design of fixed lag smoother using covariance information based on innovations approach in linear discrete time stochastic systems this paper newly designs the recursive least squares rls wiener fixed lag smoother and filter using the covariance information in linear discrete time stochastic systems the estimators require the information of the observation matrix the system matrix for the state variable related with the signal the variance of the state variable the cross variance function of the state variable with the observed value and the variance of the white observation noise it is assumed that the signal is observed with additive white noise the current fixed lag smoothing algorithm has a characteristic as shown in theorem 1 that the fixed lag smoothing estimate of the state vector is calculated in the reverse direction of time

the distribution function inequality and products of toeplitz operators and hankel operators abstract in this paper we study hankel operators and toeplitz operators through a distribution function inequality on the lusin area integral function and the littlewood paley theory a sufficient condition and a necessary condition are obtained for the boundedness of the product of two hankel operators they lead to a way to approach sarason s conjecture on products of toeplitz operators and shed light on the compactness of the product of hankel operators an elementary necessary and sufficient condition for the product of two toeplitz operators to be a compact perturbation of a toeplitz operator is obtained moreover a necessary condition is given for the product of hankel operators to be in the commutator ideal of the algebra generated by the toeplitz operators with symbols in a sarason algebra

new design of fixed lag smoother using covariance information in linear discrete time stochastic systems this paper proposes recursive least squares fixed lag smoothing and filtering algorithms in linear discrete time stochastic systems the estimators require the information of the factorized autocovariance function of the signal namely the estimation algorithms use the observation matrix the system matrix for the state variable and the crossvariance function between the state variable and the signal also it is assumed that the variance of the white observation noise is known

stability analysis of neutral type systems in hilbert space the asymtoptic stability properties of neutral type systems are studied mainly in the critical case when the exponential stability is not possible we consider an operator model of the system in hilbert space and use recent results on the existence of a riesz basis of invariant finite dimensional subspaces in order to verify its dissipativity the main results concern the conditions of asymptotic non exponential stability we show that the property of asymptotic stability is not determinated only by the spectrum of the system but essentially depends on the geometric spectral characteristic of its main neutral term moreover we present an example of two systems of neutral type which have both the same spectrum in the open left half plane and the main neutral term but one of them is asymptotically stable while the other is unstable

observer with evolutionary programming based optimal digital tracker for analog neutral multiple time delay systems abstract in this paper the finite time optimal hybrid tracking control problem for analog neutral systems with multiple discrete and distributed time delays is formulated and studied a novel approach that combining the evolutionary programming ep algorithm and the high gain property for analog neutral multiple time delay systems is proposed to achieve the best tracking performance for the first time first the newton center interpolation formula and the linear interpolation formula together with a modified rectangular rule and an augmented state vector are utilized to construct the equivalent digital linear models next according to the separation principle the control gains of the digital tracker and the digital observer are designed separately by the discrete time optimal control theory and prediction based digital redesign method and then combined together to form an observer based optimal time varying digital tracker eventually the process is to combine the high gain property with ep algorithm to search the optimal weighting matrices in the performance index to form an observer with ep based low gain digital tracker to achieve the objective of optimal tracking control an example is given for illustrating the effectiveness of the new tracker design method

controllability of a class of nonlinear neutral time delay systems abstract in this paper the problem of controllability for a class of time varying nonlinear neutral time delay systems is considered sufficient conditions based on krasnoselskii s fixed point theorem are derived for the system to be globally and locally controllable eventually some illustrative examples are given in order to present the results established

exact observability and controllability for linear neutral type systems the problem of exact observability is analyzed for a wide class of neutral type systems by an infinite dimensional approach the duality with the exact controllabil ity problem is the main tool it is based on an explicit expression of a neutral type system which corresponding to the abstract adjoint system a nontrivial relation is obtained between the initial neutral system and the system obtained via the adjoint abstract state operator the characterization of the duality between controllability and observability is deduced and then observability conditions are obtained

on stabilization by state feedback for neutral differential difference equations in this paper we consider a class of feedback operators for a linear differential difference equation of the neutral type we show that if a system has unstable neutral root chains any stabilizing feedback operator in this class must contain a derivative of the delayed state component under the assumption of exact controllability we construct a stabilizing feedback operator

exponential stabilization of volterra integrodifferential equations in hilbert space we consider exponential stabilization of an abstract linear volterra integrodifferential equation in a hilbert space u e1au t e2 01k t s au s ds f t by a feedback control f t c0u t c1u t with bounded linear operators c0 and c1 of finite rank a is a positive semidefinite self adjoint unbounded operator k is nonnegative convex and decreasing with exponential decay k 0 being finite we introduce a concept of essential growth rate for resolvent operators similar to that for c0 semigroups and prove that the resolvent for the volterra equation has the same essential growth as the solution semigroup to u t e1au t e2k 0 e1u t f t stability can be checked by the location of poles and it is shown that exponential stabilization is possible with a decay rate of at most e2k 0 2e1 we apply our results to two problems concerning stabilization of motion of viscoelastic bodies

parameter identification for hyperbolic stochastic systems parameter identification is studied for hyperbolic stochastic systems explicit sufficient conditions ensuring consistency of the maximum likelihood estimate are given

the spectrum determined growth assumption for perturbations of analytic semigroups this short paper gives useful information concerning properties of perturbations of infinitesimal generators of analytic semigroups in particular it is shown that the spectrum determined growth assumption is retained not only under bounded perturbations but also under a class of unbounded perturbations which arise in control problems for parabolic systems where the control occurs pointwise or on the boundary

robust observers for neutral jumping systems with uncertain information in this paper the problem of designing observer for a class of uncertain neutral systems the uncertainties are parametric and norm bounded both robust observation and robust h observation methods are developed by using linear state delayed observers in case of robust observation sufficient conditions are established for asymptotic stability of the system which is independent of time delay the results are then extended to robust h observation which renders the augmented system asymptotically stable independent of delay with a guaranteed performance measure furthermore a memoryless state estimate feedback is designed to stabilize the closed loop neutral system in all cases the gain matrices are determined by linear matrix inequality approach two numerical examples are presented to illustrate the validity of the theoretical results

dual truncated toeplitz operators abstract let u be a nonconstant inner function in this paper we study the dual truncated toeplitz operators on the orthogonal complement of the model space k u 2 this is a new class of toeplitz operator we show the product of two dual truncated toeplitz operators d f d g to be zero if and only if either f or g is zero we give a necessary and sufficient condition for the product of two dual truncated toeplitz operators to be a finite rank operator furthermore a necessary and sufficient condition is found for the product of two dual truncated toeplitz operators to be a dual truncated toeplitz operator the last two results are different from the classical toeplitz operator theory

on feedback stabilizability of linear systems with state and input delays in banach spaces the feedback stabilizability of a general class of well posed linear systems with state and input delays in banach spaces is studied in this paper using the properties of infinite dimensional linear systems a necessary condition for the feedback stabilizability of delay systems is presented which extends the well known results for finite dimensional systems to infinite dimensional ones this condition becomes sufficient as well if the semigroup of the delay free system is immediately compact and the control space is finite dimensional moreover under the condition that the banach space is reflexive a rank condition in terms of eigenvectors and control operators is proposed when the delay free state space and control space are all finite dimensional a very compact rank condition is obtained finally the abstract results are illustrated with examples

toeplitz products with pluriharmonic symbols on the hardy space over the ball on the hardy space over the unit ball in cn we consider operators which have the form of a finite sum of products of several toeplitz operators we study characterizing problems of when such an operator is compact or of finite rank some of our results show higher dimensional phenomena

on strong regular stabilizability for linear neutral type systems the problem of strong stabilizability of linear systems of neutral type is investigated we are interested in the case when the system has an infinite sequence of eigenvalues with vanishing real parts this is the case when the main part of the neutral equation is not assumed to be stable in the classical sense we discuss the notion of regular strong stabilizability and present an approach to stabilize the system by regular linear controls the method covers the case of multivariable control and is essentially based on the idea of infinite dimensional pole assignment proposed in g m sklyar a v rezounenko a theorem on the strong asymptotic stability and determination of stabilizing controls c r acad sci paris ser i math 333 8 2001 807 812 our approach is based on the recent results on the riesz basis of invariant finitedimensional subspaces and strong stability for neutral type systems presented in r rabah g m sklyar a v rezounenko stability analysis of neutral type systems in hilbert space j differential equations 214 2 2005 391 428

on robust stabilizability of linear differential difference systems with unstable d operator the robustness of linear delayed neutral type control systems with the unstable difference operator is considered the robustness analysis is stipulated by the impossibility of implementing precisely derivative feedback different approximations of stabilizing controls and their influence on the stability of the closed loop system are considered

periodic output feedback stabilization of neutral systems a new feedback control technique called periodic output feedback is investigated in the context of infinite dimensional linear systems modeled by neutral functional differential equations in this method discrete output samples are multiplied by a periodic gain function to generate a continuous feedback control this work focuses on stabilization of neutral systems with delayed control modeled in the state space w sub 2 sup 1 r 0 r sup n spl times l sup 2 r 0 r sup p where w sub 2 sup 1 r 0 r sup n denotes the sobolev space of r sup n valued absolutely continuous functions with square integrable derivatives on r 0 we show that a class of these systems can be stabilized by periodic output feedback even though their input operators are unbounded we overcome this difficulty by representing the system state using an abstract integral variation of constants formula an algorithm is presented at the end of this paper to construct a periodic output feedback gain function an example is provided to illustrate the construction of the gain function

the finite sum of finite products of toeplitz operators on the polydisk abstract a limit theorem is established for a finite sum of finite products of toeplitz operators on the hardy space of the polydisk as a consequence we show that the product of six toeplitz operators with pluriharmonic symbols is compact iff the product equals zero iff one of these toeplitz operators equals zero

finite dimensional compensators for parabolic distributed systems with unbounded control and observation it is proved that for a class of parabolic distributed parameter systems with unbounded control and observation there exists a finite dimensional compensator using dynamic output feedback finite dimensional means here that the dynamics relating the input to the output is finite dimensional a constructive design algorithm is presented and several examples are considered

spectral assignment for neutral type systems and moment problems for a large class of linear neutral type systems the problem of assigning eigenvalues and eigenvectors is investigated i e finding the system that has the given spectrum and in some sense allmost all eigenvectors the solution of this problem enables vector moment problems to be considered using the construction of a neutral type system the exact controllability property of the system obtained gives the solution of the vector moment problem

resolvent operators for integral equations in a banach space conditions are given which ensure the existence of a resolvent operator for an integrodifferential equation in a banach space the resolvent operator is similar to an evolution operator for nonautonomous differential equations in a banach space as in the finite dimensional case this operator is used to obtain a variation of parameters formula which can be used to obtain results concerning the asymptotic behaviour of solutions and weak solutions

zero products of toeplitz operators we prove that the product of finitely many toeplitz operators oil the hardy space is zero if and only if at least one of the operators is zero we use some new vector valued techniques that not only lead to a vector valued version of this result but also appear to be needed in the scalar case

equivalent conditions on periodic feedback stabilization for linear periodic evolution equations abstract this paper studies the periodic feedback stabilization for a class of linear t periodic evolution equations several equivalent conditions on the linear periodic feedback stabilization are obtained these conditions are related to the following subjects the attainable subspace of the controlled evolution equation under consideration the unstable subspace of the evolution equation with the null control provided by the kato projection the poincare map associated with the evolution equation with the null control and two unique continuation properties for the dual equations on different time horizons 0 t and 0 n 0 t where n 0 is the sum of algebraic multiplicities of distinct unstable eigenvalues of the poincare map it is also proved that a t periodic controlled evolution equation is linear t periodic feedback stabilizable if and only if it is linear t periodic feedback stabilizable with respect to a finite dimensional subspace some applications to heat equations with time periodic potentials are presented

obituary to a j pritchard on the 12th of august 2007 tony pritchard professor of mathematics at the university of warwick died suddenly at the age of 70 from a heart attack while on holiday with his family on the island of lanzarote both of the authors have had the privilege of working with him for many years we have lost both a colleague and a friend the following notes are dedicated to his memory

a note on stability and stabilizability of neutral systems this note presents frequency domain characterizations of exponential stability and stabilizability of neutral systems based on transfer function matrices and the existence of nice solutions of certain bezout equations it turns out that the existence of h sup spl infin solutions is not sufficient for exponential stabilizability but that they have to satisfy an additional growth assumption as well whilst the proofs of the authors results are based on an abstract infinite dimensional representation of the neutral system they emphasize that the results are expressed in terms of the original parameters of the neutral equation and do not require a reformulation of the system in an abstract state space form the sufficiency parts of the results hold even when the delay operator acting on the derivative contains a singular part

distributed system transfer functions of exponential order o is a real number we construct a transfer function algebra of fractions viz f o for modelling possibly unstable distributed systems such that i fcirc in f o is holomorphic in re s o i e is o stable iff fcirc is o exponentially stable and ii we allow delay in the direct input output transmission of the system this algebra is a a restriction of the algebra b o developed by callier and desoer 1978 1980 a b an extension of the algebra of proper rational functions such that the exponential order properties of the latter transfer functions of lumped systems are maintained the algebra f o can be used for modelling and feedback system design it is shown that standard semigroup systems are better modelled by a transfer function in f o rather than b o

invariant measures for stochastic nonlinear beam and wave equations existence of an invariant measure for a stochastic extensible beam equation and for a stochastic damped wave equation with polynomial nonlinearities is proved it is shown first that the corresponding transition semigroups map the space of all bounded sequentially weakly continuous functions on the state space into itself and then by a lyapunov functions approach solutions bounded in probability are found

essentially commuting hankel and toeplitz operators abstract we characterize when a hankel operator and a toeplitz operator have a compact commutator

on the function space controllability of linear neutral systems a criterion is derived for approximate controllability of linear autonomous neutral functional differential equations in the sobolev space w 2 1 h 0 mathbb e n controllability conditions are based on an abstract evolution equation representation of the system an abstract criterion applicable to a general class of neutral systems is obtained and for the special case of matrix systems of the form frac d dt left x t a 1 x t h right e 0 x t e 1 x t h bu t this abstract criterion leads to an algebraic criterion

zero products of toeplitz operators with harmonic symbols on the bergman space of the unit ball in cn we solve the zero product problem for two toeplitz operators with harmonic symbols that have continuous extensions to some part of the boundary in the case where symbols have lipschitz continuous extensions to the boundary we solve the zero product problem for multiple products with the number of factors depending on the dimension n of the underlying space the number of factors is n 3 we also prove a local version of this result but with loss of a factor

stochastic nonlinear beam equations an extensible beam equation with a stochastic force of a white noise type is studied lyapunov functions techniques being used to prove existence of global mild solutions and asymptotic stability of the zero solution

least squares finite impulse response fixed lag smoother and filter in linear discrete time stochastic systems abstract this paper proposes the least squares ls finite impulse response fir fixed lag smoother and filter in linear discrete time wide sense stationary stochastic systems the fir fixed lag smoothing estimate is given as a linear convolution sum of the impulse response function and the observed values it is assumed that the signal is observed with additional white noise which is uncorrelated with the signal process by solving the simultaneous linear equations transformed from the wiener hopf equation the optimal impulse response function is obtained the necessary information of the ls fir fixed lag smoothing algorithm is the auto covariance function of the signal process and the variance of the observation noise process in particular this paper proposes the levinson durbin algorithm which needs less amount of arithmetic operations than the gauss jordan elimination method in the inverse of the toeplitz matrix for the optimal impulse response function from the numerical simulation example the proposed ls fir fixed lag smoother and filter are superior in estimation accuracy to the rls wiener fir estimators

h and bibo stabilization of delay systems of neutral type frequency domain tests for the h and bibo stability of large classes of delay systems of neutral type are derived the results are applied to discuss the stabilizability of such systems by finite dimensional controllers

the analysis of exact controllability of neutral type systems by the moment problem approach the problem of exact null controllability is considered for a wide class of linear neutral type systems with distributed delay the main tool of the analysis is the application of the moment problem approach and the theory of the basis property of exponential families a complete characterization of this problem is given the minimal time of controllability is specified the results are based on the analysis of the riesz basis property of eigenspaces of the neutral type systems in hilbert space

finite sums of toeplitz products on the dirichlet space on the dirichlet space of the unit disk we consider a class of operators which contain finite sums of products of two toeplitz operators with harmonic symbols we give characterizations of when an operator in that class is zero or compact also we solve the zero product problem for products of finitely many toeplitz operators with harmonic symbols

stability and stabilizability of infinite dimensional systems in this paper we are concerned with stability problems for infinite dimensional systems first we review the theory for linear systems where the dynamics are governed by strongly continuous semigro

large time behaviour for functional differential equations with dominant eigenvalues of arbitrary order the spectral theory for linear autonomous neutral functional differential equations fde yields explicit formulas for the large time behaviour of solutions our results are based on resolvent computations and dunford calculus applied to establish explicit formulas for the large time behaviour of solutions of fde we investigate in detail a class of two dimensional systems of fde

stabilization problem in hilbert spaces the stabilization problem for linear systems on hilbert spaces is examined necessary and sufficient conditions for the state stabilization by a linear bounded feedback are given using these results and similar methods necessary and sufficient conditions for output stabilization are given

controllability radii of linear neutral systems under structured perturbations abstractin this paper we shall deal with the problem of calculation of the controllability radii of linear neutral systems of the form x t a0x t a1x t h a 1x t h bu t we will derive the definition of exact controllability radius approximate controllability radius and euclidean controllability radius for this system by using multi valued linear operators the computable formulas for these controllability radii are established in the case where the system s coefficient matrices are subjected to structured perturbations some examples are provided to illustrate the obtained results

technical communique descriptor wiener state estimators based on the modern time series analysis method a new time domain wiener filtering approach is presented asymptotically stable wiener state estimators are presented for discrete linear stochastic descriptor systems they can be implemented via the autoregressive moving average arma recursive filters they can handle the optimal state filtering smoothing and prediction problems in a unified framework and can simply be obtained based on the arma innovation model the solution of the diophantine equations and riccati equations is avoided so that the computational burden is reduced a simulation example shows the effectiveness of the new approach

the distribution function inequality for a finite sum of finite products of toeplitz operators abstract a generalized area function associated with a finite sum of finite products of toeplitz operators is introduced a distribution function inequality is established for the generalized area function by using the distribution function inequality we characterize when a finite sum of finite products of toeplitz operators on the hardy space is a compact perturbation of a toeplitz operator

a method for computing the interval of delay values for which a differential delay system is stable a test for determining the interval of delay values for which delay differential system is asymptotically stable is presented i e an explicit method is given for calculating h such that for 0

on the delay independent stabilization of linear neutral systems with limited measurable state variables abstract the delay independent stabilizability of linear neutral systems with limited measurable state variables is considered a sufficient condition for the delay independent stabilizability of linear retarded systems with limited measurable state variables and linear neutral systems with measurable state variables which had been obtained by amemiya and maet al is proved to be also valid for linear neutral systems with limited measurable state variables

berezin versus mellin we study zero products of two bergman space toeplitz operators where one symbol is harmonic our results point in the direction of the zero product problem having only a trivial solution the techniques we use are based on a formula that connects the berezin and mellin transform

products of several toeplitz operators in this paper we give a necessary and sufficient condition for ta1ta2 tan ta1a2 an where the tai s are toeplitz operators on the hardy space of the unit disk we then show that ta1ta2ta3ta4ta5ta6 0 if and only if one of ai is identically zero a criteria for the compactness of ta1ta2 tan ta1a2 an is also given

new design of fixed interval smoother using covariance information in linear stochastic continuous time systems this paper proposes recursive least squares fixed interval smoothing and filtering algorithms in linear continuous time stochastic systems the estimators require the information of the autocovariance function of the signal the variance of white observation noise and the observed value the autocovariance function of the signal is expressed in the form of the semi degenerate kernel

a theorem on neutral delay systems abstract it is known that the stabilization of neutral delay differential tems requires first the stabilization of the difference operator or d operator in case all delays in the system are commensurable necessary and sufficient conditions for the existence of suitable derivative feedback for the stabilization of the d operator have been known for some time 14 in this note we derive a result in the case of noncommensurable delays analogous to the known results for the commensurable delay case