stability margin calculation for systems with structured time delay uncertainties a method of calculating a stability margin of systems with uncertain time delay elements is presented this method utilizes the bilinear transformation of time delay elements to obtain a multilinear function in order to compute the stability margin by applying the mapping theory proposed for the robust stability test

brief paper preservation of exponential stability for linear non autonomous functional differential systems we consider preservation of exponential stability for a system of linear equations with a distributed delay under the addition of new terms and a delay perturbation as particular cases the system includes models with concentrated delays and systems of integrodifferential equations our method is based on bohl perron type theorems

explicit exponential stability conditions for linear differential equations with several delays abstract new explicit conditions of exponential stability are obtained for the nonautonomous linear equation x t k 1 m a k t x h k t 0 where k 1 m a k t 0 h k t t by comparing this equation with a nonoscillatory exponentially stable equation of the form x t k i a k t x g k t 0 where i 1 m g k t t every comparison result gives 2 m 1 different stability conditions due to the a priori choice of a subset i

state space reconstruction and spatio temporal prediction of lattice dynamical systems this paper addresses the problems of state space reconstruction and spatio temporal prediction for lattice dynamical systems it is shown that the state space of any finite lattice dynamical system can be embedded into a reconstruction space for almost every in the sense of prevalence smooth measurement mapping as long as the dimension of the reconstruction space is larger than twice the size of the lattice based on this result an input output spatio temporal dynamical relation for each site within the lattice is derived and used for spatio temporal prediction of the system in the case of infinite lattice dynamical systems an approach based on constructing local lattice dynamical systems is proposed it is shown that the finite dimensional results can be directly applied to the local modelling and spatio temporal prediction for infinite lattice dynamical systems two numerical examples are provided to demonstrate the proposed theory and approach

h sub spl infin control of systems under norm bounded uncertainties in all system matrices this paper concerns h sub spl infin control of systems under norm bounded uncertainties in all the system matrices this is an extension of the work by xie et al 1992 where only the a matrix is allowed to be uncertain it is found that the problem shares the same formulation with the h sub spl infin control problem for systems without uncertainties it can also be viewed as reducing the problem of dealing with systems with both structured uncertainties and unstructured uncertainties to one with unstructured uncertainties only

delay independent stability conditions for time varying nonlinear uncertain systems a new stability criterion for time varying systems consisting of linear and norm bounded nonlinear terms with uncertain time varying delays is formulated an explicit delay independent sufficient stability condition is formulated in the terms of the transition matrix of the given linear part without delay and the bounds for the uncertain terms the obtained condition turns out to be also necessary if the matrix of the linear part is time invariant and symmetric it is shown that these systems satisfy the well known aizerman s conjecture the obtained criterion is contrasted by some of stability estimates available in the literature for these kinds of systems in all cases the proposed criterion provides less conservative stability bounds

extension groups between simple mackey functors in order to better understand the structure of indecomposable projective mackey functors we study extension groups of degree 1 between simple mackey functors we explicitly determine these groups between simple functors indexed by distinct normal subgroups we next study the conditions under which it is possible to restrict ourselves to that case and we give methods for calculating extension groups between simple mackey functors which are not indexed by normal subgroups we then focus on the case where the simple mackey functors are indexed by the same subgroup in this case the corresponding extension group can be embedded in an extension group between modules over a group algebra and we describe the image of this embedding in particular we determine all extension groups between simple mackey functors for a p group and for a group that has a normal p sylow subgroup finally we compute higher extension groups between simple mackey functors for a group that has a p sylow subgroup of order p

uniform asymptotic stability for perturbed neutral delay differential equations abstract one dimensional perturbed neutral delay differential equations of the form x t p t x t f t x t g t x t are considered assuming that f satisfies v t m f t v t m where m max 0 max s r 0 s a typical result is the following if g t w t and t t 1 w s ds 0 then the zero solution is uniformly asymptotically stable providing that the zero solution of the corresponding equation without perturbation x t p t x t f t x t is uniformly asymptotically stable some known results associated with this equation are extended and improved

preservation of stability in delay equations under delay perturbations we consider a class of linear delay equations with perturbed time lags and present conditions which guarantee that the asymptotic stability of the trivial solution of the equation at hand is preserved under these perturbations as an example we show how our results can be used to obtain an estimate on the maximum allowable sampling interval in the stabilization of a hybrid system with feedback delays we also present applications of our perturbation theorem to obtain stability conditions for delay equations with multiple delays

simple uniform exponential stability conditions for a system of linear delay differential equations abstract uniform exponential stability of linear systems with time varying coefficients x i t j 1 m k 1 r ij a ij k t x j h ij k t i 1 m is studied where t 0 m and r ij i j 1 m are natural numbers a ij k 0 r and h ij k 0 r are measurable functions new explicit result is derived with the proof based on bohl perron theorem the resulting criterion has advantages over some previous ones in that e g it involves no m matrix to establish stability several useful and easily verifiable corollaries are deduced and examples are provided to demonstrate the advantage of the stability result over known results

standard stratifications of ei categories and alperin s weight conjecture abstract we characterize the finite ei categories whose representations are standardly stratified with respect to the natural preorder on the simple representations the orbit category of a finite group with respect to any set of subgroups is always such a category taking the subgroups to be the p subgroups of the group we reformulate alperin s weight conjecture in terms of the standard and proper costandard representations of the orbit category we do this using the properties of the ringel dual construction and a theorem of dlab which have elsewhere been described for standardly stratified algebras where there is a partial order on the simple modules we indicate that these results hold in the generality of an algebra whose simple modules are preordered rather than partially ordered

robust h sub spl infin performance for linear delay differential systems with time varying uncertainties the present paper concerns robust h spl infin performance for linear delay differential systems which involve an uncertain time delay and time varying norm bounded parameter uncertainties based on the lyapunov functional a simple criterion is proposed which assures the pseudo quadratic stability as a well as an h sub spl infin norm bound the criterion is given in the form of a linear matrix inequality which is affine or convex in additional scalar parameters a simple criterion is presented to evaluate the extent of the performance robustness

nonlinear galerkin methods the finite elements case with the increase in the computing power and the advent of supercomputers the approximation of evolution equations on large intervals of time is emerging as a new type of numerical problem in this article we consider the approximation of evolution equations on large intervals of time when the space discretization is accomplished by finite elements the algorithm that we propose called the nonlinear galerkin method stems from the theory of dynamical systems and amounts to some approximation of the attractor in the discrete finite elements space essential here is the utilization of incremental unknown which is accomplished in finite elements by using hierarchical bases beside a detailed description of the algorithm the article includes some technical results on finite elements spaces and a full study of the stability and convergence of the method

some remarks on g functors and the brauer morphism keywords finite group g functor restriction maps transfer maps mackey s formula frobenius reciprocity brauer morphism defect base nilpotent ideal burnside ring idempotent formula induction formula symmetric g functor character ring green ring reference ctg article 1988 003 record created on 2008 12 16 modified on 2017 05 12

solution estimates for linear differential equations with delay abstract in this paper we give explicit exponential estimates x t m e t t 0 where t t0 m 0 for solutions of a linear scalar delay differential equation x t k 1 m b k t x h k t f t t t 0 x t t t t 0 we consider two different cases when 0 corresponding to exponential stability and the case of in the first case together with the exponential estimate we also obtain an exponential stability test in the second case we get estimation for solution growth here both the coefficients and the delays are measurable not necessarily continuous

identification of nonlinear spatiotemporal dynamical systems with nonuniform observations using reproducing kernel based integral least square regulation the identification of nonlinear spatiotemporal dynamical systems given by partial differential equations has attracted a lot of attention in the past decades several methods such as searching principle based algorithms partially linear kernel methods and coupled lattice methods have been developed to address the identification problems however most existing methods have some restrictions on sampling processes in that the sampling intervals should usually be very small and uniformly distributed in spatiotemporal domains these are actually not applicable for some practical applications in this paper to tackle this issue a novel kernel based learning algorithm named integral least square regularization regression ilsrr is proposed which can be used to effectively achieve accurate derivative estimation for nonlinear functions in the time domain with this technique a discretization method named inverse meshless collocation is then developed to realize the dimensional reduction of the system to be identified thereafter with this novel inverse meshless collocation model the ilsrr and a multiple kernel based learning algorithm a multistep identification method is systematically proposed to address the identification problem of spatiotemporal systems with pointwise nonuniform observations numerical studies for benchmark systems with necessary discussions are presented to illustrate the effectiveness and the advantages of the proposed method

on the stability of invariant sets of functional differential equations abstract a system of functional differential equations with delay dz dt z t zt where z x y x rn y rm and z is the vector valued functional is considered it is supposed that this system has a positive invariant set x 0 definitions of its stability asymptotic stability and uniform asymptotic stability are given theorems on the uniform asymptotic stability are formulated and proved

on the stability of linear systems with uncertain delay this paper focuses on the stability of some class of delay systems including uncertainty in the delays more precisely we are interested in guaranteeing the stability of perturbed delay systems by assuming the stability of the nominal system if the delay perturbation is constant necessary and sufficient conditions are derived in terms of generalized eigenvalue distribution of some finite dimensional constant matrix pencil if the delay perturbation is time varying some sufficient stability conditions are derived using exact lyapunov krasovskii functionals illustrative examples are also included

c filtered modules and proper costratifying systems abstract in this paper we define and study the notion of a proper costratifying system which is a generalization of the so called proper costandard modules to the context of stratifying systems the proper costandard modules were defined by v dlab in his study of quasi hereditary algebras see dlab 1996 d1

consistent recursive parameter estimation of partial differential equation models this article introduces a new residual based recursive parameter estimation algorithm for linear partial differential equations the main idea is to replace the unmeasurable noise variables by estimates of the noise and to compute recursively both the model parameters and the noise estimates it is proven that under some mild assumptions the estimated parameters converge to the true values with probability one numerical examples that demonstrate the effectiveness of the proposed approach are also provided

robust stability of perturbed systems with time delays abstract motivated by dynamical system considerations a number of new results on robust stability of perturbed polynomials have been recently obtained in the literature under consideration the perturbations are known only within given bounds and enter affine linearly into the polynomial coefficients in this paper this formulation is expanded to include time delays under a properness assumption a necessary and sufficient condition for robust stability is developed an example is given to illustrate application of the main result

input output parametric models for non linear systems part ii stochastic non linear systems recursive input output models for non linear multivariate discrete time systems are derived and sufficient conditions for their existence are defined the paper is divided into two parts the first part introduces and defines concepts such as nerode realization multistructural forms and results from differential geometry which are then used to derive a recursive input output model for multivariable deterministic non linear systems the second part introduces several examples compares the derived model with other representations and extends the results to create prediction error or innovation input output models for non linear stochastic systems these latter models are the generalization of the multivariable arm ax models for linear systems and are referred to as narmax or non linear autoregressive moving average models with exogenous inputs

identification of partial differential equation models for a class of multiscale spatio temporal dynamical systems in this article the identification of a class of multiscale spatio temporal dynamical systems which incorporate multiple spatial scales from observations is studied the proposed approach is a combination of adams integration and an orthogonal least squares algorithm in which the multiscale operators are expanded using polynomials as basis functions and the spatial derivatives are estimated by finite difference methods the coefficients of the polynomials can vary with respect to the space domain to represent the feature of multiple scales involved in the system dynamics and are approximated using a b spline wavelet multi resolution analysis the resulting identified models of the spatio temporal evolution form a system of partial differential equations with different spatial scales examples are provided to demonstrate the efficiency of the proposed method

on stability of some linear and nonlinear delay differential equations abstract new explicit conditions of exponential stability are obtained for the nonautonomous equation with several delays y t k 1 l a k t y h k t 0 by the following method several delays in the left hand side are chosen and the solution is estimated using an auxiliary ordinary differential equation y t k i a k t y t 0 where i 1 2 l is the chosen set of indices these results are applied to analyze the stability of the nonlinear equation x t k 1 l a k t x h k t f t x t x g 1 t x g m t by the first approximation it is to be noted that coefficients and delays are not assumed to be continuous functions

a characteristic equation for non autonomous partial functional differential equations abstract we characterize the exponential dichotomy of non autonomous partial functional differential equations by means of a spectral condition extending known characteristic equations for the autonomous or time periodic case from this we deduce robustness results we further study the almost periodicity of solutions to the inhomogeneous equation our approach is based on the spectral theory of evolution semigroups

arithmetic of del pezzo surfaces of degree 4 and vertical brauer groups we show that brauer classes of a locally solvable degree 4 del pezzo surface x are vertical for some projection away from a plane g x p 1 i e that every brauer class is obtained by pullback from an element of br k p 1 as a consequence we prove that a brauer class obstructs the existence of a k rational point if and only if all k fibers of g fail to be locally solvable or in other words if and only if x is covered by curves that each have no adelic points using work of wittenberg we deduce that for certain quartic del pezzo surfaces with nontrivial brauer group the algebraic brauer manin obstruction is sufficient to explain all failures of the hasse principle conditional on schinzel s hypothesis and the finiteness of tate shafarevich groups the proof of the main theorem is constructive and gives a simple and practical algorithm distinct from that in 5 for computing all classes in the brauer group of x modulo constant algebras c 2014 elsevier inc all rights reserved

robust stability of time delay systems with an uncertain time delay constant frequency domain methods are described for testing the robust stability of a class of time delay systems with an uncertain time constant both parametric and non parametric uncertainties are considered our technique determines without a sweep of time delay the maximum time delay constant which preserves the robust stability

stability of perturbed systems with time varying delays abstract this paper gives easily verifiable sufficient conditions of robust asymptotic stability of linear time delay systems subject to parametric unstructured or highly structured perturbations the criteria given in this paper are delay independent or delay dependent the considered delay may be time varying an estimation of the transient behaviour of the studied systems is also provided exponential rate of convergence scalar or vectorial inequalities involving hurwitz matrices matrix measures and norms constitute the mathematical foundations of the exposed results

identification of mimo non linear systems using a forward regression orthogonal estimator abstract an orthogonal least squares estimator which was originally derived for single input single output systems is extended to multi input multi output non linear systems the estimator can provide information about the structure or which terms to include in the model and final parameter estimates in a very simple and efficient manner multivariable non linear model validity tests are also discussed and the results of applying the orthogonal estimator to both simulated and real data are included

socles and radicals of mackey functors we study the socle and the radical of a mackey functor m for a finite group g over a field k usually of characteristic p 0 for a subgroup h of g we construct bijections between some classes of the simple subfunctors of m and some classes of the simple kn g h submodules of m h we relate the multiplicity of a simple mackey functor sh vg in the socle of m to the multiplicity of v in the socle of a certain kn g h submodule of m h we also obtain similar results for the maximal subfunctors of m we then apply these general results to some special mackey functors for g including the functors obtained by inducing or restricting a simple mackey functor mackey functors for a p group the fixed point functor and the burnside functor bkg for instance we find the first four top factors of the radical series of bkg for a p group g and assuming further that g is an abelian p group we find the radical series of bkg

parabolic evolution equations with asymptotically autonomous delay we study retarded parabolic non autonomous evolution equations whose coefficients converge as t such that the autonomous problem in the limit has an exponential dichotomy then the non autonomous problem inherits the exponential dichotomy and the solution of the inhomogeneous equation tends to the stationary solution at infinity we use a generalized characteristic equation to deduce the exponential dichotomy and new representation formulas for the solution of the inhomogeneous equation

stability criterion for linear systems with nonlinear delayed perturbations a stability criterion for linear systems with nonlinear time varying delayed perturbations has been derived in light of razumikhin type methods as the proposed criterion is easily applicable and independent of the delay size it provides an effective method for the stability analysis of time delay systems

the socle of a projective mackey functor for a p group we study the simple subfunctors of indecomposable projective mackey functors for a p group p unlike the case of group algebras the mackey algebra is not in general self injective thus the socle of an indecomposable projective functor is not in general simple we first show that the simple subfunctors of a projective functor p h k where h p are indexed by the normalizer in h of a subgroup of h we then study the socle of a specific projective mackey functor namely the burnside functor b p and we focus on the case where p is abelian in particular our study enables us to determine the socle of an indecomposable projective mackey functor indexed by a cyclic p group an abelian p group of rank 2 and an elementary abelian p group of rank 3

stability conditions for scalar delay differential equations with a non delay term abstract the problem considered in the paper is exponential stability of linear equations and global attractivity of nonlinear non autonomous equations which include a non delay term and one or more delayed terms first we demonstrate that introducing a non delay term with a non negative coefficient can destroy stability of the delay equation next sufficient exponential stability conditions for linear equations with concentrated or distributed delays and global attractivity conditions for nonlinear equations are obtained the nonlinear results are applied to the mackey glass model of respiratory dynamics

identification of finite dimensional models of infinite dimensional dynamical systems the identification of finite dimensional discrete time models of deterministic linear and nonlinear infinite dimensional systems from pointwise observations is investigated the input and output observations are used to construct finite dimensional approximations of the solution and the forcing function which are expanded in terms of a finite element basis an algorithm to determine a minimal basis to approximate the data is introduced subsequently the resulting coordinate vectors are used to identify a finite dimensional discrete time model theoretical results concerning the existence stability and convergence of the finite dimensional representation are established numerical results involving identification of finite dimensional models for both linear and nonlinear infinite dimensional systems are presented

robust stability of delay dependence for linear uncertain systems a sufficient condition for the stability of the linear uncertain time delay systems is presented the result obtained can include information on the size of the delay and therefore can be a delay dependent stability condition the lyapunov method is employed to investigate the problem the result is demonstrated by an illustrative example

robust stability for time delay systems the edge theorem and graphical tests the robust stability problem is discussed for a class of uncertain delay systems where the characteristic equations involve a polytope p of quasi polynomials i e polynomials in one complex variable and exponential powers of the variable given a set d in the complex plane the goal is to find a constructive technique to verify whether all roots of every quasi polynomial in p belong to d that is to verify the d stability of p first it is demonstrated by counterexample that kharitonov s theorem does not hold for general delay systems next it is shown that under a mild assumption on the set d a polytope of quasi polynomials is d stable if and only if the edges of the polytope are d stable this extends the edge theorem for the d stability of a polytope of polynomials the third result gives a constructive graphical test for checking the d stability of a polytope of quasi polynomials which is especially simple when the set d is the open left half plane an application is given to demonstrate the power of the results

on the stability region of scalar delay differential equations on considere l equation differentielle scalaire a retard x t x t x t q ou r et q 0 on definit les regions de stabilite des solutions

quantitative measures of robustness for systems including delayed perturbations asymptotically stable linear systems subject to delayed time varying and nonlinear perturbations are considered razumikhin type theorems are used to obtain easy to compute bounds on the perturbations so that the systems remain stable results indicate that if delayed perturbations are included then the bound is reduced as compared to the one for nondelayed perturbations however in certain cases previously obtained bounds for the nondelayed perturbations guarantee stability even when delayed perturbations are in effect

exponential stability of linear delayed differential systems abstract linear delayed differential systems x i t j 1 m k 1 r i j a i j k t x j h i j k t i 1 m are analyzed on a half infinity interval t 0 it is assumed that m and rij i j 1 m are natural numbers and the coefficients a i j k 0 r and delays h i j k 0 r are measurable functions new explicit results on uniform exponential stability are derived including as partial cases recently published results

mackey functors with chain conditions abstract letabe a green functor for a finite groupgand letmbe a lefta module mis callednoetherian artinian if the lattice of all submodules ofmsatisfies acc respectively dcc mis calledtotally noetherian totally artinian ifmxis noetherian respectively artinian for every finiteg setx in this paper it is shown that the totally noetherian totally artinian lefta modules behave in the same way as the classical noetherian artinian modules the left noetherian left artinian green functors are less well behaved but some properties from classical algebra still hold it is shown that cohen s theorem holds in this setting our main result shows that if a commutative green functorais artinian then the ringsa h jac a h are semisimple artinian for all subgroupshofg

representations of non linear systems the narmax model abstract input output representations of non linear discrete time systems are discussed it is shown that the narmax non linear autoregressive moving average with exogenous inputs model is a general and natural representation of non linear systems and contains as special cases several existing non linear models the problem of approximating non linear input output systems is also addressed and several properties of non linear models are highlighted using simple examples