synchronization of chaotic lur e systems with time delays using sampled data control the asymptotical synchronization problem is investigated for two identical chaotic lur e systems with time delays the sampled data control method is employed for the system design a new synchronization condition is proposed in the form of linear matrix inequalities the error system is shown to be asymptotically stable with the constructed new piecewise differentiable lyapunov krasovskii functional lkf different from the existing work the new lkf makes full use of the information in the nonlinear part of the system the obtained stability condition is less conservative than some of the existing ones a longer sampling period is achieved with the new method the numerical examples are given and the simulations are performed on chua s circuit the results show the superiorities and effectiveness of the proposed control method

variational formula for the time constant of first passage percolation consider first passage percolation with positive stationary ergodic weights on the square lattice in d dimensions let t x be the first passage time from the origin to x in z d the convergence of t nx n to the time constant as n tends to infinity is a consequence of the subadditive ergodic theorem this convergence can be viewed as a problem of homogenization for a discrete hamilton jacobi bellman hjb equation by borrowing several tools from the continuum theory of stochastic homogenization for hjb equations we derive an exact variational formula duality principle for the timeconstant under a symmetry assumption we will use the variational formula to construct an explicit iteration that produces the limit shape

redundant cordic methods with a constant scale factor for sine and cosine computation proposes two redundant cordic coordinate rotation digital computer methods with a constant scale factor for sine and cosine computation called the double rotation method and the correcting rotation method in both methods the cordic is accelerated by the use of a redundant binary number representation as in the previously proposed redundant cordic in the proposed methods since the number of rotation extensions performed for each angle is a constant the scale factor is a constant independent of the operand hence one does not need to calculate the scale factor during the computation and can make a more efficient sine and cosine generator than that based on the previous redundant cordic

augmented zero equality approach to stability for linear systems with time varying delay abstract this work focuses the delay dependent stability problem for linear systems with time varying delays by composing a suitable augmented lyapunov krasovskii functionals using recent developed integral inequality and choosing newly states a set of sufficient conditions for stability condition is induced within framework of linear matrix inequalities lmis to enhance the feasible region of stability single augmented zero equality is established with the augmented state vectors for the first time and the equality constraint is incorporated into a simple stability criterion by utilizing finsler s lemma the comparison of maximum bounds of time delay with various results proposed by recent studies will be conducted in numerical examples to demonstrate the superiority of the theorems presented by this paper

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

positive forms and stability of linear time delay systems we consider the problem of constructing lyapunov functions for linear differential equations with delays for such systems it is known that exponential stability implies the existence of a positive lyapunov function which is quadratic on the space of continuous functions we give an explicit parameterization of a sequence of finite dimensional subsets of the cone of positive lyapunov functions using positive semidefinite matrices this allows stability analysis of linear time delay systems to be formulated as a semidefinite program

an iqc approach to robust stability of aperiodic sampled data systems conditions for robust stability of sampled data systems with non uniform sampling patterns and structural uncertainties are derived the problem is tackled under the integral quadratic constraint iqc framework where the aperiodic sampling operation is modelled by an delay integration operator characterization based on integral quadratic constrains iqc is identified for this operator and the iqc theory is applied to derive convex stability criteria compared to the dominating lyapunov approach where the candidate lyapunov krasovskii functionals or looped functionals need to be tailored for the systems under consideration and therefore the stability conditions need to be re derived whenever additional uncertainties are considered the proposed approach has the advantage of avoiding such endeavor numerical examples are given to illustrate this main point and effectiveness of the proposed approach

convex conditions for robust stability analysis and stabilization of linear aperiodic impulsive and sampled data systems under dwell time constraints stability analysis and control of linear impulsive systems is addressed in a hybrid framework through the use of continuous time time varying discontinuous lyapunov functions necessary and sufficient conditions for stability of impulsive systems with periodic impulses are first provided in order to set up the main ideas extensions to the stability of aperiodic systems under minimum maximum and ranged dwell times are then derived by exploiting further the particular structure of the stability conditions the results are non conservatively extended to quadratic stability analysis of linear uncertain impulsive systems these stability criteria are in turn losslessly extended to stabilization using a particular yet broad enough class of state feedback controllers providing then a convex solution to the open problem of robust dwell time stabilization of impulsive systems using hybrid stability criteria relying finally on the representability of sampled data systems as impulsive systems the problems of robust stability analysis and robust stabilization of periodic and aperiodic uncertain sampled data systems are straightforwardly solved using the same ideas several examples are discussed in order to show the effectiveness and reduced complexity of the proposed approach

technical communique stability and stabilization of nonuniform sampling systems this paper is concerned with nonuniform sampling systems where the sampling interval is time varying within a certain known bound the system is transformed into a time varying discrete time system where time varying parts due to the sampling interval variation are treated as norm bounded uncertainties using robust control techniques to reduce conservatism arising from modeling time varying parts as a single uncertainty the time varying parts are modeled as n uncertainties with larger n a less conservative stability condition is derived at sacrifice of more computation it is shown through a numerical example that the proposed stability condition is better than existing stability conditions

a new looped functional for stability analysis of sampled data systems abstract in this paper a new two sided looped functional is introduced for stability analysis of sampled data systems the functional fully utilizes the information on both the intervals x t to x t k and x t to x t k 1 based on the two sided functional an improved stability condition is derived in the form of linear matrix inequality lmi numerical examples show that the result computed by the presented condition approximates nearly the theoretical bound bound obtained by eigenvalue analysis and outperforms substantially others in the existing literature

sublinear variance in first passage percolation for general distributions we prove that the variance of the passage time from the origin to a point x in first passage percolation on mathbb z d is sublinear in the distance to x when d ge 2 obeying the bound c vert x vert log vert x vert under minimal assumptions on the edge weight distribution the proof applies equally to absolutely continuous discrete and singular continuous distributions and mixtures thereof and requires only 2 log moments the main result extends work of benjamini kalai schramm ann prob 31 2003 and benaim rossignol ann inst henri poincare prob stat 3 2008

new insights on stability of sampled data systems with time delay abstract this paper analyses the stability of sampled data systems with time delay by employing a two sided looped functional approach some improved conditions are derived to guarantee the stability of the system under consideration then based the conditions some intrinsic relationships between sampled data period and time delay are obtained from the illustrative example being solved by the proposed approach it is observed that the results obtained are significantly better than those obtained by existing methods more importantly from the simulation being carried out it is discovered that contrary to the findings in previous studies time delays in a system may enlarge the interval of sampled data periods and accelerate the rate of convergence of the system states rather than deteriorate the system performance

approximation of subadditive functions and convergence rates in limiting shape results for a nonnegative subadditive function h on mathbb z d with limiting approximation g x lim n h nx n it is of interest to obtain bounds on the discrepancy between g x and h x typically of order x nu with nu 1 for certain subadditive h x particularly those which are expectations associated with optimal random paths from 0 to x in a somewhat standardized way a more natural and seemingly weaker property can be established every x is in a bounded multiple of the convex hull of the set of sites satisfying a similar bound we show that this convex hull property implies the desired bound for all x applications include rates of convergence in limiting shape results for first passage percolation standard and oriented and longest common subsequences and bounds on the error in the exponential decay approximation to the off axis connectivity function for subcritical bernoulli bond percolation on the integer lattice

shape fluctuations and random matrices we study a certain random growth model in two dimensions closely related to the one dimensional totally asymmetric exclusion process the results show that the shape fluctuations appropriately scaled converges in distribution to the tracy widom largest eigenvalue distribution for the gaussian unitary ensemble gue

quantized saturated control for sampled data systems under noisy sampling intervals a confluent vandermonde matrix approach in this paper a unified framework is established to investigate both the quantized and the saturated control problems for a class of sampled data systems under noisy sampling intervals a random variable obeying the erlang distribution is used to describe the noisy sampling intervals in virtue of the matrix exponential the sampled data control system is transformed into an equivalent discrete time stochastic system and the aim of this paper is to design a quantized saturated sampled data controller such that the resulting discrete time stochastic system is stochastically stable when the sampling error follows the erlang distribution in order to deal with the case of multiple control inputs a confluent vandermonde matrix approach is proposed in the design process by using the kronecker product operation and the matrix inequality techniques the desired quantized saturated controller gains are designed in terms of the solution to certain matrix inequalities finally a simulation example is exploited to verify the effectiveness of the proposed design approach

busemann functions and infinite geodesics in two dimensional first passage percolation we study first passage percolation on mathbb z 2 where the edge weights are given by a translation ergodic distribution addressing questions related to existence and coalescence of infinite geodesics some of these were studied in the late 1990s by c newman and collaborators under strong assumptions on the limiting shape and weight distribution in this paper we develop a framework for working with distributional limits of busemann functions and use it to prove forms of newman s results under minimal assumptions for instance we show a form of coalescence of long finite geodesics in any deterministic direction we also introduce a purely directional condition which replaces newman s global curvature condition and whose assumption we show implies the existence of directional geodesics without this condition we prove existence of infinite geodesics which are directed in sectors last we analyze distributional limits of geodesic graphs proving almost sure coalescence and nonexistence of infinite backward paths this result relates to the conjecture of nonexistence of bigeodesics

double residue modular range reduction for floating point hardware implementations in this paper we present a novel algorithm and the corresponding architecture for performing range reduction which is a preprocessing task required for the evaluation of some elementary functions such as trigonometric and exponential based functions the proposed algorithm introduces a modification to the modular range reduction algorithm which increases the speed of computation and allows us to design an architecture for the floating point case the implementation presented admits as an input argument any representable number of the standard single precision ieee 754 floating point representation and provides the maximum accuracy to the final result this supposes a hardware solution to the problem of having an input argument close to a multiple of the constant a final comparison with other implementations is presented

sampled data h exponential synchronization for delayed semi markov jump cdns a looped functional approach abstract this paper investigates the h exponential synchronization problem of delayed semi markov jump complex dynamical networks by utilizing the sampled data control scheme through introducing a semi markov jump model where the transition rate is related to the sojourn time the addressed issue is therefore more general by constructing a suitable lyapunov krasovskii functional with a looped functional and adopting an advanced inequality method sufficient conditions for the h exponential synchronization of delayed semi markov jump complex dynamical networks are presented a numerical example is finally employed to confirm the validity of the proposed method

on stability of systems with aperiodic sampling devices this technical note is concerned with stability analysis of aperiodic sampled data systems the stability problem is tackled from a pure discrete time point of view where the at sampling behavior of the system is modelled as the response of a nominal discrete time lti system in feedback interconnection with a structured uncertainty conditions under which the uncertainty is positive real pr are identified based on the pr property a number of integral quadratic constraints iqc are derived and the iqc theory is applied to derive stability conditions numerical examples are given to illustrate the effectiveness of the proposed approach

nonfragile exponential synchronization of delayed complex dynamical networks with memory sampled data control this paper considers nonfragile exponential synchronization for complex dynamical networks cdns with time varying coupling delay the sampled data feedback control which is assumed to allow norm bounded uncertainty and involves a constant signal transmission delay is constructed for the first time in this paper by constructing a suitable augmented lyapunov function and with the help of introduced integral inequalities and employing the convex combination technique a sufficient condition is developed such that the nonfragile exponential stability of the error system is guaranteed as a result for the case of sampled data control free of norm bound uncertainties some sufficient conditions of sampled data synchronization criteria for the cdns with time varying coupling delay are presented as the formulations are in the framework of linear matrix inequality these conditions can be easily solved and implemented two illustrative examples are presented to demonstrate the effectiveness and merits of the proposed feedback control

reachable set estimation for markov jump lpv systems with time delays abstract this paper investigates the reachable set estimation problem for discrete time markov jump lpv systems with time varying delays and bounded disturbance the main consideration is that under zero initial conditions how to obtain a bound set as small as possible that includes system states based on this by applying a novel summation inequality integrated with the reciprocally convex approach under the framework of the lyapunov functional method the delay dependent conditions are provided to guarantee the presence of an ellipsoid that bounds the system state in the existence of bounded disturbances some derived conditions expressed by linear matrix inequalities can be solved via utilizing different computational tools and the minimum possible ellipsoidal bound can also be determined additionally the obtained results are extensively used in the case with partially known transition probability and some conditions with more universality are derived finally a numerical example is given to illustrate the effectiveness of the results

asymptotic shapes for stationary first passage percolation this paper deals with first passage percolation where the usual i i d condition is weakened to stationarity and ergodicity the well known asymptotic shape result is known to extend to this case it is easy to give necessary conditions for a compact set b subset mathbb r d to arise as the asymptotic shape for some stationary measure on the passage times our main result says that these conditions are also sufficient

the supercritical phase of percolation is well behaved we prove a general result concerning the critical probabilities of subsets of a lattice l it is a consequence of this result that the critical probability of a percolation process on l equals the limit of the critical probability of a slice of l as the thickness of the slice tends to infinity this verification of one of the standard hypotheses of the subject settles many questions concerning supercritical percolation

stabilization of sampled data control systems with control inputs missing this note is concerned with the stabilization problem for sampled data control systems with control inputs missing a sufficient condition is derived for the existence of exponentially stabilizing state feedback controllers via the switched system approach the obtained condition establishes several quantitative relations among some system parameters such as the sampling period and the exponential decay rate the actual data missing rate and the admissible data missing rate bound two illustrative examples are given to show the effectiveness of the proposed results

some remarks on the use of time varying delay to model sample and hold circuits this note revises the so called input delay approach to the control of sampled data systems with nonuniform sampling in which the sample and hold circuit is embedded into an analog system with a time varying input delay it is shown that the conservatism in calculating the maximal admissible sampling period is reduced by about 57 if the time varying delay embedding step is omitted

central limit theorem for first passage percolation time across thin cylinders we prove that first passage percolation times across thin cylinders of the form 0 n hn hn d 1 obey gaussian central limit theorems as long as hn grows slower than n1 d 1 it is an open question as to what is the fastest that hn can grow so that a gaussian clt still holds under the natural but unproven assumption about existence of fluctuation and transversal exponents and strict convexity of the limiting shape in the direction of 1 0 0 we prove that in dimensions 2 and 3 the clt holds all the way up to the height of the unrestricted geodesic we also provide some numerical evidence in support of the conjecture in dimension 2

stability analysis of some classes of input affine nonlinear systems with aperiodic sampled data control in this paper we investigate the stability analysis of nonlinear sampled data systems which are affine in the input we assume that a stabilizing controller is designed using the emulation technique we intend to provide sufficient stability conditions for the resulting sampled data system this allows to find an estimate of the upper bound on the asynchronous sampling intervals for which stability is ensured the main idea of the paper is to address the stability problem in a new framework inspired by the dissipativity theory furthermore the result is shown to be constructive numerically tractable criteria are derived using linear matrix inequality for polytopic systems and using sum of squares technique for the class of polynomial systems

pth moment asymptotic interval stability and stabilization of linear stochastic systems via generalized h representation abstract the problem of pth moment asymptotic interval stability and stabilization for linear stochastic systems is investigated in this paper firstly we define the generalized h representation which is very helpful to transform stochastic systems into deterministic systems then the problems of pth moment interval stability the decay rate of state response and the estimation of pth moment lyapunov exponent are proposed with the help of the model transformation method furthermore the criteria for pth moment interval stabilization of the linear stochastic systems are addressed some necessary numerical examples are also provided to show the effectiveness of the addressed method

stability and bifurcation of a delayed generalized fractional order prey predator model with interspecific competition abstract the present paper considers a delayed generalized fractional order prey predator model with interspecific competition the existence of the nontrivial positive equilibrium is discussed and some sufficient conditions for global asymptotic stability of the equilibrium are developed meanwhile the existence of hopf bifurcation is discussed by choosing time delay as the bifurcation parameter finally some numerical simulations are carried out to support the analytical results

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

dissipativity based sampled data control for fuzzy markovian jump systems abstract in this paper the problems of dissipativity analysis and sampled data control are considered for fuzzy markovian jump systems firstly by constructing a mode dependent lyapunov function consisting of the two sided closed loop function where the information of both intervals x tk to x t and x t to x t k 1 are fully utilized the stochastically stable criteria and strictly q s r dissipative criteria are proposed in the form of linear matrix inequalities lmis then on the basis of the strictly dissipativity criteria a controller with state feedback is designed for the studied systems at last a truck trailer model is shown to demonstrate the efficiency of the presented method

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

stability of homogeneous nonlinear systems with sampled data inputs abstract the main goal of this article is to use properties of homogeneous systems for addressing the problem of stability for a class of nonlinear systems with sampled data inputs this nonlinear strategy leads to several kinds of stability i e local asymptotic stability global asymptotic stability or global asymptotic set stability depending on the sign of the degree of homogeneity the results are illustrated with the case of the double integrator

stabilization for sampled data systems under noisy sampling interval in engineering practice the sampling interval for a sampled data system often fluctuates around a nominal ideal value based on certain probability distributions that can be specified a priori through statistical tests in this paper a fundamental stabilization problem is investigated for a class of sampled data systems under noisy sampling interval the stochastic sampled data control system under consideration is first converted into a discrete time system whose system matrix is represented as an equivalent yet tractable form via the matrix exponential computation then by introducing a vandermonde matrix the mathematical expectation of the quadratic form of the system matrix is computed by recurring to the kronecker product operation the sampled data stabilization controller is designed such that the closed loop system is stochastically stable in the presence of noisy sampling interval subsequently a special case is considered where the sampling interval obeys the continuous uniform distribution and the corresponding stabilization controller is designed finally a numerical simulation example is provided to demonstrate the effectiveness of the proposed design approach

stability of systems with controller failure and time varying delay this paper studies the stability for a class of systems with time varying delay subject to controller failure it explores under what conditions of controller failure the system is still exponentially stable the concept of controller failure frequency is introduced first the delay system with failed controller is modelled as a class of switched delay systems next based on two lemmas developed in this paper and the piecewise lyapunov functional method sufficient conditions are provided to guarantee the exponential stability of the system when controller failure occurs which is in terms of the solvability of a set of linear matrix inequalities lmis finally an example of a networked control system is given to illustrate the effectiveness of the proposed method

sampled data filtering of takagi sugeno fuzzy neural networks with interval time varying delays abstract this paper is concerned with sample data filtering of t s fuzzy neural networks with interval time varying delays which is formed by a fuzzy plant with time delay and a sampled data fuzzy controller connected in a closed loop a takagi sugeno t s fuzzy model is adopted for the neural networks and the sampled data fuzzy controller is designed for a t s fuzzy system to develop the guaranteed cost control a new stability condition of the closed loop system is guaranteed in the continuous time lyapunov sense and its sufficient conditions are formulated in terms of linear matrix inequalities by using a descriptor representation the sampled data fuzzy control system with time delay can be reduced to ease the stability analysis which effectively leads to a smaller number of lmi stability conditions information of the membership functions of both the fuzzy plant model and fuzzy controller are considered which allows arbitrary matrices to be introduced to ease the satisfaction of the stability conditions by a newly proposed inequality bounding technique the fuzzy sampled data filtering performance analysis is carried out such that the resultant neural networks is asymptotically stable numerical example and simulation result are given to illustrate the usefulness and effectiveness of the proposed theoretical results

geodesics and the competition interface for the corner growth model we study the directed last passage percolation model on the planar integer lattice with nearest neighbor steps and general i i d weights on the vertices outside the class of exactly solvable models in georgiou et al probab theory relat fields 2016 doi 10 1007 s00440 016 0729 x we constructed stationary cocycles and busemann functions for this model using these objects we prove new results on the competition interface on existence uniqueness and coalescence of directional semi infinite geodesics and on nonexistence of doubly infinite geodesics

stationary cocycles and busemann functions for the corner growth model we study the directed last passage percolation model on the planar square lattice with nearest neighbor steps and general i i d weights on the vertices outside of the class of exactly solvable models stationary cocycles are constructed for this percolation model from queueing fixed points these cocycles serve as boundary conditions for stationary last passage percolation solve variational formulas that characterize limit shapes and yield existence of busemann functions in directions where the shape has some regularity in a sequel to this paper the cocycles are used to prove results about semi infinite geodesics and the competition interface

divergence of shape fluctuations in two dimensions we consider stochastic growth models such as standard first passage percolation on z d where to leading order there is a linearly growing deterministic shape under natural hypotheses we prove that for d 2 the shape fluctuations grow at least logarithmically in all directions although this bound is far from the expected power law behavior with exponent 1 3 it does prove divergence with additional hypotheses we obtain inequalities involving and the related exponent which is expected to equal 2 3 for d 2 combining these inequalities with previously known results we obtain for standard first passage percolation the bounds 1 8 for d 2 and 3 4 for all d

shape fluctuations are different in different directions we consider the first passage percolation model on z 2 in this model we assign independently to each edge e a passage time t e with a common distribution f let t u v be the passage time from u to v in this paper we show that whenever f 0 0 and f r p c it is known that there exists m such that for all n 2 t 0 0 n n m these results tell us that shape fluctuations not only depend on distribution f but also on direction when showing this result we find the following interesting geometrical property with the special distribution above any long piece with r edges in an optimal path from 0 0 to n 0 has to be very circuitous

pinning synchronization in t s fuzzy complex networks with partial and discrete time couplings communication constraints which may lead to the degradation of performance are common and unavoidable in a real world network in this paper two kinds of communication constraints are considered during the process of information transmission in takagi sugeno ts fuzzy complex network 1 partial couplings where only some part of nodes state information can be transmitted and the channel matrices are introduced to reflect such a phenomenon and 2 discrete time couplings where the nodes information are sampled at certain time instants this is the first time when both communication constraints are simultaneously considered in fuzzy complex networks compared with the perfect communication much less information is available for synchronization to overcome this difficulty a regrouping method is employed to reconstruct the fuzzy network the concise conditions are then proposed to ensure pinning synchronization of fuzzy complex networks with partial and discrete time couplings simulation examples are also provided to demonstrate the effectiveness of the theoretical results

synchronization for complex dynamical networks with time delay and discrete time information the synchronization problem is studied for complex dynamical networks cdns with time delay based on discrete time communication pattern a new lyapunov functional is proposed which is positive definite at communication instants but not necessarily positive definite inside the communication intervals and can make full use of the available information about the discrete time communication pattern based on the lyapunov functional an exponential synchronization criterion is proposed to ensure the synchronization of the considered cdns the effectiveness of the developed results are shown by the numerical simulation

finite time stabilization for stochastic reaction diffusion systems with markovian switching via boundary control abstract this paper investigates the finite time stability fts for a class of stochastic markovian reaction diffusion systems smrdss first a boundary control strategy is put forward under the designed boundary controller a sufficient condition of fts for smrdss is provided based on the method of lyapunov krasovskii functional combined with inequality techniques when there exists the incompleteness of transition rate information we further study the problem of smrdss with partially unknown transition rates trs by adding a set of symmetric free matrices an fts criterion is also obtained for this case theoretical results show that the case of completely known trs is the special case of partially unknown trs finally simulation examples are presented to verify the validity of our derived results

sampled data control for a class of linear time varying systems this paper is concerned with the sampled data control for a class of linear time varying system a classic halanay inequality is first extended to the time varying sampled data system then based on the comparison principle and the extended halanay inequality new criteria for globally uniformly exponential stability and globally uniformly asymptotic stability of the corresponding closed loop system are derived furthermore an algorithm is presented to solve the gain synthesis problem finally one example is given to show the effectiveness of the obtained results

a new range reduction algorithm range reduction is a key point for getting accurate elementary function routines we introduce a new algorithm that is fast for input arguments belonging to the most common domains yet accurate over the full double precision range

euclidean models of first passage percolation we introduce a new family of first passage percolation fpp models in the context of poisson voronoi tesselations of d compared to standard fpp on d these models have some technical complications but also have the advantage of statistical isotropy we prove two almost sure results a shape theorem where isotropy implies an exact euclidean ball for the asymptotic shape and nonexistence of certain doubly infinite geodesics where isotropy yields a stronger result than in standard fpp

convex conditions for robust stabilization of uncertain switched systems with guaranteed minimum and mode dependent dwell time abstract alternative conditions for establishing dwell time stability properties of linear switched systems are considered unlike the hybrid conditions derived in geromel and colaneri 2006 the considered ones are affine in the system matrices allowing then for the consideration of uncertain switched systems with time varying uncertainties the low number of decision variables moreover permits to easily derive convex stabilization conditions using a specific class of state feedback control laws the resulting conditions are enforced using sum of squares programming which are shown to be less complex numerically that approaches based on piecewise linear functions or looped functionals previously considered in the literature the sums of squares conditions are also proven to 1 approximate arbitrarily well the conditions of geromel and colaneri 2006 and 2 be invariant with respect to time scaling emphasizing that the complexity of the approach does not depend on the size of the dwell time several comparative examples illustrate the efficiency of the approach

order of the variance in the discrete hammersley process with boundaries we discuss the order of the variance on a lattice analogue of the hammersley process with boundaries for which the environment on each site has independent bernoulli distributed values the last passage time is the maximum number of bernoulli points that can be collected on a piecewise linear path where each segment has strictly positive but finite slope we show that along characteristic directions the order of the variance of the last passage time is of order n 2 3 in the model with boundary these characteristic directions are restricted in a cone starting at the origin and along any direction outside the cone the order of the variance changes to o n in the boundary model and to o 1 for the non boundary model this behaviour is the result of the two flat edges of the shape function

a continued fraction analysis of trigonometric argument reduction the calculation of a trigonometric function of a large argument x is effectively carried out by finding the integer n and 0

slow state variables feedback stabilization for semi markov jump systems with singular perturbations the slow state variables feedback stabilization problem for semi markov jump discrete time systems with slow sampling singular perturbations is discussed in this work a new fairly comprehensive system model semi markov jump system with singular perturbations which is more general than markov jump model is employed to describe the phenomena of random abrupt changes in structure and parameters of the systems based on a slow state variables feedback control scheme a novel technique to design the desired controller is presented and the allowed maximum of singular perturbation parameter can be calculated with the help of the discrete time semi markov kernel approach some sojourn time dependent and less conservative sufficient conditions are established via a novel matrix decoupling technique to ensure the solvability of the problem to be addressed finally an illustrative example is given to show the superiority and usefulness of the proposed method

first passage percolation on mathbb z 2 a simulation study first passage percolation on mathbb z 2 is a model for describing the spread of an infection on the sites of the square lattice the infection is spread via nearest neighbor sites and the time dynamic is specified by random passage times attached to the edges in this paper the speed of the growth and the shape of the infected set is studied by aid of large scale computer simulations with focus on continuous passage time distributions it is found that the most important quantity for determining the value of the time constant which indicates the inverse asymptotic speed of the growth is mathbf e min tau 1 ldots tau 4 where tau 1 ldots tau 4 are i i d passage time variables the relation is linear for a large class of passage time distributions furthermore the directional time constants are seen to be increasing when moving from the axis towards the diagonal so that the limiting shape is contained in a circle with radius defined by the speed along the axes the shape comes closer to the circle for distributions with larger variability

affine characterizations of minimal and mode dependent dwell times for uncertain linear switched systems an alternative approach for minimum and mode dependent dwell time characterization for switched systems is derived while minimum dwell time results require the subsystems to be asymptotically stable mode dependent dwell time results can consider unstable subsystems and dwell times within a possibly unbounded range of values the proposed approach is related to lyapunov looped functionals a new type of functionals leading to stability conditions affine in the system matrices unlike standard results for minimum dwell time these conditions are expressed as infinite dimensional lmis which can be solved using recent polynomial optimization techniques such as sum of squares the specific structure of the conditions is finally utilized in order to derive dwell time stability results for uncertain switched systems several examples illustrate the efficiency of the approach

differentiability at the edge of the percolation cone and related results in first passage percolation we study first passage percolation in two dimensions using measures on passage times with b inf supp 0 and mu b p geq vec p c the threshold for oriented percolation we first show that for each such the boundary of the limit shape for is differentiable at the endpoints of flat edges in the so called percolation cone we then conclude that the limit shape must be non polygonal for all of these measures furthermore the associated richardson type growth model admits infinite coexistence and if is not purely atomic the graph of infection has infinitely many ends we go on to show that lower bounds for fluctuations of the passage time given by newman piza extend to these measures we establish a lower bound for the variance of the passage time to distance n of order log n in any direction outside the percolation cone under a condition of finite exponential moments for this result confirms a prediction of newman and piza ann probab 23 977 1005 1995 and zhang ann probab 36 331 362 2008 under the assumption of finite radius of curvature for the limit shape in these directions we obtain a power law lower bound for the variance and an inequality between the exponents and

dissipativity based sampled data fuzzy control design and its application to truck trailer system this paper is concerned with the problem of dissipative control for takagi sugeno fuzzy systems under time varying sampling with a known upper bound on the sampling intervals based on the time dependent lyapunov krasovskii functional approach which makes full use of the available information about the actual sampling pattern a sufficient condition is established to guarantee the sampled data systems to be exponentially stable and strictly mathcal q mathcal s mathcal r gamma dissipative based on the criterion a design algorithm for the desired sampled data controller is proposed the effectiveness and benefits of the results developed in this paper is demonstrated by a controller design for a truck trailer system

co design of aperiodic sampled data min jumping rules for linear impulsive switched impulsive and sampled data systems abstract co design conditions for the design of a jumping rule and a sampled data control law for impulsive and impulsive switched systems subject to aperiodic sampled data measurements are provided semi infinite discrete time lyapunov metzler conditions are first obtained as these conditions are difficult to check and generalize to more complex systems an equivalent formulation is provided in terms of clock dependent infinite dimensional matrix inequalities these conditions are then in turn approximated by a finite dimensional optimization problem using a sum of squares based relaxation it is proven that the sum of squares relaxation is non conservative provided that the degree of the polynomials is sufficiently large it is emphasized that acceptable results are obtained for low polynomial degrees in the considered examples

convex lifted conditions for robust l 2 stability analysis and l 2 stabilization of linear discrete time switched systems with minimum dwell time constraint stability analysis of discrete time switched systems under minimum dwell time is studied using a new type of lmi conditions these conditions are convex in the matrices of the system and shown to be equivalent to the nonconvex conditions proposed in geromel and colaneri 2006b the convexification of the conditions is performed by a lifting process which introduces a moderate number of additional decision variables the convexity of the conditions can be exploited to extend the results to uncertain systems control design and 2 gain computation without introducing additional conservatism several examples are presented to show the effectiveness of the approach

variational formulas and cocycle solutions for directed polymer and percolation models we discuss variational formulas for the law of large numbers limits of certain models of motion in a random medium namely the limiting time constant for last passage percolation and the limiting free energy for directed polymers the results are valid for models in arbitrary dimension steps of the admissible paths can be general the environment process is ergodic under spatial translations and the potential accumulated along a path can depend on the environment and the next step of the path the variational formulas come in two types one minimizes over gradient like cocycles and another one maximizes over invariant measures on the space of environments and paths minimizing cocycles can be obtained from busemann functions when these can be proved to exist the results are illustrated through 1 1 dimensional exactly solvable examples periodic examples and polymers in weak disorder