properties it is shown that all second moment stability properties are equivalent and are sufficient for almost sure sample path stability and a testable necessary and sufficient condition for second moment stability is derived the lyapunov exponent method for the study of almost sure sample stability is discussed and a theorem which characterizes the lyapunov exponents of jump linear systems is presented finally for one dimensional jump linear system it is proved that the region for delta moment stability is monotonically converging to the region for almost sure stability at delta down arrow 0 sup

robust output feedback stabilization for uncertain discrete time fuzzy markovian jump systems with time varying delays this paper provides a delay dependent approach to the design of fuzzy dynamic output feedback controllers for uncertain discrete time fuzzy markovian jump systems with interval time varying delays first by a fuzzy basis dependent and mode dependent lyapunov functional a stochastic stability condition is derived by using the finsler s lemma second in terms of linear matrix inequalities lmis a delay dependent sufficient condition is presented under which there exists a fuzzy output feedback controller such that the resulting closed loop system is robustly stochastically stable a desired controller can be constructed when these lmis are feasible finally the effectiveness of the proposed design method is demonstrated by a simulation example

on some new inequalities similar to hilbert s inequality in the present article we establish some new inequalities similar to hilbert s inequality involving series of nonnegative terms the integral analogues of the main results are also given

stabilisation of hybrid stochastic differential equations by delay feedback control this paper is concerned with the exponential mean square stabilisation of hybrid stochastic differential equations also known as stochastic differential equations with markovian switching by delay feedback controls although the stabilisation by non delay feedback controls for such equations has been discussed by several authors there is so far little on the stabilisation by delay feedback controls and our aim here is mainly to close the gap to make our theory more understandable as well as to avoid complicated notations we will restrict our underlying hybrid stochastic differential equations to a relatively simple form however our theory can certainly be developed to cope with much more general equations without any difficulty

kalman filtering for continuous time uncertain systems with markovian jumping parameters studies the problem of kalman filtering for a class of uncertain linear continuous time systems with markovian jumping parameters the system under consideration is subjected to time varying norm bounded parameter uncertainties in the state and measurement equations stochastic quadratic stability of the above system is analyzed a state estimator is designed such that the covariance of the estimation error is guaranteed to be within a certain bound for all admissible uncertainties which is in terms of solutions of two sets of coupled algebraic riccati equations

worst case control of uncertain jumping systems with multi state and input delay information in this paper the problem of worst case also called h control for a class of uncertain systems with markovian jump parameters and multiple delays in the state and input is investigated the jumping parameters are modelled as a continuous time discrete state markov process and the parametric uncertainties are assumed to be real time varying and norm bounded that appear in the state input and delayed state matrices the time delay factors are unknowns and time varying with known bounds complete results for instantaneous and delayed state feedback control designs are developed which guarantee the weak delay dependent stochastic stability with a prescribed h performance the solutions are provided in terms of a finite set of coupled linear matrix inequalities lmis application of the developed theory to a typical example has been presented

multiscale entropy analysis of complex physiologic time series there has been considerable interest in quantifying the complexity of physiologic time series such as heart rate however traditional algorithms indicate higher complexity for certain pathologic processes associated with random outputs than for healthy dynamics exhibiting long range correlations this paradox may be due to the fact that conventional algorithms fail to account for the multiple time scales inherent in healthy physiologic dynamics we introduce a method to calculate multiscale entropy mse for complex time series we find that mse robustly separates healthy and pathologic groups and consistently yields higher values for simulated long range correlated noise compared to uncorrelated noise

controllability stabilizability and continuous time markovian jump linear quadratic control consideration is given to the control of continuous time linear systems that possess randomly jumping parameters which can be described by finite state markov processes the relationship between appropriately defined controllability stabilizability properties and the solution of the infinite time jump linear quadratic jlq optimal control problems is also examined although the solution of the continuous time markov jlq problem with finite or infinite time horizons is known only sufficient conditions for the existence of finite cost constant stabilizing controls for the infinite time problem appear in the literature in this paper necessary and sufficient conditions are established these conditions are based on new definitions of controllability observability stabilizability and detectability that are appropriate for continuous time markovian jump linear systems these definitions play the same role for the jlq problem as the deterministic properties do for the linear quadratic regulator lqr problem

delay dependent robust stabilization for uncertain discrete time fuzzy markovian jump systems with mode dependent time delays this paper deals with the problem of delay dependent robust stabilization for uncertain discrete time fuzzy markovian jump systems with mode dependent time varying delays a delay dependent stochastic stability condition for a fuzzy markovian jump system with two levels of structure is obtained based on a new lyapunov functional the lyapunov functional depends not only on the fuzzy basis functions but also on the system modes furthermore a delay dependent sufficient condition for the solvability of the robust stabilization problem is proposed in terms of linear matrix inequalities finally a simulation example is given to show the effectiveness of the proposed design method

an optimal stochastic production planning problem with randomly fluctuating dem and this paper considers an infinite horizon stochastic production planning problem with demand assumed to be a continuous time markov chain the problems with control production and state inventory constraints are treated it is shown that a unique optimal feedback solution exists after first showing that convex viscosity solutions to the associated dynamic programming equation are continuously differentiable

filtering design for two dimensional markovian jump systems with state delays and deficient mode information this paper is concerned with the problem of h filtering for a class of two dimensional markovian jump linear systems described by the fornasini marchesini local state space model the systems under consideration are subject to state delays and deficient mode information in the markov chain the description of deficient mode information is comprehensive that simultaneously includes the exactly known partially unknown and uncertain transition probabilities by invoking the properties of the transition probability matrix together with the convexification of uncertain domains a new h performance analysis criterion for the filtering error system is firstly derived then via some matrix inequality linearisation procedures two approaches for the filter synthesis are proposed it is shown that both the full order and reduced order filters can be constructed by solving a set of linear matrix inequalities finally simulation studies are provided to illustrate the effectiveness of the proposed design methods

delay dependent stability analysis and controller synthesis for markovian jump systems with state and input delays this paper focuses on the problem of delay dependent robust stochastic stability analysis and controller synthesis for markovian jump systems with state and input delays it is assumed that the delays are constant and unknown but their upper bounds are known by constructing a new lyapunov krasovskii functional and introducing some appropriate slack matrices new delay dependent stochastic stability and stabilization conditions are proposed by means of linear matrix inequalities lmis an important feature of the results proposed here is that all the robust stability and stabilization conditions are dependent on the upper bound of the delays memoryless state feedback controllers are designed such that the closed loop system is robustly stochastically stable some numerical examples are provided to illustrate the effectiveness of the proposed method

a unified treatment of hilbert pachpatte type inequalities for a class of non homogeneous kernels abstract in the present paper we establish a unified treatment of hilbert pachpatte type inequalities for a class of non homogeneous kernels our results are derived in both discrete and integral versions a particular emphasis is devoted to constants and weight functions appearing on the right hand sides of the established inequalities as an application we obtain inequalities with constants and weight functions expressed in terms of generalized harmonic numbers the incomplete beta and gamma function and the logarithmic integral function

randomness and degrees of irregularity the fundamental question are sequential data random arises in myriad contexts often with severe data length constraints furthermore there is frequently a critical need to delineate nonrandom sequences in terms of closeness to randomness e g to evaluate the efficacy of therapy in medicine we address both these issues from a computable framework via a quantification of regularity apen approximate entropy defining maximal randomness for sequences of arbitrary length indicating the applicability to sequences as short as n 5 points an infinite sequence formulation of randomness is introduced that retains the operational and computable features of the finite case in the infinite sequence setting we indicate how the foundational definition of independence in probability theory and the definition of normality in number theory reduce to limit theorems without rates of convergence from which we utilize apen to address rates of convergence of a deficit from maximal randomness refining the aforementioned concepts in a computationally essential manner representative applications among many are indicated to assess i random number generation output ii well shuffled arrangements and iii the quality of bootstrap replicates

delay dependent stabilization of stochastic interval delay systems with nonlinear disturbances in this paper a delay dependent approach is developed to deal with the robust stabilization problem for a class of stochastic time delay interval systems with nonlinear disturbances the system matrices are assumed to be uncertain within given intervals the time delays appear in both the system states and the nonlinear disturbances and the stochastic perturbation is in the form of a brownian motion the purpose of the addressed stochastic stabilization problem is to design a memoryless state feedback controller such that for all admissible interval uncertainties and nonlinear disturbances the closed loop system is asymptotically stable in the mean square where the stability criteria are dependent on the length of the time delay and therefore less conservative by using ito s differential formula and the lyapunov stability theory sufficient conditions are first derived for ensuring the stability of the stochastic interval delay systems then the controller gain is characterized in terms of the solution to a delay dependent linear matrix inequality lmi which can be easily solved by using available software packages a numerical example is exploited to demonstrate the effectiveness of the proposed design procedure

half discrete hilbert type inequalities with mean operators the best constants and applications in this article we derive several new half discrete hilbert type inequalities with a general homogeneous kernel involving arithmetic geometric and harmonic mean operators the main results are proved for the case of non conjugate exponents a special emphasis is given to determining conditions under which these inequalities include the best possible constants as an application we consider some operator expressions closely connected to established inequalities

stabilization in probability and mean square of controlled stochastic dynamical system with state delay abstract although stochastic dynamical systems have received a great deal of attention in terms of stabilization studies so far there are few works on controlled stochastic dynamical systems with state delay in this paper a controlled stochastic dynamical system represented by a stochastic differential equation with state delay is considered condition under which the system is exponentially stable in mean square and in probability is examined