a relaxed quadratic function negative determination lemma and its application to time delay systems abstract the quadratic function with respect to the time varying delay has often been introduced for the analysis of systems with time varying delays to determine the negative definiteness of such function this paper develops a parameter adjustable based lemma which contains the lemma popularly used in literature as a special case and has potential to reduce the conservatism without requiring extra decision variables a stability criterion for a linear time delay system is established by using the proposed lemma whose advantage is demonstrated via a numerical example and the criterion is finally applied to analyze the stability of load frequency control scheme for a single area power system

technical communique new conditions for delay derivative dependent stability two recent lyapunov based methods have significantly improved the stability analysis of time delay systems the delay fractioning approach of gouaisbaut and peaucelle 2006 for systems with constant delays and the convex analysis of systems with time varying delays of park and ko 2007 in this paper we develop a convex optimization approach to stability analysis of linear systems with interval time varying delay by using the delay partitioning based lyapunov krasovskii functionals lkfs novel lkfs are introduced with matrices that depend on the time delays these functionals allow the derivation of stability conditions that depend on both the upper and lower bounds on delay derivatives

on model selection criteria in multimodel analysis 1 hydrologic systems are open and complex rendering them prone to multiple conceptualizations and mathematical descriptions there has been a growing tendency to postulate several alternative hydrologic models for a site and use model selection criteria to 1 rank these models 2 eliminate some of them and or 3 weigh and average predictions and statistics generated by multiple models this has led to some debate among hydrogeologists about the merits and demerits of common model selection also known as model discrimination or information criteria such as aic aicc bic and kic and some lack of clarity about the proper interpretation and mathematical representation of each criterion we examine the model selection literature to find that 1 all published rigorous derivations of aic and aicc require that the true model having generated the observational data be in the set of candidate models 2 though bic and kic were originally derived by assuming that such a model is in the set bic has been rederived by cavanaugh and neath 1999 without the need for such an assumption and 3 kic reduces to bic as the number of observations becomes large relative to the number of adjustable model parameters implying that it likewise does not require the existence of a true model in the set of alternatives we explain why kic is the only criterion accounting validly for the likelihood of prior parameter estimates elucidate the unique role that the fisher information matrix plays in kic and demonstrate through an example that it imbues kic with desirable model selection properties not shared by aic aicc or bic our example appears to provide the first comprehensive test of how aic aicc bic and kic weigh and rank alternative models in light of the models predictive performance under cross validation with real hydrologic data

new results on stability analysis for systems with discrete distributed delay the integral inequality technique is widely used to derive delay dependent conditions and various integral inequalities have been developed to reduce the conservatism of the conditions derived in this study a new integral inequality was devised that is tighter than existing ones it was used to investigate the stability of linear systems with a discrete distributed delay and a new stability condition was established the results can be applied to systems with a delay belonging to an interval which may be unstable when the delay is small or nonexistent three numerical examples demonstrate the effectiveness and the smaller conservatism of the method

further improvement of jensen inequality and application to stability of time delayed systems this paper is concerned with the delay dependent stability for the linear systems with a time varying delay to get a result in the form of lmi from a lyapunov krasovskii functional an integral inequality is necessary and jensen inequality has been a most powerful inequality in the last few years recently based on wirtinger inequality an improved integral inequality encompassing jensen inequality was proposed and its application to the stability showed a quite improvement in this paper without using wirtinger inequality a further improved integral inequality in the form of infinite series is derived and based on this a delay dependent stability condition in the form of lmi is derived finally its contribution on the stability criterion is shown by well known two examples

uniqueness and observability of conceptual rainfall runoff model parameters the percolation process examined many researchers have expressed concerns regarding the uniqueness of parameter estimates for conceptual rainfall runoff r r models obtained through calibration recent studies sorooshian et al this issue sorooshian and gupta this issue have revealed that even though stochastic parameter estimation techniques can help the problems are not all due to inefficiencies in the calibration techniques used but are caused by the manner in which the model is structurally formulated thus even when calibrated under ideal conditions simulation studies it is often impossible to obtain unique estimates for the parameters it is possible to resolve this problem at least in part by appropriate reparameterizations of the pertinent model equations in this paper the percolation equation of the soil moisture accounting model of the national weather service river forecast system sma nwsrfs will be discussed it is shown that a logical reparameterization of this equation can result in conditions that improve the chances of obtaining unique parameter estimates it is believed that these results have implications for other conceptual r r models in which similar approaches are used in the representation of the percolation infiltration process

painleve property and geometry abstract the painleve property for discrete hamiltonian systems implies the existence of a symplectic manifold which augments the original phase space and on which the flows exist and are analytic for all times the augmented manifold is constructed by expanding the hamilton jacobi equation a complete classification of the types of poles allowed in complex time is given for hamiltonians which separate into the direct product of hyperelliptic curves for such systems bounds on the degrees of the polynomial separating variable change and the other integrals in involution can be found from the pole series and the hamilton jacobi equation it is shown how branching can arise naturally in a painleve system

effective and efficient global optimization for conceptual rainfall runoff models the successful application of a conceptual rainfall runoff crr model depends on how well it is calibrated despite the popularity of crr models reports in the literature indicate that it is typically difficult if not impossible to obtain unique optimal values for their parameters using automatic calibration methods unless the best set of parameters associated with a given calibration data set can be found it is difficult to determine how sensitive the parameter estimates and hence the model forecasts are to factors such as input and output data error model error quantity and quality of data objective function used and so on results are presented that establish clearly the nature of the multiple optima problem for the research crr model sixpar these results suggest that the crr model optimization problem is more difficult than had been previously thought and that currently used local search procedures have a very low probability of successfully finding the optimal parameter sets next the performance of three existing global search procedures are evaluated on the model sixpar finally a powerful new global optimization procedure is presented entitled the shuffled complex evolution sce ua method which was able to consistently locate the global optimum of the sixpar model and appears to be capable of efficiently and effectively solving the crr model optimization problem

convergence and equivalence results for the jensen s inequality application to time delay and sampled data systems the jensen s inequality plays a crucial role in the analysis of time delay and sampled data systems its conservatism is studied through the use of the gruss inequality it has been reported in the literature that fragmentation or partitioning schemes allow to empirically improve the results we prove here that the jensen s gap can be made arbitrarily small provided that the order of uniform fragmentation is chosen sufficiently large nonuniform fragmentation schemes are also shown to speed up the convergence in certain cases finally a family of bounds is characterized and a comparison with other bounds of the literature is provided it is shown that the other bounds are equivalent to jensen s and that they exhibit interesting well posedness and linearity properties which can be exploited to obtain better numerical 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

h_ infty filtering for discrete time switched systems with known sojourn probabilities this technical note deals with the design of mode dependent h infty filters for a class of discrete time switched systems with nonlinearities in this class of systems when the system mode changes the filter designed for the specific subsystem also switches accordingly the main contribution is on the use of the information of the sojourn probability the probability of the switched system staying in each subsystem to build new kind of switched system model when this additional information is available sojourn probabilities are easier to obtain than the transition probabilities commonly used in markovian jump systems applying the lyapunov functional method the bounded real lemma brl for the resulting filtering error system is obtained in theorem 1 the filter parameters are designed in theorem 2 by solving a set of linear matrix inequalities finally two illustrative examples are given to demonstrate the effectiveness and potential of the proposed approach

extended dissipativity analysis for markovian jump neural networks with time varying delay via delay product type functionals this paper investigates the problem of extended dissipativity for markovian jump neural networks mjnns with a time varying delay the objective is to derive less conservative extended dissipativity criteria for delayed mjnns toward this aim an appropriate lyapunov krasovskii functional lkf with some improved delay product type terms is first constructed then by employing the extended reciprocally convex matrix inequality ercmi and the wirtinger based integral inequality to estimate the derivative of the constructed lkf a delay dependent extended dissipativity condition is derived for the delayed mjnns an improved extended dissipativity criterion is also given via the allowable delay sets method based on the above mentioned results the extended dissipativity condition of delayed nns without markovian jump parameters is directly derived finally three numerical examples are employed to illustrate the advantages of the proposed method

stability and stabilization of t s fuzzy systems with variable delays via new bessel legendre polynomial based relaxed integral inequality abstract this paper investigates the delay range dependent drd stability problem in regards to continuous time takagi sugeno t s fuzzy system with variable delays first a new integral inequality lemma referred herein as higher order polynomial based relaxed integral inequality hopbrii is proposed to reduce the estimation gap of the current work with that of bessel legendre polynomial based inequality blpbi next a suitable lyapunov krasovskii functional lkf is constructed with delay product terms and then using the proposed inequality suitable condition for drd stability and stabilization condition of the considered t s fuzzy system are derived in a linear matrix inequality lmi framework to analyse the advantage theoretically and less conservatism of the proposed method a new drd stability condition using similar lkfs and the blpbi approach is further derived herein finally the efficacy of the proposed stability and stabilization conditions are validated through the solutions of four numerical examples

the algebraic complete integrability of geodesic flow on so n we study for which left invariant diagonal metrics onso n the euler arnold equations dot x x lambda x x x ij in so n lambda ij x ij lambda ij lambda ji can be linearized on an abelian variety i e are solvable by quadratures we show that merely by requiring that the solutions of the differential equations be single valued functions of complex timet suffices to prove that under a non degeneracy assumption on the metric the only such metrics are those which satisfy manakov s conditions ij bi bj ai aj 1 the case of degenerate metrics is also analyzed forn 4 this provides a new and simpler proof of a result of adler and van moerbeke 3

a nonparametric wet dry spell model for resampling daily precipitation a nonparametric wet dry spell model is developed for resampling daily precipitation at a site the model considers alternating sequences of wet and dry days in a given season of the year all marginal joint and conditional probability densities of interest e g dry spell length wet spell length precipitation amount and wet spell length given prior to dry spell length are estimated nonparametrically using at site data and kernel probability density estimators procedures for the disaggregation of wet spell precipitation into daily precipitation and for the generation of synthetic sequences are proffered an application of the model for generating synthetic precipitation traces at a site in utah is presented

kowalewski s asymptotic method kac moody lie algebras and regularization we use an effective criterion based on the asymptotic analysis of a class of hamiltonian equations to determine whether they are linearizable on an abelian variety i e solvable by quadrature the criterion is applied to a system with hamiltonian h 1 mathord left vphantom 1 2 right kern nulldelimiterspace 2 sum limits i 1 l p i 2 sum limits i 1 l 1 exp left sum limits j 1 l n ij x j right parametrized by a real matrixn n ij of full rank it will be solvable by quadrature if and only if for alli j 2 n nt ij n n t jj 1 is a nonpositive integer i e the interactions correspond to the toda systems for the kac moody lie algebras the criterion is also applied to a system of gross neveu

technical communique improved delay dependent stability criteria for systems with a delay varying in a range this paper provides improved delay dependent stability criteria for systems with a delay varying in a range the criteria improve over some previous ones in that they have fewer matrix variables yet less conservatism which is established theoretically an example is given to show the advantages of the proposed results

wirtinger based integral inequality application to time delay systems in the last decade the jensen inequality has been intensively used in the context of time delay or sampled data systems since it is an appropriate tool to derive tractable stability conditions expressed in terms of linear matrix inequalities lmis however it is also well known that this inequality introduces an undesirable conservatism in the stability conditions and looking at the literature reducing this gap is a relevant issue and always an open problem in this paper we propose an alternative inequality based on the fourier theory more precisely on the wirtinger inequalities it is shown that this resulting inequality encompasses the jensen one and also leads to tractable lmi conditions in order to illustrate the potential gain of employing this new inequality with respect to the jensen one two applications on time delay and sampled data stability analysis are provided

free matrix based integral inequality for stability analysis of systems with time varying delay the free weighting matrix and integral inequality methods are widely used to derive delay dependent criteria for the stability analysis of time varying delay systems because they avoid both the use of a model transformation and the technique of bounding cross terms this technical note presents a new integral inequality called a free matrix based integral inequality that further reduces the conservativeness in those methods it includes well known integral inequalities as special cases using it to investigate the stability of systems with time varying delays yields less conservative delay dependent stability criteria which are given in terms of linear matrix inequalities two numerical examples demonstrate the effectiveness and superiority of the method

new results on dissipativity analysis of singular systems with time varying delay abstract this paper focuses on the dissipativity analysis of singular systems with time varying delay the objective is to obtain a less conservative criterion with less computational demand based on the state decomposition method singular systems are rewritten as differential subsystems and algebraic ones first of all the components of state vectors are applied to design a novel lyapunov krasovskii functional lkf for the differential subsystems then in the derivative of the lkf the algebraic ones are introduced and the wirtinger based integral inequality together with the extended reciprocally convex matrix inequality is adopted to estimate the single integral term therefore a new dissipativity criterion is obtained which realizes both less conservativeness and less computational demand finally two numerical examples are given to verify the superiority of the proposed method

a generalized free matrix based integral inequality for stability analysis of time varying delay systems abstract this paper focuses on the delay dependent stability problem of time varying delay systems a generalized free matrix based integral inequality gfmbii is presented this inequality is able to deal with time varying delay systems without using the reciprocal convexity lemma it overcomes the drawback that the bessel legendre inequality is inconvenient to cope with a time varying delay system as the resultant bound contains a reciprocal convexity through the use of the derived inequality and by constructing a suitable lyapunov krasovskii function lkf improved stability criteria are presented in the form of linear matrix inequalities lmis two numerical examples are carried out to demonstrate that the results outperform the state of the art in the literature

quantile hydrologic model selection and model structure deficiency assessment 1 theory a theory for quantile based hydrologic model selection and model structure deficiency assessment is presented the paper demonstrates that the degree to which a model selection problem is constrained by the model structure measured by the lagrange multipliers of the constraints quantifies structural deficiency this leads to a formal definition of model structure deficiency or rigidity model structure deficiency introduces a bias in the prediction of an observed quantile which is often not equal across quantiles structure deficiency is therefore diagnosed when any two quantile predictions for a given model structure cross since unequal bias across quantiles result in quantile predictions crossing the analysis further suggests that the optimal value of quantile specific loss functions order different model structures by its structure deficiencies over a range of quantiles in addition to such novelties quantile hydrologic model selection is a frequentist approach that seeks to complement existing bayesian approaches to hydrological model uncertainty

stability analysis of systems with time varying delay via novel augmented lyapunov krasovskii functionals and an improved integral inequality abstract delay dependent stability analysis of linear systems with a time varying delay is investigated in this paper firstly instead of developing a lyapunov krasovskii functional lkf including augmented non integral quadratic terms as usual this paper proposes two augmented integral function based lkfs which can reflect closer relationships among system states secondly to bound the derivative of lkf more accurately a new integral inequality with several free matrices is developed compared with the free matrix based integral inequality this inequality can provide additional freedom due to the free matrices introduced then by employing those lkfs and the improved integral inequality several delay dependent stability criteria are established for two types of delays finally two numerical examples are given to demonstrate the superiority of the proposed method

non holonomic geodesic flows on lie groups and the integrable suslov problem on so 4 we study geodesic flows on lie groups with the left invariant non holonomic constraint in the case of the existence of an invariant measure we find new integrable non hamiltonian systems on so 4 and other six dimensional lie groups

reciprocally convex approach to stability of systems with time varying delays whereas the upper bound lemma for matrix cross product introduced by park 1999 and modified by moon park kwon and lee 2001 plays a key role in guiding various delay dependent criteria for delayed systems the jensen inequality has become an alternative as a way of reducing the number of decision variables it directly relaxes the integral term of quadratic quantities into the quadratic term of the integral quantities resulting in a linear combination of positive functions weighted by the inverses of convex parameters this paper suggests the lower bound lemma for such a combination which achieves performance behavior identical to approaches based on the integral inequality lemma but with much less decision variables comparable to those based on the jensen inequality lemma

ancient numerical daemons of conceptual hydrological modeling 2 impact of time stepping schemes on model analysis and prediction 1 despite the widespread use of conceptual hydrological models in environmental research and operations they remain frequently implemented using numerically unreliable methods this paper considers the impact of the time stepping scheme on model analysis sensitivity analysis parameter optimization and markov chain monte carlo based uncertainty estimation and prediction it builds on the companion paper clark and kavetski 2010 which focused on numerical accuracy fidelity and computational efficiency empirical and theoretical analysis of eight distinct time stepping schemes for six different hydrological models in 13 diverse basins demonstrates several critical conclusions 1 unreliable time stepping schemes in particular fixed step explicit methods suffer from troublesome numerical artifacts that severely deform the objective function of the model these deformations are not rare isolated instances but can arise in any model structure in any catchment and under common hydroclimatic conditions 2 sensitivity analysis can be severely contaminated by numerical errors often to the extent that it becomes dominated by the sensitivity of truncation errors rather than the model equations 3 robust time stepping schemes generally produce better behaved objective functions free of spurious local optima and with sufficient numerical continuity to permit parameter optimization using efficient quasi newton methods when implemented within a multistart framework modern newton type optimizers are robust even when started far from the optima and provide valuable diagnostic insights not directly available from evolutionary global optimizers 4 unreliable time stepping schemes lead to inconsistent and biased inferences of the model parameters and internal states 5 even when interactions between hydrological parameters and numerical errors provide the right result for the wrong reason and the calibrated model performance appears adequate unreliable time stepping schemes make the model unnecessarily fragile in predictive mode undermining validation assessments and operational use erroneous or misleading conclusions of model analysis and prediction arising from numerical artifacts in hydrological models are intolerable especially given that robust numerics are accepted as mainstream in other areas of science and engineering we hope that the vivid empirical findings will encourage the conceptual hydrological community to close its pandora s box of numerical problems paving the way for more meaningful model application and interpretation

on hydrological model complexity its geometrical interpretations and prediction uncertainty knowledge of hydrological model complexity can aid selection of an optimal prediction model out of a set of available models optimal model selection is formalized as selection of the least complex model out of a subset of models that have lower empirical risk this may be considered equivalent to minimizing an upper bound on prediction error defined here as the mathematical expectation of empirical risk in this paper we derive an upper bound that is free from assumptions on data and underlying process distribution as well as on independence of model predictions over time we demonstrate that hydrological model complexity as defined in the presented theoretical framework plays an important role in determining the upper bound the model complexity also acts as a stabilizer to a hydrological model selection problem if it is deemed ill posed we provide an algorithm for computing complexity of any arbitrary hydrological model we also demonstrate that hydrological model complexity has a geometric interpretation as the size of model output space the presented theory is applied to quantify complexities of two hydrological model structures sac sma and sixpar it detects that sac sma is indeed more complex than sixpar we also develop an algorithm to estimate the upper bound on prediction error which is applied on five different rainfall runoff model structures that vary in complexity we show that a model selection problem is stabilized by regularizing it with model complexity complexity regularized model selection yields models that are robust in predicting future but yet unseen data

improved delay dependent stability criteria for time delay systems this note provides an improved asymptotic stability condition for time delay systems in terms of a strict linear matrix inequality unlike previous methods the mathematical development avoids bounding certain cross terms which often leads to conservatism when time varying norm bounded uncertainties appear in a delay system an improved robust delay dependent stability condition is also given examples are provided to demonstrate the reduced conservatism of the proposed conditions

further robust stability analysis for uncertain takagi sugeno fuzzy systems with time varying delay via relaxed integral inequality abstract this paper focuses on robust stability analysis for uncertain takagi sugeno fuzzy systems with time varying delays two delay product type terms are introduced for constructing a new lyapunov krasovskii functional which contains more information of time varying delay and a novel relaxed integral inequality is applied to estimate the derivative of lkf for achieving reduction of estimation gap as a result several further robust stability criteria with less conservativeness are proposed finally three numerical examples and an application to control of a truck trailer are provided to show the effectiveness and advantages of the presented methods

improved delay dependent stability criteria for linear systems with multiple time varying delays this paper concentrates on the stability analysis of continuous time linear systems with multiple time varying delays the time delays are assumed to be bounded and have or not lower and upper boun

generalized reciprocally convex combination lemmas and its application to time delay systems various efficient matrix inequalities have recently been proposed to deal with the stability analysis of linear systems with time varying delays this paper provides more insights on the relationship between some of them we present an equivalent formulation of moon et al s inequality allowing us to discover strong links not only with the most recent and efficient matrix inequalities such as the reciprocally convex combination lemma and also its relaxed version but also with some previous inequalities such as the approximation inequality introduced in 14 or free matrix based inequality more especially it is proved that these existing inequalities can be captured as particular cases of moon et al s inequality examples show the best tradeoff between the reduction of conservatism and the numerical complexity

further refinements in stability conditions for time varying delay systems abstract this paper addresses the problem of assessing the stability of linear time invariant lti systems with time varying delay the first contribution is a new stability criterion specified as a negativity condition for a quadratic function parameterized by the delay this result mainly follows from an augmented affine parameter dependent lyapunov krasovskii functional which in turn takes advantages of convexity properties then as a second contribution we invoke a result from robust control literature to show how the proposed stability condition can be checked exactly in terms of linear matrix inequality lmi conditions the improvements obtained by the proposed refinements are illustrated via numerical examples drawn from the literature

a note on wirtinger type integral inequalities for time delay systems different integral inequalities play important role when problems of stability analysis and controller synthesis for time delay systems are considered the connection of jensen s inequality and extended jensen s inequality is well understood now to reduce the conservativeness introduced by the application of jensen s inequality several versions of the wirtinger integral inequality have been published recently this note presents a comparison between some of these inequalities

on equivalence and efficiency of certain stability criteria for time delay systems in recent years there have been a number of new delay dependent stability criteria based on linear matrix inequalities published in the literature this note aims to theoretically establish the equivalence of seven of these stability criteria moreover the efficiency of these stability criteria is assessed based on the number of unknowns in the linear matrix inequalities

nonholonomic left and right flows on lie groups nonholonomic systems on lie groups with a left invariant lagrangian and a right invariant nonintegrable distribution are studied a method for construction of the first integrals is given it is applied to three dimensional lie groups and to the four dimensional nonholonomic rigid body motion new integrable problems with an invariant measure are obtained

delay variation dependent stability of delayed discrete time systems this note is concerned with the stability analysis of linear discrete time system with a time varying delay a generalized free weighting matrix gfwm approach is proposed to estimate summation terms in the forward difference of lyapunov functional and theoretical study shows that the gfwm approach encompasses several frequently used estimation approaches as special cases moreover an augmented lyapunov functional with a delay product type term is constructed to take into account delay changing information as a result the proposed gfwm approach together with the augmented lyapunov functional leads to a less conservative delay variation dependent stability criterion finally numerical examples are given to illustrate the advantages of the proposed criterion

technical communique stability and robust stability for systems with a time varying delay to concern the stability and robust stability criteria for systems with time varying delays this note uses not only the time varying delayed state x t h t but also the delay upper bounded state x email protected to exploit all possible information for the relationship among a current state x t an exactly delayed state x t h t a marginally delayed state x email protected and the derivative of the state email protected t when constructing lyapunov krasovskii functionals and some appropriate integral inequalities originally suggested by park 1999 a delay dependent stability criterion for systems with uncertain time invariant delays ieee transactions on automatic control 44 4 876 877 two fundamental criteria are provided for the cases where no bound of delay derivative is assumed and where an upper bound of delay derivative is assumed examples show the resulting criteria outperform all existing ones in the literature

stochastic simulation of nonstationary oscillation hydroclimatic processes using empirical mode decomposition 1 nonstationary oscillation nso processes are observed in a number of hydroclimatic data series stochastic simulation models are useful to study the impacts of the climatic variations induced by nso processes into hydroclimatic regimes reproducing nso processes in a stochastic time series model is however a difficult task because of the complexity of the nonstationary behaviors in the current study a novel stochastic simulation technique that reproduces the nso processes embedded in hydroclimatic data series is presented the proposed model reproduces nso processes by utilizing empirical mode decomposition emd and nonparametric simulation techniques i e k nearest neighbor resampling and block bootstrapping the model was first tested with synthetic data sets from trigonometric functions and the rossler system the north atlantic oscillation nao index was then examined as a real case study this nao index was then employed as an exogenous variable for the stochastic simulation of streamflows at the romaine river in the province of quebec canada the results of the application to the synthetic data sets and the real world case studies indicate that the proposed model preserves well the nso processes along with the key statistical characteristics of the observations it was concluded that the proposed model possesses a reasonable simulation capacity and a high potential as a stochastic model especially for hydroclimatic data sets that embed nso processes

stability of time delay systems via wirtinger based double integral inequality based on the wirtinger based integral inequality a double integral form of the wirtinger based integral inequality hereafter called as wirtinger based double integral inequality is introduced in this paper to show the effectiveness of the proposed inequality two stability criteria for systems with discrete and distributed delays are derived within the framework of linear matrix inequalities lmis the advantage of employing the proposed inequalities is illustrated via two numerical examples

event based h filtering for sampled data systems this paper is concerned with event based h filtering for sampled data systems first an event based data packet processor is introduced to release sampled measurement outputs only if an event condition is violated as a result communication resources can be saved significantly while preserving the desired h performance second the resulting filtering error system is modeled as a system with an interval time varying delay by employing the lyapunov krasovskii functional approach a new bounded real lemma brl is established such that the filtering error system is asymptotically stable with the prescribed h performance third by performing an invertible linear transformation on the filtering error system a linear matrix inequality lmi based sufficient condition which is equivalent to the condition in the brl is obtained on the feasibility of the event based h filtering problem consequently suitable h filters and the event parameters in the event condition can be co designed provided that a set of lmis are satisfied finally a mechanical system with two masses and two springs is given to show the effectiveness of the proposed method

improved stability criteria for linear systems with two additive time varying delays via a novel lyapunov functional abstract this paper consider the stability problem of linear systems with two additive time varying delays a novel lyapunov krasovskii functional lkf is constructed which consists of the delay dependent non integral items and the single integral items based on the newly developed lkf a stability criterion is derived which is less conservative than some recent existing ones furthermore to obtain a tighter bound of the integral term quadratic generalized free weighting matrix inequality qgfmi is used finally a numerical example and an application of the load frequency control for a single area power system are presented to show the effectiveness of the proposed approach

technical communique delay range dependent stability for systems with time varying delay this paper is concerned with the stability analysis for systems with time varying delay in a range an appropriate type of lyapunov functionals is proposed to investigate the delay range dependent stability problem the present results may improve the existing ones due to a method to estimate the upper bound of the derivative of lyapunov functional without ignoring some useful terms and the introduction of additional terms into the proposed lyapunov functional which take into account the range of delay numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method

brief paper new delay dependent stability criteria for systems with interval delay this paper provides a new delay dependent stability criterion for systems with a delay varying in an interval with a different lyapunov functional defined a tight upper bound of its derivative is given the resulting criterion has advantages over some previous ones in that it involves fewer matrix variables but has less conservatism which is established theoretically examples are provided to demonstrate the advantage of the stability result

technical communique new stability criteria for linear systems with interval time varying delay this paper investigates robust stability of uncertain linear systems with interval time varying delay the time varying delay is assumed to belong to an interval and is a fast time varying function the uncertainty under consideration includes polytopic type uncertainty and linear fractional norm bounded uncertainty a new lyapunov krasovskii functional which makes use of the information of both the lower and upper bounds of the interval time varying delay is proposed to drive some new delay dependent stability criteria in order to obtain much less conservative results a tighter bounding for some term is estimated moreover no redundant matrix variable is introduced finally three numerical examples are given to show the effectiveness of the proposed stability criteria

accurate approximations for posterior moments and marginal densities abstract this article describes approximations to the posterior means and variances of positive functions of a real or vector valued parameter and to the marginal posterior densities of arbitrary i e not necessarily positive parameters these approximations can also be used to compute approximate predictive densities to apply the proposed method one only needs to be able to maximize slightly modified likelihood functions and to evaluate the observed information at the maxima nevertheless the resulting approximations are generally as accurate and in some cases more accurate than approximations based on third order expansions of the likelihood and requiring the evaluation of third derivatives the approximate marginal posterior densities behave very much like saddle point approximations for sampling distributions the principal regularity condition required is that the likelihood times prior be unimodal

further improvement of free weighting matrices technique for systems with time varying delay a novel method is proposed in this note for stability analysis of systems with a time varying delay appropriate lyapunov functional and augmented lyapunov functional are introduced to establish some improved delay dependent stability criteria less conservative results are obtained by considering the additional useful terms which are ignored in previous methods when estimating the upper bound of the derivative of lyapunov functionals and introducing the new free weighting matrices the resulting criteria are extended to the stability analysis for uncertain systems with time varying structured uncertainties and polytopic type uncertainties numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method

generalizations of classical integrable nonholonomic rigid body systems nonholonomic systems with an invariant measure the suslov chaplygin and veselov veselova problem are considered new families of integrable potential perturbations of these non hamiltonian systems are constructed we also obtain a similar result for a classical hamiltonian system of the motion of a rigid body fixed at a point

summation inequalities to bounded real lemmas of discrete time systems with time varying delay summation inequality is an important technique for analysis of discrete time systems with a time varying delay it seems that from the literature a tighter inequality usually leads to a less conservative criterion based on h infty performance analysis problem this note presents different findings on the relationship between the conservatism of bounded real lemma brl and the tightness of summation inequality firstly the brl obtained by the wirtinger based inequality wbi is not always less conservative than the one by the jensen based inequality although the wbi is tighter secondly the wbi is tighter than a general free matrix based inequality gfmbi developed in this note while the brl obtained via the gfmbi is less conservative than the wbi based brl finally a numerical example is given to demonstrate those findings

nonintegrability of the suslov problem in this paper we investigate the suslov problem in the case when the vector of nonholonomic constraint coincides with the third principal axis of the body and the fixed point of the body lies in the principal plane defined by the third and the first principal axes but is out of these axes we called this version of the suslov problem the generalized kozlov case and we prove that in this case a third real meromorphic first integral functionally independent together with the energy and geometrical integrals does not exist

note on stability of linear systems with time varying delay this note considers the stability of linear systems with a time varying delay we are interested in a simple lyapunov krasovskii functional lkf approach without delay decomposition in this category all recent tractable results had a fixed bound on the allowable maximum size of the delay for years we propose a new simple lkf including the cross terms of variables and quadratic terms multiplied by a higher degree scalar function and present a new result expressed in the form of lmis we show by two well known examples that our result overcomes the previous allowable maximum size of delay and it is less conservative than the previous results having a relatively small upper bound in the derivative of time delay

a note on equivalence between two integral inequalities for time delay systems jensen s inequality and extended jensen s inequality are two important integral inequalities when problems of stability analysis and controller synthesis for time delay systems are considered the extended jensen s inequality introduces two additional free matrices and is generally regarded to be less conservative than jensen s inequality the equivalence between jensen s inequality and extended jensen s inequality in bounding the quadratic term h t h t x t s z x s d s in lyapunov functional of time delay systems is presented and theoretically proved it is shown that the extended jensen s inequality does not decrease the lower bound of this quadratic term obtained using jensen s inequality and then it does not reduce the conservativeness though two additional free matrices m 1 and m 2 are involved

nonholonomic mechanical systems with symmetry this work develops the geometry and dynamics of mechanical systems with nonholonomic constraints and symmetry from the perspective of lagrangian mechanics and with a view to control theoretical applications the basic methodology is that of geometric mechanics applied to the formulation of lagrange d alembert generalizing the use of connections and momentum maps associated with a given symmetry group to this case we begin by formulating the mechanics of nonholonomic systems using an ehresmann connection to model the constraints and show how the curvature of this connection enters into lagrange s equations unlike the situation with standard configuration space constraints the presence of symmetries in the nonholonomic case may or may not lead to conservation laws however the momentum map determined by the symmetry group still satisfies a useful differential equation that decouples from the group variables this momentum equation which plays an important role in control problems involves parallel transport operators and is computed explicitly in coordinates an alternative description using a body reference frame relates part of the momentum equation to the components of the euler poincar e equations along those symmetry directions consistent with the constraints one of the purposes of this paper is to derive this evolution equation for the momentum and to distinguish geometrically and mechanically the cases where it is conserved and those where it is not an example of the former is a ball or vertical disk rolling on a flat plane and an example of the latter is the snakeboard a modified version of the skateboard which uses momentum coupling for locomotion generation we construct a synthesis of the mechanical connection and the ehresmann connection defining the constraints obtaining an important new object we call the nonholonomic connection when the nonholonomic connection is a principal connection for the given symmetry group we show how to perform lagrangian reduction in the presence of nonholonomic constraints generalizing previous results which only held in special cases several detailed examples are given to illustrate the theory september 1994 revised march 1995 revised june 1995

stability analysis of linear systems with time varying delay via intermediate polynomial based functions abstract this note is devoted to stability analysis for linear system with time varying delay by advisably introducing slack matrices novel fractional order intermediate polynomial based functions ipfs are proposed then the stability condition is derived for the time delay system from configuration on fractional order polynomials the relationships among system states are taken into account and consolidated via slack variables and the characteristics for integral inequality are synthetically considered while avoiding higher order time delays more remarkably adjusting tunable parameters also contributes to reduction of conservatism the comparisons of computational complexity and stability region on a well known numerical example are provided to validate the advantages of the resulting stability criterion

quantile hydrologic model selection and model structure deficiency assessment 2 applications quantile hydrologic model selection and structure deficiency assessment is applied in three case studies the performance of quantile model selection problem is rigorously evaluated using a model structure on the french broad river basin data set the case study shows that quantile model selection encompasses model selection strategies based on summary statistics and that it is equivalent to maximum likelihood estimation under certain likelihood functions it also shows that quantile model predictions are fairly robust the second case study is of a parsimonious hydrological model for dry land areas in western india the case study shows that an intuitive improvement in the model structure leads to reductions in asymmetric loss function values for all considered quantiles the asymmetric loss function is a quantile specific metric that is minimized to obtain a quantile specific prediction model the case study provides evidence that a quantile wise reduction in the asymmetric loss function is a robust indicator of model structure improvement finally a case study of modeling daily streamflow for the guadalupe river basin is presented a model structure that is least deficient for the study area is identified from nine different model structures based on quantile structural deficiency assessment the nine model structures differ in interception routing overland flow and base flow conceptualizations the three case studies suggest that quantile model selection and deficiency assessment provides a robust mechanism to compare deficiencies of different model structures and helps to identify better model structures in addition to its novelty quantile hydrologic model selection is a frequentist approach that seeks to complement existing bayesian approaches to hydrological model uncertainty

parameterizations for natural exponential families with quadratic variance functions abstract parameterizations for natural exponential families nef s with quadratic variance functions qvf s are compared according to the nearness to normality of the likelihood and posterior distribution nonnormality of the likelihood posterior is measured using two criteria the first is the magnitude of a standardized third derivative of the log likelihood logposterior density the second is a comparison of the probability of particular tail regions under the normalized likelihood posterior distribution and under the corresponding normal approximation a relationship is given that links these two criteria sample sizes are recommended for adequate normality in the likelihood for various parameterizations of the nef qvf models and these results are extended to bayesian models with a conjugate prior

stability analysis for linear delayed systems via an optimally dividing delay interval approach this paper addresses the problem of stability for linear systems with time varying delay a novel augmented lyapunov krasovskii functional is constructed by using the idea of optimally dividing the delay interval 0 t into some variable sub intervals and line integral technology using the novel augmented functional the new delay dependent stability criteria are proposed for linear systems with time varying delay the gain is that this stability criterion can lead to much less conservative stability results compared to other methods for linear systems with delay two numerical examples are provided to verify the effectiveness of the proposed criteria

the discrete self trapping equation and the painleve property from the discrete self trapping dst equation for three degrees of freedom rewritten in terms of density matrix one can derive an autonomous system of real first order ordinary differential equations by using su 3 notation performing a painleve analysis it is found that depending on the parameters of the system integrable and non integrable cases can be distinguished

rates of convergence for empirical processes of stationary mixing sequences classical empirical process theory for vapnik cervonenkis classes deals mainly with sequences of independent variables this paper extends the theory to stationary sequences of dependent variables it establishes rates of convergence for mixing and mixing empirical processes indexed by classes of functions the method of proof depends on a coupling of the dependent sequence with sequences of independent blocks to which the classical theory can be applied a uniform o ns 1 s rate of convergence over v c classes is established for sequences whose mixing coefficients decay slightly faster than o n s

notes on stability of time delay systems bounding inequalities and augmented lyapunov krasovskii functionals the bounding inequalities and the lyapunov krasovskii functionals lkfs are important for the stability analysis of time delay systems much attention has been paid to develop tighter inequalities for improving stability criteria while the contribution of the lkfs has not been considered when discussing the relationship between the tightness of inequalities and the conservatism of criteria this note is concerned with this issue firstly it is proved that when a simple lkf is applied the stability criteria obtained by the wirtinger based inequality and the jensen inequality are equivalent although the wirtinger based inequality is tighter it means that the tighter inequality does not always lead to a less conservative criterion secondly it is found that a suitable augmented lkf with necessary integral vectors in its derivative is required to achieve the advantage of the wirtinger based inequality based on this observation two delay product type terms are introduced into the lkf to establish new stability criteria finally a numerical example is given to verify the equivalence statements and to show the benefit of the proposed criteria

h state estimation for neural networks with general activation function and mixed time varying delays this article deals with h state estimation of neural networks with mixed delays in order to make full use of delay information novel delay product lyapunov krasovskii functional lkf by using parameterized delay interval is first constructed then generalized free weighting matrix integral inequality is used to estimate the derivative of lkf to reduce the conservatism also a more general activation function is further applied by combining with parameterized delay interval in order to obtain a more accurate estimator model finally sufficient conditions are derived to confirm that the estimation error system is asymptotically stable with a prescribed h performance numerical examples are simulated to show the benefits of our proposed method