robust stability and stabilisation of 2d discrete state delayed systems abstract in this paper we first present sufficient stability and robust stability conditions for discrete linear state delayed 2d systems in terms of linear matrix inequalities all results are obtained with fornasini marchesini delay model but appropriate transformation to the corresponding roesser form is provided as well generalisation to the multiple state delayed case is also given then the stabilisation and robust stabilisation using static state feedback are studied stabilising feedback gain matrices are constructed based on the solutions of certain linear matrix inequalities an numerical example is used to illustrate the effectiveness of the approach

degenerate first order inverse problems in banach spaces abstract we are concerned with an inverse problem for a degenerate linear evolution equation of first order both hyperbolic and parabolic cases will be considered we indicate sufficient conditions for the existence and uniqueness of a solution all the results can be applied to inverse problems for equations from mathematical physics as a possible application of the abstract theorems some examples of partial differential equations are given

impulses induced p exponential input to state stability for a class of stochastic delayed partial differential equations abstractthis paper proposes a new stability concept called p exponential input to state stability piss for impulsive stochastic delayed partial differential equations isdpdes by employing the

goodness of fit problem and scanning innovation martingales this paper is mainly devoted to the following statistical problem in the case of random variables of any finite dimension and both simple or parametric hypotheses how to construct convenient empirical processes which could provide the basis for goodness of fit tests more or less in the same way as the uniform empirical process does in the case of simple hypothesis and scalar random variables the solution of this problem is connected here with the theory of multiparameter martingales and the theory of function parametric processes namely for the limiting gaussian processes some kind of filtration is introduced and so called scanning innovation processes are constructed the adapted standard wiener processes in one to one correspondence with initial gaussian processes this is done for the function parametric versions of the processes

global finite time stabilisation for a class of stochastic high order time varying nonlinear systems abstractin this paper the problem of global finite time stabilisation by state feedback is investigated for a class of stochastic high order nonlinear systems with time varying nonlinearities based on the generalised stochastic lyapunov theorem on finite time stability and by skillfully using the method of adding a power integrator a continuous state feedback controller is successfully constructed to guarantee that the closed loop system is globally finite time stable in probability finally several simulation examples are provided to illustrate the effectiveness of the proposed method

adding one power integrator a tool for global stabilization of high order lower triangular systems a new feedback design tool called adding a power integrator is introduced and used to solve the problem of global robust stabilization for a significant class of uncertain nonlinear systems that are of a lower triangular form but neither necessarily feedback linearizable fully or partially nor affine in the control input and therefore cannot be dealt with via conventional approaches sufficient conditions are presented under which a globally stabilizing smooth state feedback control law can be explicitly constructed using repeatedly the adding one power integrator technique this novel design technique permits removal of the feedback linearizability and linearity of the control input which have been two common assumptions so far in the literature of nonlinear control

finite time output feedback control for a class of stochastic low order nonlinear systems abstractthis paper discusses the problem of finite time stabilisation for a class of stochastic low order nonlinear systems via output feedback by generalising the adding a power integrator technique constructing an implementable reduced order observer and using the stochastic finite time stability criterion a finite time output feedback controller is presented to guarantee that the closed loop system is finite time stable in probability a simulation example is provided to verify the effectiveness of the proposed design method

almost sure exponential stability of stochastic fluid networks with nonlinear control due to the objective of controlling fluid flows fluid networks are high order nonlinear stochastic systems in essential taking the nonlinearities in pressure drop of fan branch measurement error

input output finite region stability and stabilization for discrete 2 d fornasini marchesini models abstract this paper establishes input output finite region stability i o frs and stabilization analysis methods to investigate the transient behavior of output signals for discrete two dimensional 2 d fornasini marchesini fm models for 2 d systems with two classes of input signals by building special recursive formulas sufficient i o frs conditions are formulated in terms of solvability of linear matrix inequalities lmis furthermore aiming at designing static state feedback controllers i o finite region stabilization issues are analyzed for the corresponding 2 d systems and sufficient conditions are reported to guarantee i o frs of the closed loop systems to conclude the paper we provide some numerical examples to confirm the validity of the proposed methods

finite time stabilization of stochastic nonlinear systems in strict feedback form in this paper we investigate the problem of almost surely finite time stabilization of a class of stochastic nonlinear systems based on the recently proposed almost surely finite time stability theorem in yin khoo man and yu 2011 we prove that almost surely global finite time stability of stochastic nonlinear systems in strict feedback form can be guaranteed by a continuous control law a systematic design algorithm is developed for the construction of the controller simulation results are given to illustrate the theoretical analysis

finite time stability and stabilization of nonlinear stochastic hybrid systems this paper deals with the problem of finite time stability and stabilization of nonlinear markovian switching stochastic systems which exist impulses at the switching instants using multiple lyapunov function theory a sufficient condition is established for finite time stability of the underlying systems furthermore based on the state partition of continuous parts of systems a feedback controller is designed such that the corresponding impulsive stochastic closed loop systems are finite time stochastically stable a numerical example is presented to illustrate the effectiveness of the proposed method

fixed time stability theorem of stochastic nonlinear systems to solve the fixed time stability problem for stochastic systems which has not been investigated due to the difficulty caused by the existence of stochastic the fixed time stability is investigat

checking the cox model with cumulative sums of martingale based residuals summary this paper presents a new class of graphical and numerical methods for checking the adequacy of the cox regression model the procedures are derived from cumulative sums of martingale based residuals over follow up time and or covariate values the distributions of these stochastic processes under the assumed model can be approximated by zero mean gaussian processes each observed process can then be compared both visually and analytically with a number of simulated realizations from the approximate null distribution these comparisons enable the data analyst to assess objectively how unusual the observed residual patterns are special attention is given to checking the functional form of a covariate the form of the link function and the validity of the proportional hazards assumption an omnibus test consistent against any model misspecification is also studied the proposed techniques are illustrated with two real data sets

stochastic nonlinear stabilization i a backstepping design while the current robust nonlinear control toolbox includes a number of methods for systems affine in deterministic bounded disturbances the problem when the disturbance is unbounded stochastic noise has hardly been considered we present a control design which achieves global asymptotic lyapunov stability in probability for a class of strict feedback nonlinear continuous time systems driven by white noise in a companion paper we develop inverse optimal control laws for general stochastic systems affine in the noise input and for strict feedback systems a reader of this paper needs no prior familiarity with techniques of stochastic control

mean square stability and almost sure exponential stability of two step maruyama methods of stochastic delay hopfield neural networks abstract in this paper the two step maruyama methods of stochastic delay hopfield neural networks are studied we have found that under what choices of step size the two step maruyama methods of stochastic delay hopfield networks maintain the stability of exact solutions the mean square stability of two step maruyama methods of stochastic delay hopfield neural networks is investigated under suitable conditions also the almost sure exponential stability of two step maruyama methods of stochastic delay hopfield networks is proved using the semi martingale convergence theorem further the comparisons of stability conditions to the previous results in liu and zhu 2015 rathinasamy 2012 and ronghua et al 2010 are given numerical experiments are provided to illustrate our theoretical results

goodness of fit tests in models for life history data based on cumulative hazard rates to check the validity of an assumed parametric model for survival data one may compare t the nonparametric nelson aalen plot of the cumulative hazard rate with a t the estimated parametric cumulative hazard rate being for example the maximum likelihood estimator convergence in distribution of n t a t and more general processes is studied employing the general framework of counting processes which allows for quite general models for life history data and for quite general censoring schemes the results are applied to the construction of 2 type statistics for goodness of fit cramer von mises and kolmogorov smirnov type tests are presented in the case where the unknown parameter is one dimensional

mean square exponential stability of stochastic nonlinear delay systems abstractin this paper we are concerned with the stability of stochastic nonlinear delay systems different from the previous literature we aim to show that when the determinate nonlinear delay system is globally exponentially stable the corresponding stochastic nonlinear delay system can be mean square globally exponentially stable in particular we remove the linear growth condition and introduce a new polynomial growth condition for g x t x t t which overcomes the limitation of application scope and the boundedness of diffusion term form finally we provide an example to illustrate our results

robust h_ infty filtering for two dimensional uncertain linear discrete time varying systems a krein space based method a robust h infty filtering algorithm is proposed for two dimensional 2 d linear uncertain time varying systems in this study the considered 2 d systems are subject to unknown inputs measurement noises and time varying modeling uncertainties to appropriately deal with the system uncertainties a new problem formulation of robust h infty filter design for 2 d uncertain systems is first presented by introducing an alternative indefinite quadratic performance function in lieu of the standard h infty performance index then the robust 2 d h infty filter design is converted to an optimization problem of finding the positive minimum of the new indefinite quadratic performance function under certain conditions by relating this quadratic form to a specific 2 d state space model in krein space the krein space estimation theory is used to solve the reformulated optimization problem a recursive robust 2 d time varying h infty filter and its explicit condition for the existence are obtained through projection techniques in 2 d krein space one thermal process plant is used to illustrate the effectiveness of the proposed filter

stability analysis of stochastic delayed systems with an application to multi agent systems this technical note is concerned with the stability problem of stochastic delayed systems by using a more general halanay type inequality with time varying coefficients a new comparison principle of the proposed halanay type inequality is developed to ensure the stability of stochastic delayed systems the p th moment stability p th moment asymptotic stability and p th moment exponential stability are investigated by means of the proposed general halanay type inequality two examples including one of the consensus of multi agent systems with time varying topologies and transmission delays are presented to demonstrate the effectiveness of the proposed results

brief paper finite time stability and instability of stochastic nonlinear systems this paper presents a new definition of finite time stability for stochastic nonlinear systems this definition involves stability in probability and finite time attractiveness in probability an important lyapunov theorem on finite time stability for stochastic nonlinear systems is established a theorem extending the stochastic lyapunov theorem is also proved moreover an example and a lemma are presented to illustrate the scope of extension a useful inequality extended from bihari s inequality is derived which plays an important role in showing the lyapunov theorem finally a lyapunov theorem on finite time instability is proved which states that almost surely globally asymptotical stability is not equivalent to finite time stability for some stochastic systems two simulation examples are given to illustrate the theoretical analysis

finite region dissipative dynamic output feedback control for 2 d fm systems with missing measurements abstract this paper focuses on the finite region dissipative dynamic output feedback control problem for a class of discrete time two dimensional 2 d fornasini marchesini fm systems with missing measurements firstly the definitions of finite region boundedness frb and finite region t s r dissipativity are introduced for 2 d fm systems secondly sufficient conditions on the frb and finite region t s r dissipativity of the resultant closed loop 2 d systems are obtained by the construction of the lyapunov function and the special recursive formulas thirdly based on the decoupling technique the desired dynamic output feedback controller design method for the considered 2 d systems is further provided in the end an example of the metal rolling process is given to show the effectiveness of the proposed design results

finite time and fixed time synchronization control of discontinuous fuzzy cohen grossberg neural networks with uncertain external perturbations and mixed time delays abstract this paper aims to investigate the synchronization control of a class of discontinuous fuzzy cohen grossberg neural networks dfcgnns with uncertain external perturbations and mixed time delays discrete and distributed time delays by using functional differential inclusions theory inequality technique and the non smooth analysis of lyapunov krasovskii functional a simple switching adaptive control is designed and some new criteria are obtained to achieve the finite time synchronization of the proposed drive response systems besides the upper bound of the settling time is estimated based on the finite time synchronization we further present a novel discontinuous state feedback controller to the response neural system in order to derive the fixed time synchronization criteria and estimate the settling time compared with the previous results which can only fixed timely synchronize or finite timely synchronize some simple delayed fuzzy neural network systems with continuous activation functions and without uncertain external perturbations the dfcgnns with uncertain external perturbations and mixed time delays addressed and the theoretical results of this paper are more generalized and inclusive finally several simulation examples and remarks are provided to verify the correctness and advantages of the main results

an omnibus test for independence of a survival time from a covariate it has been over 60 years since kolmogorov introduced a distribution free omnibus test for the simple null hypothesis that a distribution function coincides with a given distribution function doob subsequently observed that kolmogorov s approach could be simplified by transforming the empirical process to an empirical process based on uniform random variables recent use of more sophisticated transformations has led to the construction of asymptotically distribution free omnibus tests when unknown parameters are present the purpose of the present paper is to use the transformation approach to construct an asymptotically distribution free omnibus test for independence of a survival time from a covariate the test statistic is obtained from a certain test statistic process indexed by time and covariate which is shown to converge in distribution to a brownian sheet a simulation study is carried out to investigate the finite sample properties of the proposed test and an application to data from the british medical research council s 4th myelomatosis trial is given

brief paper adaptive state feedback stabilization for a large class of high order stochastic nonlinear systems under the more general conditions on the power order and the nonlinear functions this paper investigates the problem of adaptive state feedback stabilization for a class of high order stochastic nonlinear systems with time varying control coefficients based on the backstepping design method and homogeneous domination technique the closed loop system can be proved to be globally stable in probability and the states can be regulated to the origin almost surely the efficiency of the state feedback controller is demonstrated by a simulation example

lmi stability conditions for 2d roesser models this note is devoted to the stability analysis of linear two dimensional systems described by continuous discrete or mixed roesser models commonly used polynomial based tests of stability are reduced to that of solving a set of linear matrix inequalities the main contribution is that the approach is very general and the criteria under certain hypothesis are not conservative

finite time stabilization of high order stochastic nonlinear systems in strict feedback form this paper deals with the problem of finite time stabilization for a class of high order stochastic nonlinear systems in strict feedback form by using ito s formula mathematical induction and backstepping design method a novel state feedback controller is constructed to guarantee that the closed loop high order nonlinear system has a unique solution and the solution of the closed loop high order nonlinear system is finite time stable a systematic design algorithm is developed for the construction of the backstepping controller finally the effectiveness of the state feedback controller is illustrated by two examples

stochastic stability analysis for 2 d roesser systems with multiplicative noise this paper is concerned with the robust stochastic stability analysis for two dimensional 2 d discrete state multiplicative noisy systems smnss in the roesser form we first derive a new sufficient condition under which linear discrete 2 d smnss are 2 d robustly stochastically stable the underlying problem can then be recast as a convex problem expressed by linear matrix inequalities which can be facilitated using existing numerical algorithms we then apply the obtained result to examine the 2 d robust stochastic stability for 2 d digital filters in the roesser form with random coefficient variation and saturation overflow arithmetic based on free weighting matrices and diagonally dominant matrices an illustrative example is presented to verify the usefulness and potential of the proposed results

robust global stabilization of a class of uncertain feedforward nonlinear systems abstract the problem of global asymptotically stabilizing a certain class of uncertain feedforward nonlinear systems is considered the control law is obtained by nesting saturation functions whose amplitude can be rendered arbitrarily small with respect to previous works on the subject the design procedure is able to deal with uncertain possibly time varying parameters ranging within the prescribed compact sets which can affect also the linear approximation of the system the small gain theorem for nonlinear systems which are input to state stable with restrictions is shown to be a key tool for designing a state feedback saturated control law

new lyapunov conditions of stochastic finite time stability and instability of nonlinear time varying sdes in this paper we further consider the problem of stochastic finite time stability and instability of nonlinear stochastic differential equations sdes with time varying drift and diffusion terms

finite time stability analysis for markovian jump memristive neural networks with partly unknown transition probabilities this paper is concerned with the finite time stochastically stability ftss analysis of markovian jump memristive neural networks with partly unknown transition probabilities in the neural networks there exist a group of modes determined by markov chain and thus the markovian jump was taken into consideration and the concept of ftss is first introduced for the memristive model by introducing a markov switching lyapunov functional and stochastic analysis theory an ftss test procedure is proposed from which we can conclude that the settling time function is a stochastic variable and its expectation is finite the system under consideration is quite general since it contains completely known and completely unknown transition probabilities as two special cases more importantly a nonlinear measure method was introduced to verify the uniqueness of the equilibrium point compared with the fixed point theorem that has been widely used in the existing results this method is more easy to implement besides the delay interval was divided into four subintervals which make full use of the information of the subsystems upper bounds of the time varying delays finally the effectiveness and superiority of the proposed method is demonstrated by two simulation examples

finite time state feedback stabilisation of stochastic high order nonlinear feedforward systems abstractthis paper studies the finite time state feedback stabilisation of stochastic high order nonlinear feedforward systems based on the stochastic lyapunov theorem on finite time stability by using the homogeneous domination method the adding one power integrator and sign function method constructing a c2 lyapunov function and verifying the existence and uniqueness of solution a continuous state feedback controller is designed to guarantee the closed loop system finite time stable in probability

technical communique finite time stability theorem of stochastic nonlinear systems a new concept of finite time stability called stochastically finite time attractiveness is defined for a class of stochastic nonlinear systems described by the ito differential equation the settling time function is a stochastic variable and its expectation is finite a theorem and a corollary are given to verify the finite time attractiveness of stochastic systems based on lyapunov functions two simulation examples are provided to illustrate the applications of the theorem and the corollary established in this paper

brief paper finite time control of discrete time linear systems analysis and design conditions in this paper we deal with some finite time control problems for discrete time time varying linear systems first we provide necessary and sufficient conditions for finite time stability these conditions require either the computation of the state transition matrix of the system or the solution of a certain difference lyapunov inequality then we address the design problem the proposed conditions allow us to find output feedback controllers which stabilize the closed loop system in the finite time sense all these conditions can be expressed in terms of lmis and therefore are numerically tractable as shown in the example included in the paper

brief paper h filtering for 2d markovian jump systems this paper is concerned with the problem of h filtering for 2d discrete markovian jump systems the mathematical model of 2d jump systems is established upon the well known roesser model our attention is focused on the design of a full order filter which guarantees the filtering error system to be mean square asymptotically stable and has a prescribed h disturbance attenuation performance sufficient conditions for the existence of a desired filter are established in terms of linear matrix inequalities lmis and the corresponding filter design is cast into a convex optimization problem which can be efficiently solved by using commercially available numerical software a numerical example is provided to illustrate the effectiveness of the proposed design method

state feedback stabilization for stochastic feedforward nonlinear systems with time varying delay this paper investigates a class of stochastic feedforward nonlinear systems with time varying delay by introducing the homogeneous domination approach to stochastic systems a state feedback controller is constructed to render the closed loop system globally asymptotically stable in probability

projection method for solving degenerate first order identification problem in this paper we study an inverse problem for a degenerate differential equation on a banach space a projection method will be used to reduce the problem to a regular abstract inverse problem to this end some conditions on the operators are assumed to avoid the calculations of some inverses of the involved operators

smoothed cox regression nonparametric regression was shown by beran and mckeague and utikal to provide a flexible method for analysis of censored failure times and more general counting processes models in the presence of covariates we discuss application of kernel smoothing towards estimation in a generalized cox regression model with baseline intensity dependent on a covariate under regularity conditions we show that estimates of the regression parameters are asymptotically normal at rate root n and we also discuss estimation of the baseline cumulative hazard function and related parameters

identification problems for singular integro differential equations of parabolic type ii abstract we recover unknown kernels depending on time only in linear singular first order integro differential cauchy problems in banach spaces singular means here that the integro differential equation is not in normal form nor it can be reduced to such a form for this class of problems we prove an existence and uniqueness theorem in the framework of general banach spaces under the condition that the resolvent operator cf 1 5 admits a polar singularity at 0 see section 3 moreover when the banach space under consideration is reflexive we can prove a local in time existence and uniqueness result when the resolvent operator decays as 1 1 finally we give a few applications to explicit singular partial integro differential equations of parabolic type

new criteria on finite time stability of fractional order hopfield neural networks with time delays in this article the finite time stability fts of fractional order hopfield neural networks with time delays fhnntds is studied a widely used inequality in investigating the stability of the fractional order neural networks is fractional order gronwall inequality related to the mittag leffler function which cannot be directly used to study the stability of the factional order neural networks with time delays in the existing works related to fractional order gronwall inequality with time delays the order 0 was divided into two cases 0 0 5 and 0 5 in this article a new fractional order gronwall integral inequality with time delay and the unified form for all the fractional order 0 is developed which can be widely applied to investigate fts of various fractional order systems with time delays based on this new inequality a new criterion for the fts of fhnntds is derived compared with the existing criteria in which fractional order 0 1 was divided into two cases 0 0 5 and 0 5 1 the obtained results in this article are presented in the unified form of fractional order 0 1 and convenient to verify more importantly the criteria in this article are less conservative than some existing ones finally two numerical examples are given to demonstrate the validity of the proposed results

dissipativity analysis and synthesis for discrete time t s fuzzy stochastic systemswith time varying delay this paper is concerned with the problems of dissipativity analysis and synthesis for discrete time takagi sugeno fuzzy systems with stochastic perturbation and time varying delay first a novel model transformation method is introduced to pull the time varying delay uncertainty out of the original system consequently the transformed model is composed of a linear time invariant system and a norm bounded uncertain subsystem by using this model transformation method combined with the lyapunov krasovskii technique sufficient conditions of the dissipativity are established then a fuzzy controller is designed to guarantee the dissipative performance of the closed loop system finally three examples are presented one shows the effectiveness of model transformation method the second performs the comparison with alternative approaches and the third illustrates the applicability of the proposed dissipative control methods

distributed h state estimation for stochastic delayed 2 d systems with randomly varying nonlinearities over saturated sensor networks in this paper the distributed h state estimation problem is investigated for the two dimensional 2 d time delay systems the target plant is characterized by the generalized fornasini marchesini 2 d equations where both stochastic disturbances and randomly varying nonlinearities rvns are considered the sensor measurement outputs are subject to saturation restrictions due to the physical limitations of the sensors based on the available measurement outputs from each individual sensor and its neighboring sensors the main purpose of this paper is to design distributed state estimators such that not only the states of the target plant are estimated but also the prescribed h disturbance attenuation performance is guaranteed by defining an energy like function and utilizing the stochastic analysis as well as the inequality techniques sufficient conditions are established under which the augmented estimation error system is globally asymptotically stable in the mean square and the prescribed h performance index is satisfied furthermore the explicit expressions of the individual estimators are also derived finally numerical example is exploited to demonstrate the effectiveness of the results obtained in this paper

identifying nonlinear covariate effects in semimartingale regression models letxt be a semimartingale which is either continuous or of counting process type and which satisfies the stochastic differential equationdxt yt t zt dt dmt wherey andz are predictable covariate processes m is a martingale and is an unknown nonrandom function we study inference for by introducing an estimator for a t z int limits 0 z int limits 0 t alpha s x dsdx and deriving a functional central limit theorem for the estimator the asymptotic distribution turns out to be given by a gaussian random field that admits a representation as a stochastic integral with respect to a multiparameter wiener process this result is used to develop a test for independence ofx from the covariatez a test for time homogeneity of and a goodness of fit test for the proportional hazards model t z 1 t a2 z used in survival analysis