quantile and quantile function estimations under density ratio model 1 introduction forestry plays a major role in the canadian economy maintaining the high quality of wood products is vital economically and socially we are designing an effective long term monitoring plan for the quality of forestry products in canada two important quality indices for a piece of lumber are the modulus of elasticity moe and the modulus of rupture mor its strength in terms of elasticity and toughness the reliability of lumber based structures may depend heavily on the lower population quantiles of these indices however it is costly time consuming and laborious to obtain these quality measurements therefore efficient estimates of the population quantiles and their functions are important the estimation of quantiles based on a single random sample is a wellresearched topic empirical quantiles have been shown to admit a bahadur representation bahadur 1966 kiefer 1967 serfling 1980 making it simple to study the joint limiting distributions of any number of sample quantiles and their smooth functions in the presence of auxiliary information the empirical likelihood el owen 1988 2001 can be utilized to improve efficiency the bahadur

on the distribution of inversive congruential pseudorandom numbers in parts of the period the inversive congruential method is an attractive alternative to the classical linear congruential method for pseudorandom number generation in this paper we present the first nontrivial bounds on the discrepancy of individual sequences of inversive congruential pseudorandom numbers in parts of the period the proof is based on a new bound for certain incomplete exponential sums

sequences related to legendre jacobi sequences two families of binary sequences are constructed from dth order cyclotomic generator and from dth order generalized cyclotomic generator with respect to two distinct primes respectively by using estimates of certain exponential sums over rings or fields the upper bounds of both the well distribution measure and the order k at least for small k correlation measure of the resulting binary sequences are evaluated and some lower bounds on the linear complexity profile of d ary cyclotomic sequences and d ary generalized cyclotomic sequences are presented our results indicate that such binary sequences possess very good local pseudo randomness

on symmetric semiparametric two sample problem we consider a two sample problem where data come from symmetric distributions usual two sample data with only magnitudes recorded arising from case control studies or logistic discriminant analyses may constitute a symmetric two sample problem we propose a semiparametric model such that in addition to symmetry the log ratio of two unknown density functions is modeled in a known parametric form the new semiparametric model tailor made for symmetric two sample data can also be viewed as a biased sampling model subject to symmetric constraint a maximum empirical likelihood estimation approach is adopted to estimate the unknown model parameters and the corresponding profile empirical likelihood ratio test is utilized to perform hypothesis testing regarding the two population distributions symmetry however comes with irregularity it is shown that under the null hypothesis of equal symmetric distributions the maximum empirical likelihood estimator has degenerate fisher information and the test statistic has a mixture of 2 type asymptotic distribution extensive simulation studies have been conducted to demonstrate promising statistical powers under correct and misspecified models we apply the proposed methods to two real examples

cryptographic properties of some binary generalized cyclotomic sequences with the length p2 herein the cryptographic properties of some generalized cyclotomic sequences with the period p 2 are investigated results show that these sequences always possess good balance and linear complexity larger than half the period their autocorrelation functions are shown to be three valued if p 3 mod4 and five valued otherwise moreover the distribution of patterns of length 2 are discussed

new finite sum inequalities with applications to stability of discrete time delay systems this paper is concerned with the problem of stability analysis of discrete time delay systems new finite sum inequalities which encompass the ones based on abel lemma or wirtinger type inequality are first proposed the potential capability of the newly derived inequalities is then demonstrated by establishing less conservative stability conditions for some classes of linear discrete time systems with delay the derived stability criteria are theoretically and numerically proved to be less conservative than existing results

exponential stabilization of switched time varying systems with delays and disturbances abstract this paper deals with exponential stabilization for a class of switched time varying systems by taking time varying delays and nonlinear disturbances into consideration time dependent switching signals have been characterized in terms of metzler matrices such that the resulting system is globally exponentially stable compared with preceding works we introduce a model transformation and an approach without involving the lyapunov krasovskii functional to derive new exponential stability criteria for switched time varying systems under the average dwell time switching numerical examples show that the obtained theoretical results can be applied to some cases not covered by some existing results

some notes on the two prime generator of order 2 the two prime generator of order 2 has several desirable randomness properties if the two primes are chosen properly in particular ding deduced exact formulas for the periodic autocorrelation and the linear complexity of these sequences in this note we analyze parts of the period of the two prime generator of order 2 and obtain bounds on the aperiodic autocorrelation and linear complexity profile

transformations of the explanatory variables in the logistic regression model for binary data summary some results are presented on improving the fit of the logistic regression model for binary data by transforming the vector of explanatory variables the methods are based on consideration of the distributions of these variables conditional on outcome group the transformations required are the functions of the explanatory variables which appear in the log density ratio of the conditional distributions

new criteria for exponential stability of nonlinear difference systems with time varying delay general nonlinear time varying difference systems with time varying delay are considered some new explicit criteria for global exponential stability are given two examples are given to illustrate the obtained results

on the 2 adic complexity of the two prime generator hu introduced a simple method to compute the 2 adic complexity of any periodic binary sequence with ideal two level autocorrelation we extend this approach to some other sequences first we provide a substantially shorter proof of the maximality of the 2 adic complexity of the legendre sequence of period n equiv 1 bmod 4 first proved by xiong et al then we show that the 2 adic complexity of the two prime generator of period pq with two odd primes p ne q attains the maximum if q 1 4 le p le 4q 1 this result was only known for twin primes q p 2 before for arbitrary odd primes p ne q we can still prove that the 2 adic complexity of the two prime generator is close to its period

technical communique reachable set bounding for delayed systems with polytopic uncertainties the maximal lyapunov krasovskii functional approach this paper deals with the problem of reachable set estimation for time delay systems subject to both polytopic parameter uncertainties and bounded peak inputs the maximal lyapunov krasovskii functional is constructed as the pointwise maximum of a family of lyapunov krasovskii functionals each functional corresponds to a vertex of uncertain polytope some criteria bounding the reachable set are derived this approach shows great advantages over the traditional methods based on the common lyapunov functionals by introducing a modified integral inequality the limitation imposed on the derivative of time delay being less than one is relaxed furthermore the obtained results involve less computational burden when the number of vertices of the polytope is small two examples are given to illustrate the theoretical results

technical communique improved delay range dependent stability criteria for linear systems with time varying delays this paper is concerned with the stability analysis of linear systems with time varying delays in a given range a new type of augmented lyapunov functional is proposed which contains some triple integral terms in the proposed lyapunov functional the information on the lower bound of the delay is fully exploited some new stability criteria are derived in terms of linear matrix inequalities without introducing any free weighting matrices numerical examples are given to illustrate the effectiveness of the proposed method

robust exponential convergence of a class of linear delayed systems with bounded controllers and disturbances this brief paper deals with the problem of robust exponential stabilization of a class of dynamic systems subject to time varying delays external disturbances and control saturation a linear memoryless state feedback controller is synthesized to guarantee that there is a domain of admissible initial conditions from which all solutions of the class of systems considered converge exponentially to a ball with a prespecified convergence rate the problem is formulated as a two step optimization problem with matrix inequality constraints to enlarge the size of the ball of admissible initial conditions

bounds and invariant sets for a class of discrete time switching systems with perturbations we present a novel method to compute componentwise ultimate bounds and invariant regions for a class of switching discrete time linear systems with perturbation bounds that may depend nonlinearly on a delayed state the method has the important advantage that it allows each component of the perturbation vector to have an independent bound and that the bounds and sets obtained are also given componentwise this componentwise method does not employ a standard norm for bounding either the perturbation or state vectors and thus may avoid conservativeness due to different perturbation or state vector components having substantially different bounds we also establish the relationship between the class of switching linear systems to which the proposed method can be applied and those that admit a common quadratic lyapunov function we illustrate the application of our method via numerical examples including the fault tolerance analysis of the feedback control of a winding machine

e bounded state estimation for time delay systems with bounded disturbances a new problem on e bounded functional state estimation for time delay systems with unknown bounded disturbances is studied in this paper in the presence of unknown bounded disturbances the common assumption regarding the observer s matching condition is no longer required in this regard instead of achieving asymptotic convergence for the observer error the error is now required to converge exponentially within a ball with a small radius e 0 this means that the estimate converges exponentially within an e bound of the true value a general observer that utilises multiple delayed output and input information is proposed sufficient conditions for the existence of the proposed observer are first given we then employ an extended lyapunov krasovskii functional which combines the delay decomposition technique with a triple integral term to study the e convergence problem of the observer error system moreover the obtained results are shown to be more effective than the existing results for the cases w

technical communique further result on reachable set bounding for linear uncertain polytopic systems with interval time varying delays the problem of reachable set estimation of linear uncertain polytopic time varying delay systems subject to bounded peak inputs is studied in this paper the delays considered in this paper are assumed to be non differentiable and vary within an interval where the lower and upper bounds are known based on the lyapunov krasovskii method and delay decomposition technique a sufficient condition for the existence of a ball that bounds the reachable set of the system is proposed in terms of matrix inequalities containing only one scalar which can be solved by using an one dimensional search method and matlab s lmi toolbox and allow us to find the smallest radius a numerical example is given to illustrate the effectiveness of the proposed result

technical communique improved ellipsoidal bound of reachable sets for time delayed linear systems with disturbances we consider the problem of finding an ellipsoidal reachable set that bounds the states of time delayed linear systems with bounded peak disturbances the considered time delay is time varying but it has an upper bound in magnitude and rate based on the modified lyapunov krasovskii l k type functional we derive a delay dependent result expressed in the form of matrix inequalities containing only one non convex scalar the result is extended to uncertain time delayed linear systems finally we show the usefulness of our result by a comparative numerical example

a note on profile likelihood for exponential tilt mixture models suppose that independent observations are drawn from multiple distributions each of which is a mixture of two component distributions such that their log density ratio satisfies a linear model with a slope parameter and an intercept parameter inference for such models has been studied using empirical likelihood and mixed results have been obtained the profile empirical likelihood of the slope and intercept has an irregularity at the null hypothesis so that the two component distributions are equal we derive a profile empirical likelihood and maximum likelihood estimator of the slope alone and obtain the usual asymptotic properties for the estimator and the likelihood ratio statistic regardless of the null furthermore we show the maximum likelihood estimator of the slope and intercept jointly is consistent and asymptotically normal regardless of the null at the null the joint maximum likelihood estimator falls along a straight line through the origin with perfect correlation asymptotically to the first order

technical communique on reachable sets for linear systems with delay and bounded peak inputs linear systems with constant coefficients and time varying delays are considered we address the problem of finding an ellipsoid that bounds the set of the states in the euclidean space that are reachable from the origin in finite time by inputs with peak value that is bounded by a prechosen positive scalar the system may encounter uncertainties in the matrices of its state space model and in the delay length the lyapunov razumikhin approach is applied and a bounding ellipsoid is obtained by solving a set of linear matrix inequalities that depend on the upper bound of the delay length

on input to state stability of stochastic nonlinear systems with markovian jumping parameters in this article the input to state stability iss properties of stochastic nonlinear systems with markovian jump parameters are considered firstly the notions of stochastic iss e t weighted integral iss in mean and in the pth mean are introduced then by the lyapunov like function method some corresponding criteria are provided lastly a simulation example is provided to illustrate the effectiveness of our results

optimal sequences for channel estimation using discrete fourier transform techniques this paper addresses the problem of selecting the optimum training sequence for channel estimation in communication systems over time dispersive channels by processing in the frequency domain a new explicit form of search criterion is found the gain loss factor glf which minimizes the variance of the estimation error and is easy to compute theoretical upper and lower bounds on the glf are derived an efficient directed search strategy and optimal sequences up to length 42 are given these sequences are optimal only for frequency domain estimation not for time domain estimation

componentwise ultimate bounds for positive discrete time delay systems perturbed by interval disturbances this paper presents a method to derive componentwise ultimate upper bounds and componentwise ultimate lower bounds for linear positive systems with time varying delays and bounded disturbances the disturbance vector is assumed to vary within a known interval whose lower bound may be different from zero we first derive a sufficient condition for the existence of componentwise ultimate bounds this condition is given in terms of the spectral radius of the system matrices which is easy to check and allows us to compute directly both the smallest componentwise ultimate upper bound and the largest componentwise ultimate lower bound then by using the comparison method we extend the obtained result to a class of nonlinear time delay systems which has linear positive bounds two numerical examples are given to illustrate the effectiveness of the obtained results

asymptotic behavior of switched delay systems with nonlinear disturbances the objective of this paper is to study the asymptotic behavior of switched delay systems with nonlinear disturbances by establishing a new delay gronwall bellman integral inequality and an elementary inequality we obtain some asymptotic results for the systems under arbitrary switching laws which extend some existing results in the literature to the more general nonlinear case finally two examples are provided to illustrate the effectiveness of our results

spectral density ratio models for multivariate extremes the modeling of multivariate extremes has received increasing recent attention because of its importance in risk assessment in classical statistics of extremes the joint distribution of two or more extremes has a nonparametric form subject to moment constraints this article develops a semiparametric model for the situation where several multivariate extremal distributions are linked through the action of a covariate on an unspecified baseline distribution through a so called density ratio model theoretical and numerical aspects of empirical likelihood inference for this model are discussed and an application is given to pairs of extreme forest temperatures supplementary materials for this article are available online

exponential ultimate boundedness of nonlinear stochastic difference systems with time varying delays in this paper we discuss the boundedness of nonlinear stochastic difference systems with time varying delays several criteria on exponential ultimate boundedness in mean square are derived examples are also discussed to illustrate the effectiveness of the obtained results

almost difference sets and their sequences with optimal autocorrelation almost difference sets have interesting applications in cryptography and coding theory we give a well rounded treatment of known families of almost difference sets establish relations between some difference sets and some almost difference sets and determine the numerical multiplier group of some families of almost difference sets we also construct six new classes of almost difference sets and four classes of binary sequences of period n spl equiv 0 mod 4 with optimal autocorrelation we have also obtained two classes of relative difference sets and four classes of divisible difference sets ddss we also point out that a result due to jungnickel 1982 can be used to construct almost difference sets and sequences of period 4l with optimal autocorrelation

autocorrelation values of generalized cyclotomic sequences of order two the generalized cyclotomic sequence of order two has several good randomness properties and behaves like the legendre sequence in several aspects we calculate the autocorrelation values of the generalized cyclotomic sequence of order two our result shows that this sequence could have very good autocorrelation property and pattern distributions of length two if the two primes are chosen properly

linear complexity of binary whiteman generalized cyclotomic sequences of order 2k in this correspondence we obtain the linear complexity and minimal polynomials of binary whiteman generalized cyclotomic sequences of order 2 k where k 1 our result shows that all of these sequences possess large linear complexity

on empirical likelihood for a semiparametric mixture model summary plant and animal studies of quantitative trait loci provide data which arise from mixtures of distributions with known mixing proportions previous approaches to estimation involve modelling the distributions parametrically we propose a semiparametric alternative which assumes that the log ratio of the component densities satisfies a linear model with the baseline density unspecified it is demonstrated that a constrained empirical likelihood has an irregularity under the null hypothesis that the two densities are equal a factorisation of the likelihood suggests a partial empirical likelihood which permits unconstrained estimation of the parameters and which is shown to give consistent and asymptotically normal estimators regardless of the null the asymptotic null distribution of the log partial likelihood ratio is chi squared theoretical calculations show that the procedure may be as efficient as the full empirical likelihood in the regular set up the usefulness of the robust methodology is illustrated with a rat study of breast cancer resistance genes

on the reachable set bounding of uncertain dynamic systems with time varying delays and disturbances in this paper improved conditions are proposed for finding an ellipsoidal bound of reachable sets which bound the state trajectories of uncertain dynamic systems with time varying delays and bounded peak disturbances a more generalized time derivative condition is considered in comparison with previous work by the use of convex hull properties and application of the lyapunov method sufficient conditions for finding an ellipsoidal bound of reachable sets of the concerned systems are established in terms of linear matrix inequalities lmis two numerical examples are included to show the superiority and effectiveness of our results

semiparametric inference in a genetic mixture model abstractin genetic backcross studies data are often collected from complex mixtures of distributions with known mixing proportions previous approaches to the inference of these genetic mixture models involve parameterizing the component distributions however model misspecification of any form is expected to have detrimental effects we propose a semiparametric likelihood method for genetic mixture models the empirical likelihood under the exponential tilting model assumption in which the log ratio of the probability density functions from the components is linear in the observations an application to mice cancer genetics involves random numbers of offspring within a litter in other words the cluster size is a random variable we wish to test the null hypothesis that there is no difference between the two components in the mixture model but unfortunately we find that the fisher information is degenerate as a consequence the conventional two term expansion in the likelihood ratio statistic doe

an ultimate state bound for a class of linear systems with delay abstract a new method is given to estimate an ultimate state bound on a time varying linear system with delay and bounded disturbances by using some results on metzler matrices the effectiveness of the obtained results is illustrated by a numerical example

empirical likelihood ratio based confidence intervals for mixture proportions we consider the problem of estimating a mixture proportion using data from two different distributions as well as from a mixture of them under the model assumption that the log likelihood ratio of the two densities is linear in the observations we develop an empirical likelihood ratio based statistic for constructing confidence intervals for the mixture proportion under some regularity conditions it is shown that this statistic converges to a chi squared random variable simulation results indicate that the performance of this statistic is satisfactory as a by product we give estimators for the two distribution functions connections with case control studies and discrimination analysis are pointed out

ultimate boundedness control for networked systems with try once discard protocol and uniform quantization effects this paper is concerned with the ultimate boundedness control problem for a class of networked nonlinear systems subject to the try once discard tod protocol scheduling and uniform quantization effects to prevent the transmission data from collisions the communication between sensor nodes and the controller is implemented via a constrained communication channel where only one sensor node is permitted to transmit data at each time instant the tod protocol is utilized to regulate the signal transmission over the communication network under which the scheduling behavior is described by a special switching function on the other hand the uniform quantization effects of the network are characterized by a round function i e the nearest integer function the purpose of the addressed problem is to design an observer based controller for the networked nonlinear systems such that in the presence of tod protocol and uniform quantization effects the closed loop system is ultimately bounded and the controlled output is locally minimized sufficient conditions are established to guarantee the ultimate boundedness of the dynamics of the closed loop system in mean square by applying the stochastic analysis approach furthermore the desired controller gains are derived by solving a convex optimization problem finally a numerical example is given to illustrate the effectiveness of the proposed controller design scheme

sliding mode control in the presence of input delay a singular perturbation approach sliding mode control smc in the presence of small unavoidable input delay as may be present in controller implementation is studied linear systems with bounded matched disturbances and uncertain system matrices are considered where input delay in the smc will produce oscillations or potentially even unbounded solutions without a priori knowledge of the bounds on the state dependent terms as required by existing methods the design objective is to achieve ultimate boundedness of the closed loop system with a bound proportional to the delay and disturbance bounds this is a non trivial problem because the relay gain depends on the state bound whereas the latter bound depends on the relay gain a controller with linear gain proportional to the scalar email protected is proposed which for small enough m 0 produces a closed loop singularly perturbed system and yields the desired ultimate bound a constructive linear matrix inequality lmi based solution for evaluation of both the design parameters and the ultimate bound is derived the superiority of the proposed control over existing methodologies that ignore input delay within the design is demonstrated through an example

on the convergence properties of the em algorithm two convergence aspects of the em algorithm are studied i does the em algorithm find a local maximum or a stationary value of the incomplete data likelihood function ii does the sequence of parameter estimates generated by em converge several convergence results are obtained under conditions that are applicable to many practical situations two useful special cases are a if the unobserved complete data specification can be described by a curved exponential family with compact parameter space all the limit points of any em sequence are stationary points of the likelihood function b if the likelihood function is unimodal and a certain differentiability condition is satisfied then any em sequence converges to the unique maximum likelihood estimate a list of key properties of the algorithm is included

a new approach to state bounding for linear time varying systems with delay and bounded disturbances abstract in this note the problem of state bounding for linear time varying systems with delay and bounded disturbances input is considered for the first time by using a novel approach which does not involve the lyapunov krasovskii functional method new explicit delay independent conditions are derived for the existence of a ball such that all the state trajectories of the system converge exponentially within it a numerical example is given to illustrate the effectiveness of the obtained result

on uniform ultimate boundedness of linear systems with time varying delays and peak bounded disturbances abstract this paper is devoted to a problem of uniform ultimate boundedness uub for a class of linear systems with interval time varying delays and peak bounded disturbances by using the lyapunov krasovskii functional method a general uub condition and an estimation of the ultimate bound on system trajectories are developed on the basis of the above results linear matrix inequality lmi conditions on uub of the perturbed systems under consideration are derived by constructing an appropriate lyapunov krasovskii functional meanwhile the ultimate bound for a prescribed disturbance attenuation level is given in the form of an ellipsoidal surface the feasibility and effectiveness of the derived results are illustrated by two numerical examples

exponential stability of time delay systems via new weighted integral inequalities in this paper new weighted integral inequalities wiis are first derived based on jensen s integral inequalities in single and double forms it is theoretically shown that the newly derived inequalities in this paper encompass both the jensen inequality and its most recent improvement based on wirtinger s integral inequality the potential capability of wiis is demonstrated through applications to exponential stability analysis of some classes of time delay systems in the framework of linear matrix inequalities lmis the effectiveness and least conservativeness of the derived stability conditions using wiis are shown by various numerical examples

brief paper componentwise ultimate bound and invariant set computation for switched linear systems we present a novel ultimate bound and invariant set computation method for continuous time switched linear systems with disturbances and arbitrary switching the proposed method relies on the existence of a transformation that takes all matrices of the switched linear system into a convenient form satisfying certain properties the method provides ultimate bounds and invariant sets in the form of polyhedral and or mixed ellipsoidal polyhedral sets is completely systematic once the aforementioned transformation is obtained and provides a new sufficient condition for practical stability we show that the transformation required by our method can easily be found in the well known case where the subsystem matrices generate a solvable lie algebra and we provide an algorithm to seek such transformation in the general case an example comparing the bounds obtained by the proposed method with those obtained from a common quadratic lyapunov function computed via linear matrix inequalities shows a clear advantage of the proposed method in some cases

brief paper razumikhin type stability theorems for discrete delay systems in this paper by employing the razumikhin technique and lyapunov functions razumikhin type theorems that guarantee the uniform stability uniformly asymptotic stability and uniformly exponential stability for the general discrete delay systems are established respectively moreover razumikhin type uniformly exponential stability theorem gives the estimation of the convergence speed as theoretic application the razumikhin type uniformly exponential stability result is further studied and used to show some well known stability results for some kinds of discrete delay systems finally examples are also worked through to illustrate our results

almost sure estimation and synthesis of ultimate bounds for discrete time markov jump linear systems this paper is concerned with the problems of almost sure ultimate bound estimation and controller design for markov jump linear systems with bounded stochastic disturbances by utilising a lyapunov based scheme proposed in this paper an almost sure estimation of ellipsoidal ultimate bound eub of the system is obtained through tractable matrix inequalities on the basis of the estimation results the problem of designing mode dependent state feedback controllers that make the closed loop system admit a prescribed ellipsoid as an eub is considered the obtained results on estimation and synthesis are then extended to the case of systems with deficient mode information finally a practical example in dc motor devices is presented to demonstrate the applicability of the obtained results

autocorrelation of legendre sidelnikov sequences we combine the concepts of the p periodic legendre sequence the q 1 periodic sidelnikov sequence and the two prime generator to introduce a new p q 1 periodic sequence called legendre sidelnikov sequence we show that this new sequence is balanced if p q for an arbitrary odd prime p and an arbitrary power q of an odd prime with gcd p q 1 1 we determine the exact values of its periodic autocorrelation function and deduce an upper bound on its aperiodic autocorrelation function showing that it is small compared to its period

moment stability of nonlinear discrete stochastic systems with time delays based on h representation technique in this paper mean square stability of nonlinear discrete stochastic systems with time delays is investigated we obtain the second order moment equations of discrete stochastic systems by virtue of the h representation technique by the comparison principle and the established moment equations some moment stability theorems for nonlinear discrete stochastic systems with time delays are established a numerical example is presented to illustrate the efficiency of our results at the end of the paper

stability analysis of nonlinear time delay systems using a novel piecewise positive systems method we propose a method that uses piecewise positive comparison systems to analyze the stability of nonlinear differential systems with time varying delays a new stability criterion is provided and two numerical examples are given to demonstrate the advantages of our obtained result

finite time stability of a class of non autonomous neural networks with heterogeneous proportional delays in this paper the problem of finite time stability analysis for a class of non autonomous neural networks with heterogeneous proportional delays is considered by introducing a novel constructive approach we derive new explicit conditions in terms of matrix inequalities ensuring that the state trajectories of the system do not exceed a certain threshold over a pre specified finite time interval as a result we also obtain conditions for the power rate global stability of the system numerical examples are given to demonstrate the effectiveness and less restrictiveness of the results obtained in this paper

an accurate and efficient two stage channel estimation method utilizing training sequences with closed form expressions a novel two stage frequency domain channel estimation method especially suitable for the estimation of long channels such as ultra wide band channels is proposed the proposed method can efficiently use the sequences with closed form analytical expressions such as the legendre sequences the suggested method does not require a computationally intense search for good training sequences which is infeasible for long training sequences the method is shown to present a minor improvement in the total estimation error variance when compared with the conventional single stage frequency domain channel estimation in addition the proposed method has a very efficient time domain implementation requiring at most 2n multiplications where n is the training sequence length in comparison to o n log n multiplications required for the conventional method

on backwards and forwards reachable sets bounding for perturbed time delay systems linear systems with interval time varying delay and unknown but bounded disturbances are considered in this paper we study the problem of finding outer bound of forwards reachable sets and inter bound of backwards reachable sets of the system firstly two definitions on forwards and backwards reachable sets where initial state vectors are not necessary to be equal to zero are introduced then by using the lyapunov krasovskii method two sufficient conditions for the existence of i the smallest possible outer bound of forwards reachable sets and ii the largest possible inter bound of backwards reachable sets are derived these conditions are presented in terms of linear matrix inequalities with two parameters need to tuned which therefore can be efficiently solved by combining existing convex optimization algorithms with a two dimensional search method to obtain optimal bounds lastly the obtained results are illustrated by four numerical examples

stability analysis of a general family of nonlinear positive discrete time delay systems in this paper we propose a new approach to analyse the stability of a general family of nonlinear positive discrete time delay systems first we introduce a new class of nonlinear positive discrete time delay systems which generalises some existing discrete time delay systems second through a new technique that relies on the comparison and mathematical induction method we establish explicit criteria for stability and instability of the systems three numerical examples are given to illustrate the feasibility of the obtained results

bounds and invariant sets for a class of switching systems with delayed state dependent perturbations we present a novel method to compute componentwise transient bounds componentwise ultimate bounds and invariant regions for a class of switching continuous time linear systems with perturbation bounds that may depend nonlinearly on a delayed state the main advantage of the method is its componentwise nature i e the fact that it allows each component of the perturbation vector to have an independent bound and that the bounds and sets obtained are also given componentwise this componentwise method does not employ a norm for bounding either the perturbation or state vectors avoids the need for scaling the different state vector components in order to obtain useful results and may also reduce conservativeness in some cases the present paper builds upon and extends to switching systems with delayed state dependent perturbations previous results by the authors in this sense the contribution is three fold the derivation of the aforementioned extension the elucidation of the precise relationship between the class of switching linear systems to which the proposed method can be applied and those that admit a common quadratic lyapunov function a question that was left open in our previous work and the derivation of a technique to compute a common quadratic lyapunov function for switching linear systems with perturbations bounded componentwise by affine functions of the absolute value of the state vector components in this latter case we also show how our componentwise method can be combined with standard techniques in order to derive bounds possibly tighter than those corresponding to either method applied individually