aging of asymmetric dynamics on the random energy model we show aging of glauber type dynamics on the random energy model in the sense that we obtain the annealed scaling limits of the clock process and of the age process the latter encodes the gibbs weight of the configuration occupied by the dynamics both limits are expressed in terms of stable subordinators

exponential stability of impulsive systems with application to uncertain sampled data systems we establish exponential stability of nonlinear time varying impulsive systems by employing lyapunov functions with discontinuity at the impulse times our stability conditions have the property that when specialized to linear impulsive systems the stability tests can be formulated as linear matrix inequalities lmis then we consider lti uncertain sampled data systems in which there are two sources of uncertainty the values of the process parameters can be unknown while satisfying a polytopic condition and the sampling intervals can be uncertain and variable we model such systems as linear impulsive systems and we apply our theorem to the analysis and state feedback stabilization we find a positive constant which determines an upper bound on the sampling intervals for which the stability of the closed loop is guaranteed the control design lmis also provide controller gains that can be used to stabilize the process we also consider sampled data systems with constant sampling intervals and provide results that are less conservative than the ones obtained for variable sampling intervals

stabilization of boolean control networks under aperiodic sampled data control a novel technique is provided for the global stability analysis of boolean control networks bcns under aperiodic sampled data control asdc the sampling period is allowed to be taken from a lim

brief paper fault tolerant control for singular systems with actuator saturation and nonlinear perturbation in this paper the problem of robust fault tolerant control for a class of singular systems subject to both time varying state dependent nonlinear perturbation and actuator saturation is investigated a sufficient condition for the existence of a fixed gain controller is first proposed which guarantees the regularity impulse free and stability of the closed loop system under all possible faults an optimization problem with lmi constraints is formulated to determine the largest contractively invariant ellipsoid an adaptive fault tolerant controller is then developed to compensate for the failure effects on the system by estimating the fault and updating the design parameter matrices online both of these two controllers are in the form of a saturation avoidance feedback with the advantage of relatively small actuator capacities compared with the high gain counterpart an example is included to illustrate the proposed procedures and their effectiveness

adaptive reliable h_ infty filtering against sensor failures this paper is concerned with the adaptive reliable hinfin filtering problem against sensor failures for continuous time linear systems an adaptive hinfin performance index is defined to describe the disturbance attenuation performance of systems with time varying parameter estimations by combining the linear matrix inequality lmi approach for hinfin filter design and adaptive method a method of designing adaptive reliable hinfin filters is proposed where the filter parameter matrices are updated automatically to compensate the sensor failures effects on systems based on the online estimations of eventual faults it is shown that the design condition for the newly proposed adaptive hinfin filtering is more relaxed than that for the traditional fixed gain filter design based on lmi approach an illustrative example and its simulation results are given to illustrate the effectiveness of the proposed design method

an improved input delay approach to stabilization of fuzzy systems under variable sampling in this paper we investigate the problem of stabilization for sampled data fuzzy systems under variable sampling a novel lyapunov krasovskii functional lkf is defined to capture the characteristic of sampled data systems and an improved input delay approach is proposed by the use of an appropriate enlargement scheme new stability and stabilization criteria are obtained in terms of linear matrix inequalities lmis compared with the existing results the newly obtained ones contain less conservatism some illustrative examples are given to show the effectiveness of the proposed method and the significant improvement on the existing results

fuzzy model based quantized guaranteed cost control of nonlinear networked systems this paper is concerned with the problem of guaranteed cost control for a class of continuous time networked control systems based on the takagi sugeno fuzzy model approach in this study network induced transmission delays and packet dropouts are taken into simultaneous consideration by the improved lyapunov krasovskii functionals a less conservative delay dependent condition is proposed for the stability analysis of the resulting closed loop system furthermore the sufficient condition under which the guaranteed cost controller exists is formulated in terms of linear matrix inequalities and the suboptimum solution is obtained by a cone complementarity linearization algorithm finally numerical examples are provided to illustrate the effectiveness of the proposed method

h sub infinity control and quadratic stabilization of systems with parameter uncertainty via output feedback the article concerns linear systems which are subject to both time varying norm bounded parameter uncertainty and exogenous disturbance it addresses the robust h sub infinity control problem of designing a linear dynamic output feedback controller such that the closed loop system is quadratically stable and achieves a prescribed level of disturbance attenuation for all admissible parameter uncertainties it is shown that such a problem is equivalent to a scaled h sub infinity control problem

on the dynamics of trap models in z d we consider trap models in z d these are stochastic processes in a random environ ment as follows the environment is given by a family x x 2 z d of positive iid random variables in the basin of attraction of an stable law 0 1 given our process is a continuous time markov pure jump process whose jump chain is a in principle generic random walk in z d d 1 independent of andrepresents the holding time averages of the continuous time process we may think of the sites of z d as traps and ofx as the depth of trap x we are interested in the trap process namely the process that associates to time t the depth of the currently visited trap our first result is the convergence of the law of that process under a suitable scaling the limit process is given by the jumps of a certain stable subordinator at the inverse of another stable subor dinator correlated with the first subordinator for that result the requirements on the underlying random walk are a the validity of a law of large numbers for its range and b the slow variation at infinity of the tail of the distribution of its time of return to the origin this includes all transient random walks as well as all random walks in d 2 and also many one dimensional random walks we then derive aging results for our process namely scaling limits for some two time correlation functions of the process the scaling limit result mentioned above is an integrated result with respect to the environment un der an additional condition on the size of the intersection of the ranges of two independent copies of the underlying random walk roughly saying that it is relatively small compared with the range we derive a stronger scaling limit result roughly stating that it holds in probability with respect to the environment with that additional condition we also strengthen the aging results from the integrated version mentioned above to convergence in probability with respect to the environment

the arcsine law as a universal aging scheme for trap models we give a general proof of aging for trap models using the arcsine law for stable subordinators this proof is based on abstract conditions on the potential theory of the underlying graph and on the randomness of the trapping landscape we apply this proof to aging for trap models on large two dimensional tori and for trap dynamics of the random energy model on a broad range of time scales c 2006 wiley periodicals inc

a presentation for the virasoro and super virasoro algebras it is shown that the entire virasoro ramond and neveu schwarz algebras can each be constructed from a finite number of well chosen generators satisfying a small number of conditions the most economical sets consist of just two starting generators in all cases subject to eight conditions for the virasoro case five conditions for the ramond case and nine conditions for the neveu schwarz case

further results on stabilization of chaotic systems based on fuzzy memory sampled data control this note investigates sampled data control for chaotic systems a memory sampled data control scheme that involves a constant signal transmission delay is employed for the first time to tackle the stabilization problem for takagi sugeno fuzzy systems the advantage of the constructed lyapunov functional lies in the fact that it is neither necessarily positive on sampling intervals nor necessarily continuous at sampling instants by introducing a modified lyapunov functional that involves the state of a constant signal transmission delay a delay dependent stability criterion is derived so that the closed loop system is asymptotically stable the desired sampled data controller can be achieved by solving a set of linear matrix inequalities compared with the existing results a larger sampling period is obtained by this new approach a simulation example is presented to illustrate the effectiveness and conservatism reduction of the proposed scheme

a robust h observer based controller design for uncertain t s fuzzy systems with unknown premise variables via lmi this paper addresses the problem of robust h fuzzy observer based controller design for the takagi sugeno t s fuzzy systems with unmeasurable premise variables the proposed design method considers uncertainty for such a problem for the first time using some linear transformations for the output matrices of each local model of the t s fuzzy system and employing finsler s lemma the robust stability conditions in the form of linear matrix inequalities lmis are derived two numerical simulations are provided to show the validity of the proposed method

technical communique reliable h control for discrete time piecewise linear systems with infinite distributed delays in this paper the reliable h control problem is investigated for discrete time piecewise linear systems with time delays and actuator failures the time delays are assumed to be infinitely distributed in the discrete time domain and the possible failure of each actuator is described by a variable varying in a given interval the aim of the addressed reliable h control problem is to design a controller such that for the admissible infinite distributed delays and possible actuator failures the closed loop system is exponentially stable with a given disturbance attenuation level c the controller gain is characterized in terms of the solution to a linear matrix inequality that can be easily solved by using standard software packages a simulation example is exploited in order to illustrate the effectiveness of the proposed design procedures

fluctuations of the free energy in the rem and the p spin sk models we consider the random fluctuations of the free energy in the p spin version of the sherrington kirkpatrick sk model in the high temperature regime using the martingale approach of comets and neveu as used in the standard sk model combined with truncation techniques inspired by a recent paper by talagrand on the p spin version we prove that the random corrections to the free energy are on a scale n p 2 2 only and after proper rescaling converge to a standard gaussian random variable this is shown to hold for all values of the inverse temperature smaller than a critical p we also show that p 2 in 2 as p additionally we study the formal p limit of these models the random energy model here we compute the precise limit theorem for the properly rescaled partition function at all temperatures for 2 in 2 fluctuations are found at an exponentially small scale with two distinct limit laws above and below a second critical value in 2 2 for up to that value the rescaled fluctuations are gaussian while below that there are non gaussian fluctuations driven by the poisson process of the extreme values of the random energies for larger than the critical 2 in 2 the fluctuations of the logarithm of the partition function are on a scale of 1 and are expressed in terms of the poisson process of extremes at the critical temperature the partition function divided by its expectation converges to 1 2

universality of the rem for dynamics of mean field spin glasses we consider a version of glauber dynamics for a p spin sherrington kirkpatrick model of a spin glass that can be seen as a time change of simple random walk on the n dimensional hypercube we show that for all p 3 and all inverse temperatures 0 there exists a constant p 0 such that for all exponential time scales exp n with p the properly rescaled clock process time change process converges to an stable subordinator where 2 1 moreover the dynamics exhibits aging at these time scales with a time time correlation function converging to the arcsine law of this stable subordinator in other words up to rescaling on these time scales that are shorter than the equilibration time of the system the dynamics of p spin models ages in the same way as the rem and by extension bouchaud s rem like trap model confirming the latter as a universal aging mechanism for a wide range of systems the sk model the case p 2 seems to belong to a different universality class

sampled data fuzzy control of chaotic systems based on a t s fuzzy model in this paper a sampled data fuzzy controller is designed to stabilize a class of chaotic systems a takagi sugeno t s fuzzy model is employed to represent the chaotic systems based on this general model the exponential stability issue of the closed loop systems with an input constraint is first investigated by a novel time dependent lyapunov functional which is positive definite at sampling times but not necessary between the sampling times then two sufficient conditions are developed for sampled data fuzzy controller synthesis of the underlying t s fuzzy model with or without input constraint all the proposed results in this paper depend on both the upper and lower bounds on a sampling interval and the available information about the actual sampling pattern is fully utilized the proposed sampled data fuzzy control scheme is successfully applied to the chaotic lorenz system which is shown to be effective and less conservative compared with existing results

metastability and low lying spectra in reversible markov chains we study a large class of reversible markov chains with discrete state space and transition matrix pn we define the notion of a set of metastable points as a subset of the state space n such that i this set is reached from any point x n without return to x with probability at least bn while ii for any two points x y in the metastable set the probability t 1x y to reach y from x without return to x is smaller than an 1 bn under some additional non degeneracy assumption we show that in such a situation

universality and extremal aging for dynamics of spin glasses on subexponential time scales we consider random hopping time rht dynamics of the sherrington kirkpatrick sk model and p spin models of spin glasses for any of these models and for any inverse temperature 0 we prove that on time scales that are subexponential in the dimension the properly scaled clock process time change process of the dynamics converges to an extremal process moreover on these time scales the system exhibits aging like behavior which we call extremal aging in other words the dynamics of these models ages as the random energy model rem does hence by extension this confirms bouchaud s rem like trap model as a universal aging mechanism for a wide range of systems that for the first time includes the sk model 2011 wiley periodicals inc

glauber dynamics of the random energy model i metastable motion on the extreme states we investigate the long time behavior of the glauber dynamics for the random energy model below the critical temperature we give very precise estimates on the motion of the process to and between the states of extremal energies we show that when disregarding time the consecutive steps of the process on these states are governed by a markov chain that jumps uniformly on all possible states the mean times of these jumps are also computed very precisely and are seen to be asymptotically independent of the terminal point a first indicator of aging is the observation that the mean time of arrival in the set of states that have waiting times of order t is itself of order t the estimates proven in this paper will furnish crucial input for a follow up paper where aging is analysed in full detail

a novel approach to stability and stabilization of fuzzy sampled data markovian chaotic systems abstract this paper studies the problems of stability and stabilization of a class of markovian chaotic systems via fuzzy sampled data control different from some existing results the markovian jumping with general uncertain transition rates is considered for such systems a novel approach i e input delay dependent vector approach is proposed for the first time based on this approach an input delay dependent lyapunov krasovskii functional lkf with cubic function of input delay is successfully constructed and the convex combination technique is used with ease to derive stability and stabilization criteria compared with some existing stability and stabilization criteria for chaotic systems our results are not only less conservative but also with reduced calculation complexity finally the superiorities of proposed results are illustrated by two numerical examples

aging in two dimensional bouchaud s model let e x be a collection of i i d exponential random variables symmetric bouchaud s model on 2 is a markov chain x t whose transition rates are given by w xy exp e x if x y are neighbours in 2 we study the behaviour of two correlation functions x t w t x t w and x t x t w t t w t w t we prove the sub aging behaviour of these functions when 1

brief paper stability and stabilization of aperiodic sampled data control systems using robust linear matrix inequalities stability analysis of an aperiodic sampled data control system is considered for application to networked and embedded control the stability condition is described in a linear matrix inequality to be satisfied for all possible sampling intervals although this condition is numerically intractable a tractable sufficient condition can be constructed with the mean value theorem special attention is paid to tightness of the sufficient condition for less conservative stability analysis a region dividing technique for the reduction of conservatism and generalization to stabilization are also discussed an example demonstrates the efficacy of the approach

aging of spherical spin glasses sompolinski and zippelius 1981 propose the study of dynamical systems whose invariant measures are the gibbs measures for hard to analyze statistical physics models of interest in the course of doing so physicists often report of an aging phenomenon for example aging is expected to happen for the sherrington kirkpatrick model a disordered mean field model with a very complex phase transition in equilibrium at low temperature we shall study the langevin dynamics for a simplified spherical version of this model the induced rotational symmetry of the spherical model reduces the dynamics in question to an n dimensional coupled system of ornstein uhlenbeck processes whose random drift parameters are the eigenvalues of certain random matrices we obtain the limiting dynamics for n approaching infinity and by analyzing its long time behavior explain what is aging mathematically speaking what causes this phenomenon and what is its relationship with the phase transition of the corresponding equilibrium invariant measures

microscopic realizations of the trap model monte carlo optimizations of number partitioning and of diophantine approximations are microscopic realizations of trap model dynamics this offers a fresh look at the physics behind this model and points at other situations in which it may apply our results strongly suggest that in any such realization of the trap model the response and correlation functions of smooth observables obey the fluctuation dissipation theorem even in the aging regime our discussion of the number partitioning problem may be relevant for the class of optimization problems whose cost function does not scale linearly with the size and are thus awkward from the statistical mechanic point of view

an improved result on exponential stabilization of sampled data fuzzy systems this brief paper studies the exponential stabilization problem for the takagi sugeno fuzzy systems with a variable sampling different from previous results the gains of fuzzy state feedback controller adopted in this paper are time varying during two consecutive sampling instants which can contribute to the enlargement of the allowable sampling interval by choosing a suitable design parameter to reduce the design conservativeness a novel fuzzy time dependent lyapunov functional ftdlf is put forward to fully exploit the accessible information about the sampling pattern and the fuzzy basis functions moreover a more relaxed constraint condition is presented to ensure the positive definiteness of the ftdlf on sampling intervals by resorting to the novel ftdlf and the relaxed constraint condition new exponential stabilization criteria dependent on and independent of upper bounds on time derivatives of fuzzy basis functions are established by which a larger sampling interval can be achieved one example is offered to demonstrate the validity and superiorities of the obtained new results

control of switched nonlinear systems via t s fuzzy modeling this paper is concerned with the control problem for a class of switched nonlinear systems possibly composed of all unstable modes by using time controlled switching signals to tackle the problem a new mode dependent average dwell time mdadt switching property is proposed which is different from the existing one in the literature then the stabilization condition under such mdadt switching signals is established for the switched nonlinear systems with possibly all unstable subsystems by proposing a class of time scheduled multiple quadratic lyapunov function and applying t s fuzzy models to represent the underlying nonlinear subsystems numerically easily verified stabilization conditions are further derived in the form of linear matrix inequalities a numerical example is finally provided to illustrate the effectiveness of the obtained theoretical results

stabilization of chaotic systems under variable sampling and state quantized controller abstract this paper investigates the problem of stabilization for chaotic systems based on a t s fuzzy model under sampled data control and state quantization a novel lyapunov krasovskii functional lkf is introduced to the sampled data systems the benefit of the new approach is that the lkf develops more information about the actual sampling pattern in addition some symmetric matrices involved in the lkf are not required to be positive definite based on a recently introduced wirtinger based integral inequality that has been shown to be less conservative than jensen s inequality much less conservative stabilization conditions are obtained to ensure the maximal sampling period then the corresponding sampled data controllers can be synthesized by solving a set of linear matrix inequalities lmis finally an illustrative example is given to show the feasibility and effectiveness of the proposed method

aging of the metropolis dynamics on the random energy model we study the metropolis dynamics of the simplest mean field spin glass model the random energy model we show that this dynamics exhibits aging by showing that the properly rescaled time change process between the metropolis dynamics and a suitably chosen fast markov chain converges in distribution to a stable subordinator the rescaling might depend on the realization of the environment but we show that its exponential growth rate is deterministic

metastability in stochastic dynamics of disordered mean field models we study a class of markov chains that describe reversible stochastic dynamics of a large class of disordered mean field models at low temperatures our main purpose is to give a precise relation between the metastable time scales in the problem to the properties of the rate functions of the corresponding gibbs measures we derive the analog of the wentzell freidlin theory in this case showing that any transition can be decomposed with probability exponentially close to one into a deterministic sequence of admissible transitions for these admissible transitions we give upper and lower bounds on the expected transition times that differ only by a constant factor the distributions of the rescaled transition times are shown to converge to the exponential distribution we exemplify our results in the context of the random field curie weiss model

a new approach to stability and stabilization analysis for continuous time takagi sugeno fuzzy systems with time delay till now there are lots of stability and stabilization results about takagi sugeno t s fuzzy systems with time delay but most of them are independent of the analysis of membership functions since the membership functions are an essential component to make a fuzzy system different from others the conditions without its information are conservative in this brief paper a new lyapunov krasovskii functional is designed to investigate the stability and stabilization of continuous time t s fuzzy systems with time delay different from the existing results in the literature the integrand of the lyapunov krasovskii functional in this paper depends not only on the integral variable but also on the membership functions and thus the information of the time derivative of membership functions can also be used to reduce the conservativeness of finding the maximum delay bounds utilizing the information of the time derivative of membership a number of controllers are designed according to their sign and then a switching idea is applied to stabilize the fuzzy system in the end two examples are given to illustrate the feasibility and validity of the design and analysis

glauber dynamics of the random energy model ii aging below the critical temperature we investigate the long time behavior of the glauber dynamics for the ran dom energy model below the critical temperature we establish that for a suitably chosen timescale that diverges with the size of the system one can prove that a natural auto correlation function exhibits aging moreover we show that the long time asymptotics of this function coincide with those of the so called rem like trap model proposed by bouchaud and dean our results rely on very precise estimates on the distribution of transition times of the process between different states of extremely low energy

brief paper a novel stability analysis of linear systems under asynchronous samplings this article proposes a novel approach to assess the stability of continuous linear systems with sampled data inputs the method which is based on the discrete time lyapunov theorem provides easy tractable stability conditions for the continuous time model sufficient conditions for asymptotic and exponential stability are provided dealing with synchronous and asynchronous samplings and uncertain systems an additional stability analysis is provided for the cases of multiple sampling periods and packet losses several examples show the efficiency of the method

h stabilization criterion with less complexity for nonuniform sampling fuzzy systems abstract this paper investigates the problem of h stabilization for nonuniform sampling fuzzy systems a method to design a fuzzy controller is proposed by taking the variation ranges of membership functions within sampling intervals into consideration to reduce the computational complexity jensen s integral inequality method is employed based on a well known inequality a convex combination technique is developed to deal with nonlinear time varying coefficients derived from jensen s integral inequality combining with capturing the characteristic of sampled data systems with a novel piecewise lyapunov krasovskii functional lkf a less complex and less conservative h stabilization criterion is formulated as linear matrix inequalities lmis which can be easily checked by using standard numerical software some illustrative examples are given to show the effectiveness of the proposed method and the significant improvement on the existing results

improved criteria for the stabilization of t s fuzzy systems with actuator failures via a sampled data fuzzy controller abstract this paper studies a problem of the sampled data stabilization for takagi sugeno fuzzy systems with actuator failures an improved lyapunov functional is constructed which is dependent on the fuzzy membership functions fmfs and includes the sampling states with two sampling instants a new integral term including the fmfs is introduced into this lyapunov functional for the first time each term in this lyapunov functional need not be positive but it should be positive at sampling instants the variation range of the fmfs is taken into account in dealing with the derivative of this lyapunov functional as well then improved stabilization criteria guaranteeing a larger sampling interval are obtained by applying the developed fuzzy controller simulation examples are given to illustrate the effectiveness and less conservatism of the proposed method

fault detection for t s fuzzy systems with past output measurements abstract this paper is concerned with the fault detection fd filter design problem for the discrete time nonlinear systems with past output measurements and sensor saturation the considered discrete time nonlinear systems are described by t s fuzzy models a decomposition method is used to deal with the characteristics of sensor saturation a new fd filter with past output measurements is firstly proposed by using the lyapunov functional method subsequently the design conditions are given in terms of convex problems constrained by linear matrix inequalities lmi moreover it is shown that the fd filter with past output measurements can achieve better fd performances than the existing ones with current output measurements finally some simulation results are given to illustrate the advantages of the proposed design method

the behaviour of aging functions in one dimensional bouchaud s trap model let i be a collection of i i d positive random variables with distribution in the domain of attraction of an stable law with 1 the symmetric bouchaud s trap model on is a markov chain x t whose transition rates are given by w xy 2 x 1 if x y are neighbours in we study the behaviour of two correlation functions x t w t x t w and open image in new window it is well known that for any of these correlation functions a time scale t f t w such that aging occurs can be found we study these correlation functions on time scales different from f t w and we describe more precisely the behaviour of a singular diffusion obtained as the scaling limit of bouchaud s trap model

aging in metropolis dynamics of the rem a proof we consider metropolis dynamics of the random energy model we prove that the classical two time correlation function that allows one to establish aging converges almost surely to the arcsine law distribution function as predicted in the physics literature in the optimal domain of the time scale and temperature parameters where this result can be expected to hold to do this we link the two time correlation function to a certain continuous time clock process which after proper rescaling is proven to converge to a stable subordinator almost surely in the random environment and in the fine j 1 topology of skorohod this fine topology then enables us to deduce from the arcsine law for stable subordinators the asymptotic behavior of the two time correlation function that characterizes aging