synchronization of continuous dynamical networks with discrete time communications in this paper synchronization of continuous dynamical networks with discrete time communications is studied though the dynamical behavior of each node is continuous time the communications between every two different nodes are discrete time i e they are active only at some discrete time instants moreover the communication intervals between every two communication instants can be uncertain and variable by choosing a piecewise lyapunov krasovskii functional to govern the characteristics of the discrete communication instants and by utilizing a convex combination technique a synchronization criterion is derived in terms of linear matrix inequalities with an upper bound for the communication intervals obtained the results extend and improve upon earlier work simulation results show the effectiveness of the proposed communication scheme some relationships between the allowable upper bound of communication intervals and the coupling strength of the network are illustrated through simulations on a fully connected network a star like network and a nearest neighbor network

asynchronous l 2 l filtering for discrete time stochastic markov jump systems with randomly occurred sensor nonlinearities this paper is concerned with the problem of asynchronous l 2 l filtering for discrete time stochastic markov jump systems with sensor nonlinearity the sensor nonlinearity is assumed to occur randomly according to a stochastic variable satisfying the bernoulli distribution a sufficient condition is first given such that the resultant filtering error system which is a kind of nonhomogeneous markov jump system is stochastically stable with a guaranteed l 2 l performance index then the existence criterion of the desired asynchronous filter with piecewise homogeneous markov chain is proposed in terms of a set of linear matrix inequalities a numerical example is given to show the effectiveness and potential of the developed theoretical results

brief paper h filtering for uncertain stochastic time delay systems with sector bounded nonlinearities in this paper we deal with the robust h filtering problem for a class of uncertain nonlinear time delay stochastic systems the system under consideration contains parameter uncertainties ito type stochastic disturbances time varying delays as well as sector bounded nonlinearities we aim at designing a full order filter such that for all admissible uncertainties nonlinearities and time delays the dynamics of the filtering error is guaranteed to be robustly asymptotically stable in the mean square while achieving the prescribed h disturbance rejection attenuation level by using the lyapunov stability theory and ito s differential rule sufficient conditions are first established to ensure the existence of the desired filters which are expressed in the form of a linear matrix inequality lmi then the explicit expression of the desired filter gains is also characterized finally a numerical example is exploited to show the usefulness of the results derived

self organized growth model for the quenched herring mullin equation we introduce a simple self organized growth model mimicking the dynamics of a driven tensionless interface in a random medium near the depinning threshold the roughness and growth exponents for the model are obtained as ensuremath zeta ensuremath simeq 1 93 and ensuremath beta ensuremath simeq 0 96 respectively we discuss the possible continuum equation describing the motion of a driven interface in our model

stabilization of linear systems with distributed input delay and input saturation this paper is concerned with stabilization of a linear system with distributed input delay and input saturation both constant and time varying delays are considered in the case that the input delay is constant under the stabilizability assumption on an auxiliary system it is shown that the system can be stabilized by state feedback for an arbitrarily large delay as long as the open loop system is not exponentially unstable in the case that the input delay is time varying but bounded it is shown that the system can be stabilized by state feedback if the non asymptotically stable poles of the open loop system are all located at the origin in both cases stabilizing controllers are explicitly constructed by utilizing the parametric lyapunov equation based low gain design approach we recently developed it is also shown that in the presence of actuator saturation and under the same assumptions on the system these controllers achieve semi global stabilization some discussions on the assumptions we impose on the system are given a numerical example illustrates the effectiveness of the proposed stabilization approach

viscosity solutions of the bellman equation for exit time optimal control problems with vanishing lagrangians we study the hamilton jacobi bellman equation for undiscounted exit time optimal control problems for fully nonlinear systems and fully nonlinear singular lagrangians using the dynamic programming approach we prove a local uniqueness theorem characterizing the value functions for these problems as the unique viscosity solutions of the corresponding hamilton jacobi bellman equations that satisfy appropriate boundary conditions the novelty of this theorem is in the relaxed hypotheses on the lower bound on the lagrangian and the very general assumptions on the target set as a corollary we show that the value function for the fuller problem is the unique viscosity solution of the corresponding hamilton jacobi bellman equation that vanishes at the origin and satisfies certain growth conditions this implies as special cases first that the value function of this problem is the unique proper viscosity solution of the corresponding hamilton jacobi bellman equation in the class of all functions which are continuous in the plane and null at the origin and second that this value function is the unique viscosity solution of that equation in a class which includes functions which are not bounded below we also apply our results to the degenerate eikonal equation of geometric optics and to the shape from shading equations in image processing our theorem also applies to problems with noncompact targets and unbounded control sets whose lagrangians take negative values

exponential synchronization of lure complex dynamical networks with uncertain inner coupling and pinning impulsive control this paper is concerned with the exponential synchronization of lure type complex dynamical networks with uncertain coupling strength a novel pinning impulsive controller is designed to achieve synchronization in which only selection of nodes are chosen to control instead of the whole network in addition the proposed control scheme is digital and it can lead to low installation cost and less time in order to realize synchronization of lure type complex dynamical networks crucial delay dependent stability conditions are derived by utilizing lyapunov functional together with information of the time varying delay and convex combination technique the resulting stability conditions are formulated in the form of linear matrix inequalities lmis and by solving the obtained lmis desired impulsive control gain matrices are calculated which are capable to guarantee the exponential stability of error system finally the effectiveness of the proposed method is demonstrated through numerical simulations

fluctuations and correlations in two dimensional bak sneppen model the self organized criticality in the two dimensional bak sneppen model is studied from the fluctuations of the mean fitness and the jump of the minimum sites an ensemble having the same number of updates from the initial state is used in the investigation from the gaussian distribution of the mean fitness in the ensemble the lattice size dependence of the ensemble averaged fitness is found from the dependence a solution to the gap equation is found and the critical gap and an exponent are calculated a spatial temporal correlation function is investigated from the jump of the minimum site

sampled data synchronization of chaotic lur e systems with time delays this paper studies the problem of sampled data control for master slave synchronization schemes that consist of identical chaotic lur e systems with time delays it is assumed that the sampling periods are arbitrarily varying but bounded in order to take full advantage of the available information about the actual sampling pattern a novel lyapunov functional is proposed which is positive definite at sampling times but not necessarily positive definite inside the sampling intervals based on the lyapunov functional an exponential synchronization criterion is derived by analyzing the corresponding synchronization error systems the desired sampled data controller is designed by a linear matrix inequality approach the effectiveness and reduced conservatism of the developed results are demonstrated by the numerical simulations of chua s circuit and neural network

user s guide to viscosity solutions of second order partial differential equations the notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems existence theorems and theorems about continuous dependence may now be proved by very efficient and striking arguments the range of important applications of these results is enormous this article is a self contained exposition of the basic theory of viscosity solutions

self organized interface growth with the negative nonlinearity in a random medium we introduce two self organized growth models that describe the motion of the driven interfaces in random media including the kardar parisi zhang kpz nonlinearity one model follows the quenched kpz equation with a positive nonlinear term while the other model follows the quenched kpz equation with a negative nonlinear term by obtaining the critical exponents for two models we confirm that the sign of the kpz nonlinear term does not affect the universality class

passivity analysis for discrete time stochastic markovian jump neural networks with mixed time delays in this paper passivity analysis is conducted for discrete time stochastic neural networks with both markovian jumping parameters and mixed time delays the mixed time delays consist of both discrete and distributed delays the markov chain in the underlying neural networks is finite piecewise homogeneous by introducing a lyapunov functional that accounts for the mixed time delays a delay dependent passivity condition is derived in terms of the linear matrix inequality approach the case of markov chain with partially unknown transition probabilities is also considered all the results presented depend upon not only discrete delay but also distributed delay a numerical example is included to demonstrate the effectiveness of the proposed methods

bounded h_ infty synchronization and state estimation for discrete time varying stochastic complex networks over a finite horizon in this paper new synchronization and state estimation problems are considered for an array of coupled discrete time varying stochastic complex networks over a finite horizon a novel concept of bounded h synchronization is proposed to handle the time varying nature of the complex networks such a concept captures the transient behavior of the time varying complex network over a finite horizon where the degree of bounded synchronization is quantified in terms of the h norm a general sector like nonlinear function is employed to describe the nonlinearities existing in the network by utilizing a timevarying real valued function and the kronecker product criteria are established that ensure the bounded h synchronization in terms of a set of recursive linear matrix inequalities rlmis where the rlmis can be computed recursively by employing available matlab toolboxes the bounded h state estimation problem is then studied for the same complex network where the purpose is to design a state estimator to estimate the network states through available output measurements such that over a finite horizon the dynamics of the estimation error is guaranteed to be bounded with a given disturbance attenuation level again an rlmi approach is developed for the state estimation problem finally two simulation examples are exploited to show the effectiveness of the results derived in this paper

an ode comparison theorem with application in the optimal exit time control problem the optimal exit time control oetc problem tries to find the feedback control law with a reasonable cost that can keep the system state inside a certain subset of the state space called the safe set for the longest time under random perturbations the symmetry property of its solutions has been proved previously when the state dimension is higher than one in this note a comparison theorem is established that compares the solutions to two odes arising in the 1 d oetc problem the symmetry of solutions to the 1 d oetc problem is proved using this comparison theorem an example is presented to show how the symmetry result can help to solve the oetc problem analytically in certain cases

robust synchronization for 2 d discrete time coupled dynamical networks in this paper a new synchronization problem is addressed for an array of 2 d coupled dynamical networks the class of systems under investigation is described by the 2 d nonlinear state space model which is oriented from the well known fornasini marchesini second model for such a new 2 d complex network model both the network dynamics and the couplings evolve in two independent directions a new synchronization concept is put forward to account for the phenomenon that the propagations of all 2 d dynamical networks are synchronized in two directions with influence from the coupling strength the purpose of the problem addressed is to first derive sufficient conditions ensuring the global synchronization and then extend the obtained results to more general cases where the system matrices contain either the norm bounded or the polytopic parameter uncertainties an energy like quadratic function is developed together with the intensive use of the kronecker product to establish the easy to verify conditions under which the addressed 2 d complex network model achieves global synchronization finally a numerical example is given to illustrate the theoretical results and the effectiveness of the proposed synchronization scheme

synchronization of complex dynamical networks with hybrid coupling delays on time scales by handling multitude kronecker product terms the problem of synchronization is studied for complex dynamical networks with hybrid coupling delays on time scales the hybrid coupling delays consist of both discrete and distributed coupling delays some novel and useful synchronization criteria of complex dynamical networks are derived based on stability theory of error dynamical system by employing the standard lyapunov krasovskii functional matrix expansion method to handle multitude kronecker product terms and the modified jensen s inequalities on time scale new sufficient conditions guaranteeing the global exponential stability of the origin of complex dynamical networks are established interms of linear matrix inequality lmi numerical examples are included to demonstrate the effectiveness of the proposed method

global synchronization for discrete time stochastic complex networks with randomly occurred nonlinearities and mixed time delays in this paper the problem of stochastic synchronization analysis is investigated for a new array of coupled discrete time stochastic complex networks with randomly occurred nonlinearities rons and time delays the discrete time complex networks under consideration are subject to 1 stochastic nonlinearities that occur according to the bernoulli distributed white noise sequences 2 stochastic disturbances that enter the coupling term the delayed coupling term as well as the overall network and 3 time delays that include both the discrete and distributed ones note that the newly introduced rons and the multiple stochastic disturbances can better reflect the dynamical behaviors of coupled complex networks whose information transmission process is affected by a noisy environment e g internet based control systems by constructing a novel lyapunov like matrix functional the idea of delay fractioning is applied to deal with the addressed synchronization analysis problem by employing a combination of the linear matrix inequality lmi techniques the free weighting matrix method and stochastic analysis theories several delay dependent sufficient conditions are obtained which ensure the asymptotic synchronization in the mean square sense for the discrete time stochastic complex networks with time delays the criteria derived are characterized in terms of lmis whose solution can be solved by utilizing the standard numerical software a simulation example is presented to show the effectiveness and applicability of the proposed results

a new synchronization tracking technique for uncertain discrete network with spatiotemporal chaos behaviors abstract we propose a novel scheme to achieve synchronization tracking of uncertain discrete network with spatiotemporal chaos behaviors in this work the traditional method of sliding mode control is firstly modified for researching conveniently the synchronization tracking of uncertain discrete network further the network sliding mode surface and control input are designed and their effectiveness are analyzed at the same time we also design the adaptive law to identify availably the uncertain configuration coefficient of the network sliding mode surface finally an example about the small world network is considered to illustrate the application and effectiveness of the proposed scheme

robust extended dissipative control for sampled data markov jump systems this paper investigates the problem of the sampled data extended dissipative control for uncertain markov jump systems the systems considered are transformed into markov jump systems with polytopic uncertainties and sawtooth delays by using an input delay approach the focus is on the design of a mode independent sampled data controller such that the resulting closed loop system is mean square exponentially stable with a given decay rate and extended dissipative a novel exponential stability criterion and an extended dissipativty condition are established by proposing a new integral inequality the reduced conservatism of the criteria is demonstrated by two numerical examples furthermore a sufficient condition for the existence of a desired mode independent sampled data controller is obtained by solving a convex optimisation problem finally a resistance inductance and capacitance rlc series circuit is employed to illustrate the effectiveness of the proposed approach

brief paper wirtinger s inequality and lyapunov based sampled data stabilization discontinuous lyapunov functionals appeared to be very efficient for sampled data systems fridman 2010 naghshtabrizi hespanha teel 2008 in the present paper new discontinuous lyapunov functionals are introduced for sampled data control in the presence of a constant input delay the construction of these functionals is based on the vector extension of wirtinger s inequality these functionals lead to simplified and efficient stability conditions in terms of linear matrix inequalities lmis the new stability analysis is applied to sampled data state feedback stabilization and to a novel sampled data static output feedback problem where the delayed measurements are used for stabilization

delay dependent state estimation for delayed neural networks in this letter the delay dependent state estimation problem for neural networks with time varying delay is investigated a delay dependent criterion is established to estimate the neuron states through available output measurements such that the dynamics of the estimation error is globally exponentially stable the proposed method is based on the free weighting matrix approach and is applicable to the case that the derivative of a time varying delay takes any value an algorithm is presented to compute the state estimator finally a numerical example is given to demonstrate the effectiveness of this approach and the improvement over existing ones

brief paper a unified synchronization criterion for impulsive dynamical networks this paper focuses on the problem of globally exponential synchronization of impulsive dynamical networks two types of impulses are considered synchronizing impulses and desynchronizing impulses in previous literature all of the results are devoted to investigating these two kinds of impulses separately thus a natural question arises is there any unified synchronization criterion which is simultaneously effective for synchronizing impulses and desynchronizing impulses in this paper a unified synchronization criterion is derived for directed impulsive dynamical networks by proposing a concept named average impulsive interval the derived criterion is theoretically and numerically proved to be less conservative than existing results numerical examples including scale free and small world structures are given to show that our results are applicable to large scale networks

advanced sampled data synchronization control for complex dynamical networks with coupling time varying delays abstract this study addresses sampled data control in the synchronization problem of complex dynamical networks systems with a coupling time varying delay by constructing the augmented lyapunov krasovskii functionals and using some mathematical techniques a sampled data synchronization criterion is derived as the first result with the framework of linear matrix inequalities based on the first result a sampled data synchronization control method is proposed as the second result finally the effectiveness and superiority of the proposed results will be shown by comparing the maximum sampling period with the established results in two numerical examples

synchronization of a complex dynamical network with coupling time varying delays via sampled data control abstract in this paper the synchronization problem of a complex dynamical network with coupling time varying delays via delayed sampled data controller is investigated in order to make full use of the sawtooth structure characteristic of the sampling input delay a discontinuous lyapunov functional is proposed based on the extended wirtinger inequality from a convex representation of the sector restricted nonlinearity in system dynamics the stability condition based on lyapunov stability theory is obtained by utilization of linear matrix inequality formulation to find the controller which achieves the synchronization of a complex dynamical network with coupling time varying delay finally two numerical examples are given to illustrate the effectiveness of the proposed methods

exponential estimates and stabilization of uncertain singular systems with discrete and distributed delays this paper is concerned with exponential estimates and stabilization for a class of uncertain singular systems with discrete and distributed delays a sufficient condition which does not only guarantee the exponential stability and admissibility but also gives the estimates of decay rate and decay coefficient is established in terms of the linear matrix inequality lmi technique and a new lyapunov krasovskii functional the estimating procedure is implemented by solving a set of lmis which can be checked easily by effective algorithms under the proposed condition the algebraic subsystems possess the same decay rate as the differential ones moreover a state feedback stabilizing controller which makes the closed loop system exponentially stable and admissible with a prescribed lower bound of the decay rate is designed numerical examples are provided to illustrate the effectiveness of the theoretical results

synchronization of nonlinear singularly perturbed complex networks with uncertain inner coupling via event triggered control this study is concerned with the synchronization problem of nonlinear singularly perturbed complex networks with time varying coupling delays in an aim to shrink the treatment of network resources event triggered control strategy is proposed to achieve the synchronization criteria by developing the novel lyapunov krasovskii functional some adequate conditions which ensure the asymptotic synchronization are obtained in the form of linear matrix inequalities besides that synchronization problem of nonlinear singularly perturbed complex networks with uncertain inner coupling are also taken into account the uncertain inner coupling is represented by making use of the interval matrix approach finally simulation results are displayed to show the efficacy of the proposed 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

observer based output feedback control of linear systems with input and output delays abstract this paper is concerned with observer based output feedback control of linear systems with both multiple input and output delays our recently developed truncated predictor feedback tpf approach for state feedback stabilization of time delay systems is generalized to the design of observers by imposing some restrictions on the open loop system two classes of observer based output feedback controllers one being finite dimensional and the other infinite dimensional are constructed it is further shown that the infinite dimensional observer based output feedback controllers can be generalized to linear systems with both time varying input and output delays it is also shown that the separation principle holds for the infinite dimensional observer based output feedback controllers but does not hold for the finite dimensional ones numerical examples are worked out to illustrate the effectiveness of the proposed approaches

extended dissipative synchronization of complex dynamical networks with additive time varying delay and discrete time information abstract the problem of extended dissipativity analysis of complex dynamical networks with additive time varying delays and discrete time information is considered in this article by utilizing the lyapunov functional method jensen s inequality and free weighting matrix analysis techniques we established sufficient criterion such that the complex dynamical networks is synchronized further the extended dissipativity analysis problem which contains h performance passivity performance and l 2 l performance in a unified framework is studied the derived criteria are expressed in terms of linear matrix inequalities that can be easily checked by using the standard numerical softwares illustrative examples are presented to demonstrate the effectiveness and usefulness of the proposed 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