output feedback h_ infty control of continuous time infinite markovian jump linear systems via lmi methods the output feedback h infty control is addressed for a class of continuous time markov jump linear systems with the markov process taking values in an infinite countable set mathcal s we consider that only an output and the jump parameters are available to the controller via a certain bounded real lemma together with some extensions of schur complements and of the projection lemma a theorem which characterizes whether there exists a full order solution to the disturbance attenuation problem is devised in terms of two different linear matrix inequality lmi feasibility problems this result connects a certain projection approach to an lmi problem which is more amenable to computer solution and hence for design we conclude the paper with some design algorithms for the construction of such controllers and an illustrative example

discrete time lq optimal control problems for infinite markov jump parameter systems optimal control problems for discrete time linear systems subject to markovian jumps in the parameters are considered for the case in which the markov chain takes values in a countably infinite set two situations are considered the noiseless case and the case in which an additive noise is appended to the model the solution for these problems relies in part on the study of a countably infinite set of coupled algebraic riccati equations icare conditions for existence and uniqueness of a positive semidefinite solution to the icare are obtained via the extended concepts of stochastic stabilizability ss and stochastic detectability sd which turn out to be equivalent to the spectral radius of certain infinite dimensional linear operators in a banach space being less than one for the long run average cost ss and sd guarantee existence and uniqueness of a stationary measure and consequently existence of an optimal stationary control policy furthermore an extension of a lyapunov equation result is derived for the countably infinite markov state space case

a systolic design for connectivity problems in this paper we present a design suited to vlsi implementation for a one dimensional array to solve graph connectivity problems the computational model is relatively primitive in that only the two end cells of the array can interact with the external environment and only adjacent cells in the array are allowed to communicate however we show that an array of n 1 cells can be used for a graph with n vertices to find the connected components a spanning tree or when used in conjunction with a systolic priority queue a minimum spanning tree the area time and i o requirements compare favorably with other models proposed for this problem in the case of sparse graphs

dissipativity analysis for singular systems with time varying delays this paper is concerned with the dissipativity analysis problem for singular systems with time varying delays a delay dependent criterion is established to guarantee the dissipativity of the underlying systems using the delay partitioning technique all the results given in this paper are not only dependent upon the time delay but also dependent upon the number of delay partitions the effectiveness and the reduced conservatism of the derived results are demonstrated by two illustrative examples

stochastic stability of jump linear systems in this note some testable conditions for mean square i e second moment stability for discrete time jump linear systems with time homogenous and time inhomogenous finite state markov chain form processes are presented

admissibility and dissipativity analysis for discrete time singular systems with mixed time varying delays abstract the problems of admissibility and dissipativity are studied for discrete time singular systems with mixed time varying delays the mixed time delays consist of both discrete and distributed delays by taking advantage of the delay partitioning technique a criterion that warrants the admissibility of the considered systems is established based on the criterion a dissipativity condition is also given all the results presented depend upon not only discrete delay and distributed delay but also depend upon the number of delay partitions some numerical examples are included to demonstrate the improvement and effectiveness of the proposed methods

aging arcsine law in brownian motion and its generalization classical arcsine law states that the fraction of occupation time on the positive or the negative side in brownian motion does not converge to a constant but converges in distribution to the arcsine distribution here we consider how a preparation of the system affects the arcsine law i e aging of the arcsine law we derive an aging distributional theorem for occupation time statistics in brownian motion where the ratio of time when measurements start to the measurement time plays an important role in determining the shape of the distribution furthermore we show that this result can be generalized as an aging distributional limit theorem in renewal processes

observer synthesis method for lipschitz nonlinear discrete time systems with time delay an lmi approach abstract in this paper we address the problem of observer design for a class of lipschitz nonlinear discrete time systems with time delay the main contribution lies in the use of a new structure of the proposed observer with a novel lyapunov krasovskii functional thanks to these designs new nonrestrictive synthesis conditions expressed in terms of linear matrix inequalities lmis are obtained indeed the obtained lmis contain more degree of freedom than those established by the approaches available in the literature which consider a simple luenberger observer with a simple lyapunov function for the stability analysis an extension of the presented result to h performance analysis is given in order to take into account the noise if it exists affecting the considered system

synchronization in complex dynamical networks with nonsymmetric coupling based on the work of nishikawa and motter who have extended the well known master stability framework to include non diagonalizable cases we develop another extension of the master stability framework to obtain criteria for global synchronization several criteria for global synchronization are provided which generalize some previous results the jordan canonical transformation method is used in stead of the matrix diagonalization method especially we show clearly that the synchronizability of a dynamical network with nonsymmetric coupling is not always characterized by its second largest eigenvalue even though all the eigenvalues of the nonsymmetric coupling matrix are real furthermore the effects of the asymmetry of coupling on synchronizability of networks with different structures are analyzed numerical simulations are also done to illustrate and verify the theoretical results on networks in which each node is a dynamical limit cycle oscillator consisting of a two cell cellular neural network

stabilization of continuous time randomly switched systems via the lmi approach this paper is concerned on the stabilization problem of continuous time switched systems with random switching signal where the dwell time in each subsystem consists of a fixed part and random part new sufficient conditions for stabilizing controllers including mode independent case are provided in terms of lmis which could be solved directly moreover the obtained results are extended to a more general case that the corresponding operation mode of a controller experiences a disordering phenomenon without designing a controller depending on new operation modes noms a kind of controller only depending on the original operation modes ooms is proposed and satisfies a minimum variance approximation whose solvable conditions are also with lmi forms finally numerical examples are used to demonstrate the effectiveness of the proposed methods

finite time h filtering for a class of discrete time markovian jump systems with switching transition probabilities subject to average dwell time switching an extension of fixed transition probability markovian switching model to combine time varying transition probabilities has offered another set of useful regime switching models this paper investigated the problem of finite time h filtering for a class of discrete time markovian jump systems with switching transition probabilities subject to average dwell time switching based on the results of finite time boundness and average dwell time a novel sufficient condition for finite time bounded of h filtering is derived and the system trajectory stays within a prescribed bound finally an example is provided to illustrate the usefulness and effectiveness of the proposed method

fast efficient parallel algorithms for some graph problems algorithms for solving graph problems on an unbounded parallel model of computation are considered parallel algorithms of time complexity o log 2 n are described for finding biconnected components bridges minimum spanning trees and fundamental cycles in the algorithms for finding minimum spanning trees bridges and fundamental cycles the number of processors used is small enough that the parallel algorithm is efficient in comparison with the best sequential algorithms for these problems several other algorithms are presented which are especially suitable for processing sparse graphs

stochastic solution of space time fractional diffusion equations classical and anomalous diffusion equations employ integer derivatives fractional derivatives and other pseudodifferential operators in space in this paper we show that replacing the integer time derivative by a fractional derivative subordinates the original stochastic solution to an inverse stable subordinator process whose probability distributions are mittag leffler type this leads to explicit solutions for space time fractional diffusion equations with multiscaling space fractional derivatives and additional insight into the meaning of these equations

intrinsic randomness of transport coefficient in subdiffusion with static disorder fluctuations in the time averaged mean square displacement for random walks on hypercubic lattices with static disorder are investigated it is analytically shown that the diffusion coefficient becomes a random variable as a manifestation of weak ergodicity breaking for two and higher dimensional systems the distribution function of the diffusion coefficient is found to be the mittag leffler distribution which is the same as for the continuous time random walk whereas for one dimensional systems a different distribution a modified mittag leffler distribution arises we also present a comparison of these two distributions in terms of an ergodicity breaking parameter and show that the modified mittag leffler distribution has a larger deviation from ergodicity some remarks on similarities between these results and observations in biological experiments are presented

fractional brownian motion versus the continuous time random walk a simple test for subdiffusive dynamics fractional brownian motion with hurst index less then 1 2 and continuous time random walk with heavy tailed waiting times and the corresponding fractional fokker planck equation are two different processes that lead to a subdiffusive behavior widespread in complex systems we propose a simple test based on the analysis of the so called p variations which allows distinguishing between the two models on the basis of one realization of the unknown process we apply the test to the data of golding and cox phys rev lett 96 098102 2006 describing the motion of individual fluorescently labeled mrna molecules inside live e coli cells it is found that the data does not follow heavy tailed continuous time random walk the test shows that it is likely that fractional brownian motion is the underlying process

fractional langevin equation we investigate fractional brownian motion with a microscopic random matrix model and introduce a fractional langevin equation we use the latter to study both subdiffusion and superdiffusion of a free particle coupled to a fractal heat bath we further compare fractional brownian motion with the fractal time process the respective mean square displacements of these two forms of anomalous diffusion exhibit the same power law behavior here we show that their lowest moments are actually all identical except the second moment of the velocity this provides a simple criterion that enable us to distinguish these two non markovian processes

graph problems on a mesh connected processor array on donne des algorithmes fonctionnant par etapes de o n pour resoudre un certain nombre de problemes de graphes sur un reseau n n de processeurs le probleme considere comprend la recherche des ponts et points d articulation d un graphe non oriente la recherche de la longueur du cycle le plus court la recherche d un arbre maximal minimal et d autres problemes

mathcal h_ infty control for 2 d markov jump systems in roesser model this paper considers the problem of asynchronous mathcal h infty control for two dimensional 2 d markov jump systems the underlying system is described based upon the roesser model especially the hidden markov model is employed when dealing with the asynchronization between a controlled system and a controller and the relation between them is constructed through a conditional probability matrix based on the lyapunov function technique the asymptotic mean square stability and mathcal h infty noise attenuation performance are investigated for the closed loop 2 d system moreover the controller gain can be obtained by solving a convex optimization problem an example is presented to show the effectiveness and potential of the proposed new design technique

iterative solution to linear matrix inequality arising from time delay descriptor systems linear matrix inequalities lmis are widely used to analyze the stability or performance of time delay descriptor systems tddss they are solved by the well known interior point method ipm via minimizing a strictly convex function by transforming the matrix variable into an expanded vector variable newton s method is used to get the unique minimizer of the strictly convex function by the iteration involving its gradient and hessian the obvious disadvantage of the ipm is the high storage requirement for the hessian hence this often renders that the ipm cannot solve large lmi problems due to finite memory limit to overcome this shortcoming for the first time an iterative algorithm based on the steepest descent method sdm is proposed to solve lmis by keeping matrix variable form instead of transforming it to an expanded vector and without using hessian matrix the gradient of the proposed objective function is explicitly given by a matrix function with the same dimension of the original matrix variable the efficiency of the proposed method is verified with numerical examples

stochastic stabilization of singular systems with markovian switchings this paper studies the stochastic stabilization problem for a class of singular markovian jump system the aim is to determine whether or not there is a stochastic feedback controller stabilizing a given singular markovian jump system smjs a new kind of stochastic controller only in the diffusion part is proposed such that the closed loop system has a unique solution and is almost surely exponentially admissible new sufficient condition for the existence of such a controller is given as linear matrix inequalities lmis based on this more extensions to transition probability matrix tpm with elements partially unknown and system states partially observable are developed a numerical example is used to demonstrate the effectiveness of the proposed methods

role of infinite invariant measure in deterministic subdiffusion statistical properties of the transport coefficient for deterministic subdiffusion are investigated from the viewpoint of infinite ergodic theory we find that the averaged diffusion coefficient is characterized by the infinite invariant measure of the reduced map we also show that when the time difference is much smaller than the total observation time the time averaged mean square displacement depends linearly on the time difference furthermore the diffusion coefficient becomes a random variable and its limit distribution is characterized by the universal law called the mittag leffler distribution

ergodic properties of continuous time random walks finite size effects and ensemble dependences the effects of spatial confinements and smooth cutoffs of the waiting time distribution in continuous time random walks are studied analytically we also investigate dependences of ergodic properties on initial ensembles i e distributions of the first waiting time here we consider two ensembles the equilibrium and a typical nonequilibrium ensemble for both ensembles it is shown that the time averaged mean square displacement tamsd exhibits a crossover from normal to anomalous diffusion due to the spatial confinement and this crossover does not vanish even in the long measurement time limit moreover for the nonequilibrium ensemble we show that the probability density function of the diffusion constant of tamsd follows the transient mittag leffler distribution and that scatter in the tamsd shows a clear transition from weak ergodicity breaking an irreproducible regime to ordinary ergodic behavior a reproducible regime as the measurement time increases this convergence to ordinary ergodicity requires a long measurement time compared to common distributions such as the exponential distribution in other words the weak ergodicity breaking persists for a long time in addition it is shown that aside from the tamsd a class of observables also exhibits this slow convergence to ergodicity we also point out that even though the system with the equilibrium initial ensemble shows no aging its behavior is quite similar to that for the nonequilibrium ensemble

distributional ergodicity in stored energy driven levy flights we study a class of random walk the stored energy driven l evy flight sedlf whose jump length is determined by a stored energy during a trapped state the sedlf is a continuous time random walk with jump lengths being coupled with the trapping times it is analytically shown that the ensemble averaged mean square displacements exhibit subdiffusion as well as superdiffusion depending on the coupling parameter we find that time averaged mean square displacements increase linearly with time and the diffusion coefficients are intrinsically random a manifestation of distributional ergodicity the diffusion coefficient shows aging in subdiffusive regime whereas it increases with the measurement time in superdiffusive regime

ergodicity convergence test suggests telomere motion obeys fractional dynamics anomalous diffusion observed in many biological processes is a generalized description of a wide variety of processes all obeying the same law of mean square displacement identifying the basic mechanisms of these observations is important for deducing the nature of the biophysical systems measured we implement a previously suggested method for distinguishing between fractional langevin dynamics fractional brownian motion and continuous time random walk based on the ergodic nature of the data we apply the method together with the recently suggested p variation test and the displacement correlation to the lately measured dynamics of telomeres in the nucleus of mammalian cells and find strong evidence that the telomeres motion obeys fractional dynamics the ergodic dynamics are observed experimentally to fit fractional brownian or langevin dynamics

a unified approach for stochastic and mean square stability of continuous time linear systems with markovian jumping parameters and additive disturbances necessary and sufficient conditions for stochastic stability ss and mean square stability mss of continuous time linear systems subject to markovian jumps in the parameters and additive disturbances are established we consider two scenarios regarding the additive disturbances one in which the system is driven by a wiener process and one characterized by functions in l 2 m omega cal f mathbb p which is the usual scenario for the h infty approach the markov process is assumed to take values in an infinite countable set mathcal s it is shown that ss is equivalent to the spectrum of an augmented matrix lying in the open left half plane to the existence of a solution for a certain lyapunov equation and implies is equivalent for mathcal s finite asymptotic wide sense stationarity awss it is also shown that ss is equivalent to the state x t belonging to l 2 n omega cal f mathbb p whenever the disturbances are in l 2 m omega cal f mathbb p for the case in which mathcal s is finite ss and mss are equivalent and the lyapunov equation can be written down in two equivalent forms with each one providing an easier to check sufficient condition

stochastic stabilization of hybrid differential equations this paper aims to determine whether or not a stochastic state feedback control can stabilize a given linear or nonlinear hybrid system new methods are developed and sufficient conditions on the stability for hybrid stochastic differential equations are provided these results are then used to examine stochastic stabilization by stochastic feedback controls two types of structure controls namely state feedback and output injection are discussed our stabilization criteria are in terms of linear matrix inequalities lmis whence the feedback controls can be designed more easily in practice a couple of examples and computer simulations are worked out to illustrate our theory

on extended dissipativity of discrete time neural networks with time delay in this brief the problem of extended dissipativity analysis for discrete time neural networks with time varying delay is investigated the definition of extended dissipativity of discrete time neural networks is proposed which unifies several performance measures such as the h infty performance passivity l 2 l infty performance and dissipativity by introducing a triple summable term in lyapunov function the reciprocally convex approach is utilized to bound the forward difference of the triple summable term and then the extended dissipativity criterion for discrete time neural networks with time varying delay is established the derived condition guarantees not only the extended dissipativity but also the stability of the neural networks two numerical examples are given to demonstrate the reduced conservatism and effectiveness of the obtained results

finite horizon h_ 2 h_ infty control for discrete time stochastic systems with markovian jumps and multiplicative noise in this note we consider the finite horizon mixed h 2 h control problem for discrete time stochastic linear systems subject to markov jump parameters and multiplicative noise firstly we derive a stochastic bounded real lemma sbrl which is used to establish a necessary and sufficient condition for the existence of the mixed h 2 h control via the solvability of four coupled difference matrix valued recursions cdmrs moreover a state feedback h 2 h controller is designed by means of the solutions of cdmrs

infinite invariant density in a semi markov process with continuous state variables we report on a fundamental role of a non normalized formal steady state i e an infinite invariant density in a semi markov process where the state is determined by the interevent time of successive renewals the state describes certain observables found in models of anomalous diffusion e g the velocity in the generalized levy walk model and the energy of a particle in the trap model in our model the interevent time distribution follows a fat tailed distribution which makes the state value more likely to be zero because long interevent times imply small state values we find two scaling laws describing the density for the state value which accumulates in the vicinity of zero in the long time limit these laws provide universal behaviors in the accumulation process and give the exact expression of the infinite invariant density moreover we provide two distributional limit theorems for time averaged observables in these nonstationary processes we show that the infinite invariant density plays an important role in determining the distribution of time averages

exponential stabilization of a class of stochastic system with markovian jump parameters and mode dependent mixed time delays in this technical note the globally exponential stabilization problem is investigated for a general class of stochastic systems with both markovian jumping parameters and mixed time delays the mixed mode dependent time delays consist of both discrete and distributed delays we aim to design a memoryless state feedback controller such that the closed loop system is stochastically exponentially stable in the mean square sense first by introducing a new lyapunov krasovskii functional that accounts for the mode dependent mixed delays stochastic analysis is conducted in order to derive a criterion for the exponential stabilizability problem then a variation of such a criterion is developed to facilitate the controller design by using the linear matrix inequality lmi approach finally it is shown that the desired state feedback controller can be characterized explicitly in terms of the solution to a set of lmis numerical simulation is carried out to demonstrate the effectiveness of the proposed methods

subdiffusion in time averaged confined random walks certain techniques characterizing diffusive processes such as single particle tracking or molecular dynamics simulation provide time averages rather than ensemble averages whereas the ensemble averaged mean squared displacement msd of an unbounded continuous time random walk ctrw with a broad distribution of waiting times exhibits subdiffusion the time averaged msd delta2 does not we demonstrate that in contrast to the unbounded ctrw in which delta2 is linear in the lag time delta the time averaged msd of the ctrw of a walker confined to a finite volume is sublinear in delta i e for long lag times delta2 approximately delta1 alpha the present results permit the application of ctrw to interpret time averaged experimental quantities

on designing of sliding mode control for stochastic jump systems in this note we consider the problems of stochastic stability and sliding mode control for a class of linear continuous time systems with stochastic jumps in which the jumping parameters are modeled as a continuous time discrete state homogeneous markov process with right continuous trajectories taking values in a finite set by using linear matrix inequalities lmis approach sufficient conditions are proposed to guarantee the stochastic stability of the underlying system then a reaching motion controller is designed such that the resulting closed loop system can be driven onto the desired sliding surface in a limited time it has been shown that the sliding mode control problem for the markovian jump systems is solvable if a set of coupled lmis have solutions a numerical example is given to show the potential of the proposed techniques

weakly non ergodic statistical physics for weakly non ergodic systems the probability density function of a time average observable overline mathcal o is f alpha overline mathcal o 1 over pi lim epsilon to 0 mbox im sum j 1 l p mathrm eq j overline mathcal o mathcal o j i epsilon alpha 1 over sum j 1 l p mathrm eq j overline mathcal o mathcal o j i epsilon alpha where mathcal o j is the value of the observable when the system is in state j 1 l pjeq is the probability that a member of an ensemble of systems occupies state j in equilibrium for a particle undergoing a fractional diffusion process in a binding force field with thermal detailed balance conditions pjeq is boltzmann s canonical probability within the unbiased sub diffusive continuous time random walk model the exponent 0 1 is the anomalous diffusion exponent x2 t found for free boundary conditions when 1 ergodic statistical mechanics is recovered lim alpha to 1 f alpha overline mathcal o delta overline mathcal o langle mathcal o rangle we briefly discuss possible physical applications in single particle experiments

observer based synchronization in complex dynamical networks with nonsymmetric coupling abstract based on a general complex dynamical network model with nonsymmetric coupling some criteria for synchronization are proposed based on the approach of state observer design unlike the nonobserver based dynamical networks where the coupling between two connected nodes is defined by an inner coupling matrix and full state coupling is typically needed in this paper smaller amount of coupling variables or even only a scalar output signal of each node is needed to synchronize the network unlike the commonly researched complex network model where the coupling between nodes is symmetric here in our network model the coupling configuration matrix is not assumed to be symmetric and may have complex eigenvalues the matrix jordan canonical formalization method is used instead of the matrix diagonalization method so in our synchronization criteria the coupling configuration matrix is not required to be diagonalizable especially the proposed step by step approach is simpler in computation than the existent ones which usually rely heavily on numerical toolbox and may be done by hand completely an example is given to illustrate the step by step approach in which each node is a two dimensional dynamical limit cycle oscillator system consisting of a two cell cellular neural network and numerical simulations are also done to verify the results of design

passivity analysis and passification of discrete time hybrid systems for discrete time hybrid systems in piecewise affine or piece wise polynomial pwp form this note proposes sufficient passivity analysis and synthesis criteria based on the computation of piecewise quadratic or pwp storage functions by exploiting linear matrix inequality techniques and sum of squares decomposition methods passivity analysis and synthesis of passifying controllers can be carried out through standard semidefinite programming packages providing a tool particularly important for stability of interconnected heterogeneous dynamical systems

analytic approach to the problem of convergence of truncated levy flights towards the gaussian stochastic process an analytic expression for characteristic function defining a truncated l evy flight is derived it is shown that the characteristic function yields results in agreement with recent simulations of truncated l evy flights by mantegna and stanley phys rev lett 73 2946 1994 with the analytic expression for the characteristic function the convergence of the l evy process towards the gaussian is demonstrated without simulations in the calculation of first return probability the simulations are replaced by numerical integration using simple quadratures

markowitz s mean variance portfolio selection with regime switching from discrete time models to their continuous time limits we study a discrete time version of markowitz s mean variance portfolio selection problem where the market parameters depend on the market mode regime that jumps among a finite number of states the random regime switching is delineated by a finite state markov chain based on which a discrete time markov modulated portfolio selection model is presented such models either arise from multiperiod portfolio selections or result from numerical solution of continuous time problems the natural connections between discrete time models and their continuous time counterpart are revealed since the markov chain frequently has a large state space to reduce the complexity an aggregated process with smaller state space is introduced and the underlying portfolio selection is formulated as a two time scale problem we prove that the process of interest yields a switching diffusion limit using weak convergence methods next based on the optimal control of the limit process obtained from our recent work we devise portfolio selection strategies for the original problem and demonstrate their asymptotic optimality

infinite horizon h2 h control for discrete time time varying markov jump systems with multiplicative noise in this paper we consider the infinite horizon h 2 h control problem for discrete time time varying linear systems subject to markov jump parameters and state multiplicative noise a stochastic version of a bounded real lemma is firstly developed for a general class of discrete time time varying markov jump systems with state and disturbance multiplicative noise by which we present a necessary and sufficient condition for the solvability of the h 2 h control problem in terms of four coupled discrete time riccati equations moreover the obtained design is applied to a macroeconomic problem to verify its effectiveness

phase diagram in stored energy driven levy flight phase diagram based on the mean square displacement msd and the distribution of diffusion coefficients of the time averaged msd for the stored energy driven levy flight sedlf is presented in the sedlf a random walker cannot move while storing energy and it jumps by the stored energy the sedlf shows a whole spectrum of anomalous diffusions including subdiffusion and superdiffusion depending on the coupling parameter between storing time trapping time and stored energy this stochastic process can be investigated analytically with the aid of renewal theory here we consider two different renewal processes i e ordinary renewal process and equilibrium renewal process when the mean trapping time does not diverge we analytically show the phase diagram according to the coupling parameter and the power exponent in the trapping time distribution in particular we find that distributional behavior of time averaged msd intrinsically appears in superdiffusive as well as normal diffusive regime even when the mean trapping time does not diverge

dissipativity based asynchronous filtering for periodic markov jump systems abstract this paper is devoted to developing a periodic and asynchronous filter for periodic markov jump systems a periodic and asynchronous filter means that the filter parameters are s periodic for a given operating mode and its operating modes are unnecessary to be identical but form a periodic hidden markov model together with the modes of the plant a sufficient condition is proposed to guarantee that the filtering error system is exponentially mean square stable and strictly q s r dissipative to realize this filter a slack matrix is introduced to deal with the nonlinearity and finsler s lemma is applied such that the decision variables are reduced finally a numerical simulation provides verification for the effectiveness of our designed filter

bibo stabilization of feedback control systems with time dependent delays abstract this paper investigates the bounded input bounded output bibo stability in a class of control system of nonlinear differential equations with time delay the proofs are based on our studies on the boundedness of the solutions of a general class of nonlinear volterra integral equations

fractional feynman kac equation for weak ergodicity breaking the continuous time random walk ctrw is a model of anomalous subdiffusion in which particles are immobilized for random times between successive jumps a power law distribution of the waiting times 1 leads to subdiffusion x 2 t for 0 1 in closed systems the long stagnation periods cause time averages to divert from the corresponding ensemble averages which is a manifestation of weak ergodicity breaking the time average of a general observable u t 1 t 0 t u x d is a functional of the path and is described by the well known feynman kac equation if the motion is brownian here we derive forward and backward fractional feynman kac equations for functionals of ctrw in a binding potential we use our equations to study two specific time averages the fraction of time spent by a particle in half box and the time average of the particle s position in a harmonic field in both cases we obtain the probability density function of the time averages for t and the first two moments our results show that both the occupation fraction and the time averaged position are random variables even for long times except for 1 when they are identical to their ensemble averages using our fractional feynman kac equation we also study the dynamics leading to weak ergodicity breaking namely the convergence of the fluctuations to their asymptotic values

stability analysis of continuous time switched systems with a random switching signal this technical note is concerned with the stability analysis of continuous time switched systems with a random switching signal the switching signal manifests its characteristics with that the dwell time in each subsystem consists of a fixed part and a random part the stochastic stability of such switched systems is studied using a lyapunov approach a necessary and sufficient condition is established in terms of linear matrix inequalities the effect of the random switching signal on system stability is illustrated by a numerical example and the results coincide with our intuition

robust finite time stability and stabilization of uncertain markovian jump systems with time varying delay this paper deals with the robust finite time stability and stabilization problems of uncertain stochastic delayed jump systems where the uncertainty is in the form of additive perturbations and exists in the drift and diffusion sections simultaneously though perturbation time varying delay and brownian motion existing at the same time two conditions checking its robust finite time stability are proposed by a mode dependent parameter approach which are different from some existing methods based on the proposed results sufficient conditions for the existence of the state feedback controller are provided with lmis which could be solved directly it is seen that all the features of the underlying system such as time varying delay perturbation diffusion mode dependent parameters and uncertain transition rate matrix play important roles in the system analysis and synthesis of finite time stability finally numerical examples are used to demonstrate the effectiveness and superiority of the proposed methods

on exponential almost sure stability of random jump systems this paper is concerned with a class of random jump systems represented by transition operators which includes switched linear systems with strictly stationary switching signals in infinite modes space as its special case a series of necessary and sufficient conditions are established for almost sure stability of this class of random jump systems under different scenarios the stability criteria obtained are further extended to markov jump linear systems with infinite states and hence a unified approach to describing the almost sure stability of mjlss is addressed under this context all the results in the work are developed for both the continuous and discrete time systems

distributional behavior of time averages of non l 1 observables in one dimensional intermittent maps with infinite invariant measures in infinite ergodic theory two distributional limit theorems are well known one is characterized by the mittag leffler distribution for time averages of l 1 m functions i e integrable functions with respect to an infinite invariant measure the other is characterized by the generalized arc sine distribution for time averages of non l 1 m functions here we provide another distributional behavior of time averages of non l 1 m functions in one dimensional intermittent maps where each has an indifferent fixed point and an infinite invariant measure observation functions considered here are non l 1 m functions which vanish at the indifferent fixed point we call this class of observation functions weak non l 1 m function our main result represents a first step toward a third distributional limit theorem i e a distributional limit theorem for this class of observables in infinite ergodic theory to prove our proposition we propose a stochastic process induced by a renewal process to mimic a birkoff sum of a weak non l 1 m function in the one dimensional intermittent maps

fractional fokker planck equation with tempered α stable waiting times langevin picture and computer simulation in this paper we introduce a langevin type model of subdiffusion with tempered stable waiting times we consider the case of space dependent external force fields the model displays subdiffusive behavior for small times and it converges to standard gaussian diffusion for large time scales we derive general properties of tempered anomalous diffusion from the theory of tempered stable processes in particular we find the form of the fractional fokker planck equation corresponding to the tempered subdiffusion we also construct an algorithm of simulation of sample paths of the introduced process we apply the algorithm to approximate solutions of the fractional fokker planck equation and to study statistical properties of the tempered subdiffusion via monte carlo methods

coupled continuous time random walks in finance continuous time random walks ctrws are used in physics to model anomalous diffusion by incorporating a random waiting time between particle jumps in finance the particle jumps are log returns and the waiting times measure delay between transactions these two random variables log return and waiting time are typically not independent for these coupled ctrw models we can now compute the limiting stochastic process just like brownian motion is the limit of a simple random walk even in the case of heavy tailed power law price jumps and or waiting times the probability density functions for this limit process solve fractional partial differential equations in some cases these equations can be explicitly solved to yield descriptions of long term price changes based on a high resolution model of individual trades that includes the statistical dependence between waiting times and the subsequent log returns in the heavy tailed case this involves operator stable space time random vectors that generalize the familiar stable models in this paper we will review the fundamental theory and present two applications with tick by tick stock and futures data

adaptive tracking for stochastic nonlinear systems with markovian switching the problem of the adaptive tracking for a class of stochastic nonlinear systems with stationary markovian switching is considered in this note an ito formula is proposed for stochastic integral equations with an integral about martingale measure an adaptive backstepping controller is designed such that the closed loop system has a unique solution that is globally bounded in probability and l4 norm of the tracking error converges to an arbitrarily small neighborhood of zero a simulation example demonstrates the efficiency of the proposed scheme

nonergodic property of the space time coupled ctrw dependence on the long tailed property and correlation abstract the space time coupled continuous time random walk model is a stochastic framework of anomalous diffusion with many applications in physics geology and biology in this manuscript the time averaged mean squared displacement and nonergodic property of a space time coupled continuous time random walk model is studied which is a prototype of the coupled continuous time random walk presented and researched intensively with various methods the results in the present manuscript show that the time averaged mean squared displacements increase linearly with lag time which means ergodicity breaking occurs besides we find that the diffusion coefficient is intrinsically random which shows both aging and enhancement the analysis indicates that the either aging or enhancement phenomena are determined by the competition between the correlation exponent and the waiting time s long tailed index

anomalous diffusion testing ergodicity breaking in experimental data recent advances in single molecule experiments show that various complex systems display nonergodic behavior in this paper we show how to test ergodicity and ergodicity breaking in experimental data exploiting the so called dynamical functional we introduce a simple test which allows us to verify ergodic properties of a real life process the test can be applied to a large family of stationary infinitely divisible processes we check the performance of the test for various simulated processes and apply it to experimental data describing the motion of mrna molecules inside live escherichia coli cells we show that the data satisfy necessary conditions for mixing and ergodicity the detailed analysis is presented in the supplementary material

ultraslow convergence to ergodicity in transient subdiffusion we investigate continuous time random walks with truncated ensuremath alpha stable trapping times we prove distributional ergodicity for a class of observables namely the time averaged observables follow the probability density function called the mittag leffler distribution this distributional ergodic behavior persists for a long time and thus the convergence to the ordinary ergodicity is considerably slower than in the case in which the trapping time distribution is given by common distributions we also find a crossover from the distributional ergodic behavior to the ordinary ergodic behavior

langevin picture of levy walks and their extensions in this paper we derive langevin picture of levy walks applying recent advances in the theory of coupled continuous time random walks we find a limiting process of the properly scaled levy walk next we introduce extensions of levy walks in which jump sizes are some functions of waiting times we prove that under proper scaling conditions such generalized levy walks converge in distribution to the appropriate limiting processes we also derive the corresponding fractional diffusion equations and investigate behavior of the mean square displacements of the limiting processes showing that different coupling functions lead to various types of anomalous diffusion

generalized arcsine law and stable law in an infinite measure dynamical system limit theorems for the time average of some observation functions in an infinite measure dynamical system are studied it is known that intermittent phenomena such as the rayleigh benard convection and belousov zhabotinsky reaction are described by infinite measure dynamical systems we show that the time average of the observation function which is not the l 1 m function whose average with respect to the invariant measure m is finite converges to the generalized arcsine distribution this result leads to the novel view that the correlation function is intrinsically random and does not decay moreover it is also numerically shown that the time average of the observation function converges to the stable distribution when the observation function has the infinite mean

state estimation for asynchronous sensor systems with markov jumps and multiplicative noises abstract this paper is concerned with the asynchronous state estimation problem for sensor systems subject to markov jump parameters and multiplicative noises the asynchronous sensors considered can have arbitrary sampling rates and arbitrary initial sampling instants by transforming the asynchronous measurements within each fusion interval into an augmented measurement the equivalent measurement equation and state equation at the fusion time instant are constructed based on the two equations a linear minimum mean squared error lmmse estimator is developed using the orthogonality projection principle due to the existence of the common process noise in the equivalent process and measurement noises the equivalent process and measurement noises are cross correlated and the equivalent measurement noises are autocorrelated these correlations are taken into account in the estimator design the stationary case is also studied and the sufficient condition is established for the stability of the proposed estimator a target tracking example is provided to illustrate the effectiveness of the proposed estimator

on stability and lq control of mjls with a markov chain with general state space we study the mean square stability and the lq control of discrete time markov jump linear systems where the markov chain has a general state space the mean square stability is characterized by the spectral radius of an operator describing the evolution of the second moment of the state vector two equivalent tests for the mean square stability are obtained based on the existence of a positive definite solution to a lyapunov equation and a uniformity result respectively an algorithm for testing the mean square stability is also developed based on the uniformity result the finite and infinite horizon lq problems are considered and their solutions are characterized by appropriate riccati integral equations an application to networked control systems ncs is finally presented and a simple example is studied via simulation

random walks with infinite spatial and temporal moments the continuous time random walk of montroll and weiss has been modified by scher and lax to include a coupled spatial temporal memory we treat novel cases for the random walk and the corresponding generalized master equation when combinations of both spatial and temporal moments of the memory are infinite the asymptotic properties of the probability distribution for being at any lattice site as a function of time and its variance are calculated the resulting behavior includes localized diffusive wavelike and levy s stable laws for the appropriate scaled variable we show that an infinite mean waiting time can lead to long time diffusive behavior while a finite mean waiting time is not sufficient to ensure the same

power spectra and random walks in intermittent chaotic systems abstract we investigate anomalous diffusion and the corresponding power spectra generated by iterated maps and analyze the motion in terms of the probabilistic continous time random walk approach both stationary and non stationary conditions are considered demonstrating the dependence of the mean squared displacement and of the power spectra on the initial conditions the theoretical results are corroborated by numerical calculations and excellent and agreement is obtained

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

dissipativity analysis and design for uncertain markovian jump systems with time varying delays this paper deals with the problems of dissipativity analysis and dissipativity based controller design for markovian jump systems with both time varying delays and norm bounded parametric uncertainties improved delay dependent conditions for the system concerned to be strictly dissipative are established by using a mode dependent lyapunov krasovskii functional and introducing some slack variables these conditions are expressed by means of linear matrix inequalities lmis which are easy to check it is also shown that these conditions are less conservative than those obtained by using the existing methods the dissipativity synthesis problem is considered and on the basis of the obtained dissipativity conditions both the state feedback and dynamic output feedback controllers are designed to guarantee the strict dissipativity of the closed loop systems numerical examples are provided to demonstrate the utility of the developed methods

efficient parallel algorithms for a class of graph theoretic problems in this paper we present efficient parallel algorithms for the following graph problems finding the lowest common ancestors for vertex pairs of a directed tree finding all fundamental cycles a directed spanning forest all bridges all bridge connected components all separation vertices all biconnected components and testing the biconnectivity of an undirected graph all these algorithms achieve the o lg 2 n time bound with the first two algorithms using n lceil n lg n rceil processors and the remaining algorithms using n lceil n lg 2 n rceil processors in all cases our algorithms are better than the previously known algorithms and in most cases reduce the number of processors used by a factor of n lg n moreover our algorithms are optimal with respect to the time processor product for dense graphs with the exception of the first two algorithms the machine model we use is the pram which is a simd model allowing simultaneous reads but not simultaneous writes to the same memory

optimal graph algorithms on a fixed size linear array parallel algorithms for computing the minimum spanning tree of a weighted undirected graph and the bridges and articulation points of an undirected graphs on a fixed size linear array of processors are presented for a graph of n vertices the algorithms operate on a linear array of p processors and require o n2 p time for all p 1 p n in particular using n processors the algorithms require o n time which is optimal on this model the paper describes two approaches to limit the communication requirements for solving the problems the first is a divide and conquer strategy applied to sollin s algorithm for finding the minimum spanning tree of a graph the second uses a novel data reduction technique that constructs an auxiliary graph with no more than 2n 2 edges whose bridges and articulation points are the bridges and articulation points of the original graph

generalized h2 fault detection for two dimensional markovian jump systems this paper is concerned with the generalized h 2 fault detection for two dimensional 2 d discrete time markovian jump systems the mathematical model of the 2 d system is established upon the well known roesser model and the measurement missing phenomenon which appears typically in a network environment is modeled by a stochastic variable satisfying the bernoulli random binary distribution in addition the transition probabilities of the markovian jump process are assumed to be partly accessed that is the transition probabilities are partly known our attention is focused on the design of a fault detection filter or a residual generation system which guarantees the fault detection system to be mean square asymptotically stable and to have a prescribed generalized h 2 performance sufficient conditions for the existence of a desired fault detection filter are established in terms of linear matrix inequalities lmis a numerical example is provided to illustrate the effectiveness of the proposed design method

continuous time random walk with jump length correlated with waiting time abstract a coupled continuous time random walk ctrw model is proposed in which the jump length of a walker is correlated with waiting time the power law distribution is chosen as the probability density function of waiting time and the gaussian like distribution as the probability density function of jump length normal diffusion subdiffusion and superdiffusion can be realized within the present model it is shown that the competition between long tailed distribution and correlation of jump length and waiting time will lead to different diffusive behavior

stochastic stability of jump discrete time linear systems with markov chain in a general borel space necessary and sufficient conditions for stochastic stability ss of discrete time linear systems subject to markov jumps in the parameters are considered assuming that the markov chain takes values in a general borel space s it is shown that ss is equivalent to the spectrum radius of a bounded linear operator in a banach space being less than 1 or to the existence of a solution of a lyapunov type equation these results generalize several previous results in the literature which considered only the case of the markov chain taking values in a finite or infinite countable space

exponential stability for discrete time infinite markov jump systems this technical note addresses a class of discrete time stochastic systems with infinite markov jump parameter first of all spectral criterion and lyapunov type criteria are presented for the exponential stability of considered systems further under the condition of strong detectability a barbashin krasovskii stability theorem is shown in terms of a generalized lyapunov equation with a positive semi definite term as an application of the proposed lyapunov stability criterion a sufficient condition of ell 2 input state stability is derived for the infinite markov jump systems disturbed by finite energy random disturbance

distributional response to biases in deterministic superdiffusion we report on a novel response to biases in deterministic superdiffusion for its reduced map we show using infinite ergodic theory that the time averaged velocity tav is intrinsically random and its distribution obeys the generalized arcsine distribution a distributional limit theorem indicates that the tav response to a bias appears in the distribution which is an example of what we term a distributional response induced by a bias although this response in single trajectories is intrinsically random the ensemble averaged tav response is linear

stabilization of stochastic delay systems via a disordered controller abstract in this paper the stabilization for stochastic delay systems is achieved by a disordered controller different from the traditionally stabilizing controllers the controller designed here experiences a disorder between control gains and system states by exploiting the robust method the above disorder is described as a controller having special uncertainties moreover the probability distribution of such uncertainties is embodied by a bernoulli variable a sufficient condition for the existence of such a disordered controller is given with lmis where the probability is considered in its design procedure based on this description a more general but complicated case where the corresponding probability is not exact but has a uncertainty is further studied whose lmi conditions are presented too finally a numerical example is exploited to demonstrate the effectiveness and superiority of the proposed methods