a non hyponormal operator generating stieltjes moment sequences abstract a linear operator s in a complex hilbert space h for which the set d s of its c vectors is dense in h and s n f 2 n 0 is a stieltjes moment sequence for every f d s is said to generate stieltjes moment sequences it is shown that there exists a closed non hyponormal operator s which generates stieltjes moment sequences what is more d s is a core of any power s n of s this is established with the help of a weighted shift on a directed tree with one branching vertex the main tool in the construction comes from the theory of indeterminate stieltjes moment sequences as a consequence it is shown that there exists a non hyponormal composition operator in an l 2 space over a finite measure space which is injective paranormal and which generates stieltjes moment sequences the independence assertion of barry simon s theorem which parameterizes von neumann extensions of a closed real symmetric operator with deficiency indices 1 1 is shown to be false

unbounded subnormal weighted shifts on directed trees ii abstract a new method of verifying the subnormality of unbounded hilbert space operators based on an approximation technique is proposed diverse sufficient conditions for subnormality of unbounded weighted shifts on directed trees are established an approach to this issue via consistent systems of probability measures is invented the role played by determinate stieltjes moment sequences is elucidated lambert s characterization of subnormality of bounded operators is shown to be valid for unbounded weighted shifts on directed trees that have sufficiently many quasi analytic vectors which is a new phenomenon in this area

control of an unstable reaction diffusion pde with long input delay abstract a smith predictor like design for compensation of arbitrarily long input delays is available for general controllable possibly unstable lti finite dimensional systems such a design has not been proposed previously for problems where the plant is a pde we present a design and stability analysis for a prototype problem where the plant is a reaction diffusion parabolic pde with boundary control the plant has an arbitrary number of unstable eigenvalues and arbitrarily long delay with an unbounded input operator the predictor based feedback design extends fairly routinely within the framework of infinite dimensional backstepping however the stability analysis contains interesting features that do not arise in predictor problems when the plant is an ode the unbounded character of the input operator requires that the stability be characterized in terms of the h 1 rather than the usual l 2 norm of the actuator state the analysis involves an interesting structure of interconnected pdes of parabolic and first order hyperbolic types where the feedback gain kernel for the undelayed problem becomes an initial condition in a pde arising in the compensator design for the problem with input delay space and time variables swap their roles in an interesting manner throughout the analysis

energy decay problems in the design of a point stabilizer for coupled string vibrating systems this paper solves completely the following problem posed by chen coleman and west siam j appl math 47 pp 751 780 when can we achieve the desirable uniform exponential decay property of the vibration energy for two coupled vibrating strings with a stabilizer or damper installed at the coupling point an approach using abstract semigroups is shown the paper proves the following for the cases when the stabilizers are symmetrically placed the system s energy does not decay to zero with respect to time for some initial states for all the other cases if the proportion of the wave speeds on the two vibrating strings c 2 c 1 is a rational number applying the formula of the growth order of a c 0 semigroup on a hilbgrt space derived by huang 2 proves that the semigroup satisfies the spectrum determined growth assumption so the uniform exponential decay property depends completely on the representative form of the ratio c 2 c 1 finally the paper proves that if

admissibility of unbounded control operators for linear systems described by dot x t ax t bu t where a generates a semigroup on the state space x and b is an unbounded operator some necessary as well as some sufficient conditions are given for b to be admissible i e for any t the state x t should be in x and should depend continuously on the input u in l p this approach begins with an axiomatic description of such a system in terms of a functional equation the results are applied to the wave equation on a bounded interval

an optimization problem with applications to optimal design theory on utilise les resultats d un probleme d optimisation pour montrer que pour certains plans s ils sont optimaux relativement a deux criteres alors ils sont optimaux relativement a plusieurs autres criteres

quasinormal extensions of subnormal operator weighted composition operators in l2 spaces abstract we prove the subnormality of an operator weighted composition operator whose symbol is a transformation of a discrete measure space and whose weights are multiplication operators in l 2 spaces under the assumption of existence of a family of probability measures whose radon nikodym derivatives behave regular along the trajectories of the symbol we build the quasinormal extension which is a weighted composition operator induced by the same symbol we give auxiliary results concerning commutativity of operator weighted composition operators with multiplication operators

subnormality of unbounded composition operators over one circuit directed graphs exotic examples abstract a recent example of a non hyponormal injective composition operator in an l 2 space generating stieltjes moment sequences invented by three of the present authors was built over a non locally finite directed tree the main goal of this paper is to solve the problem of whether there exists such an operator over a locally finite directed graph and in the affirmative case to find the simplest possible graph with these properties simplicity refers to local valency the problem is solved affirmatively for the locally finite directed graph g 2 0 which consists of two branches and one loop the only simpler directed graph for which the problem remains unsolved consists of one branch and one loop the consistency condition the only efficient tool for verifying subnormality of unbounded composition operators is intensively studied in the context of g 2 0 which leads to a constructive method of solving the problem the method itself is partly based on transforming the krein and the friedrichs measures coming either from shifted al salam carlitz q polynomials or from a quartic birth and death process

an example for the switching delay feedback stabilization of an infinite dimensional system the boundary stabilization of a string abstract for vibrating systems a delay in the application of a feedback control may destroy the stabilizing effect of the control in this paper we consider a vibrating string that is fixed at one end and stabilized with a boundary feedback with delay at the other end we show that certain delays in the boundary feedback preserve the exponential stability of the system in particular we show that the system is exponentially stable with delays freely switching between the values 4 l c and 8 l c where l is the length of the string and c is the wave speed

d optimal 0 1 weighing designs for eight objects abstract let g m n max det w t w w m m n 0 1 a matrix w m m n 0 1 with det w t w g m n is called d optimal here we determine g m 8 for m large with the help of a variation of mitchell s detmax algorithm and describe the d optimal examples

probleme des moments sur un compact de rn et decomposition de polynomes a plusieurs variables on donne la solution du probleme des moments pour un compact d interieur non vide quelconque de r n on utilise cette resolution pour obtenir un resultat de decomposition des polynomes strictement positifs sur un compact d interieur non vide

notes on d optimal designs abstract the purpose of this paper is to exhibit new infinite families of d optimal 0 1 matrices we show that hadamard designs lead to d optimal matrices of size j mj and j 1 mj for certain integers j 3 mod 4 and all positive integers m for j a power of a prime and j 1 mod 4 supplementary difference sets lead to d optimal matrices of size j 2mj and j 1 2mj for all positive integers m we also show that for a given j and d sufficiently large about half of the entries in each column of a d optimal matrix are ones this leads to a new relationship between d optimality for 0 1 matrices and for 1 matrices known results about d optimal 1 matrices are then used to obtain new d optimal 0 1 matrices

unbounded subnormal composition operators in l2 spaces abstract a novel criterion for subnormality of unbounded composition operators in l 2 spaces written in terms of measurable families of probability measures satisfying the so called consistency condition is established it becomes a new characterization of subnormality in the case of bounded composition operators pseudo moments of a measurable family of probability measures that satisfies the consistency condition are proved to be given by the radon nikodym derivatives which appear in lambert s characterization of bounded composition operators a criterion for subnormality of composition operators induced by matrices is provided the question of subnormality of composition operators over discrete measure spaces is studied two new classes of subnormal composition operators over discrete measure spaces are introduced a recent criterion for subnormality of weighted shifts on directed trees by the present authors is essentially improved in the case of rootless directed trees and nonzero weights by dropping the assumption of density of c vectors in the underlying l 2 space

two examples of ill posedness with respect to time delays revisited we revisit two examples of elastic control systems which are stabilized by boundary feedback and then destabilized when time delays occur in the feedback in the first example a wave equation with a feedback gain greater than or equal to one arbitrary divergence rates are obtained for small time delays in the second example a euler bernoulli beam any time delay results in an arbitrary divergence rate

stability and stabilization of switched linear systems with mode dependent average dwell time in this paper the stability and stabilization problems for a class of switched linear systems with mode dependent average dwell time mdadt are investigated in both continuous time and discrete time contexts the proposed switching law is more applicable in practice than the average dwell time adt switching in which each mode in the underlying system has its own adt the stability criteria for switched systems with mdadt in nonlinear setting are firstly derived by which the conditions for stability and stabilization for linear systems are also presented a numerical example is given to show the validity and potential of the developed techniques

stabilisation of an anti stable joint string with boundary disturbance in this paper we consider the boundary stabilisation for a one dimensional joint anti stable string equation with input disturbance entering the control end a backstepping transformation is used

a optimal weighing designs when n equiv 3 operatorname mod 4 on considere le probleme des plans de pesage a optimaux pour n objets dans n pesages concernant un bilan chimique quand n 3 modulo 4 sort d n n la classe des matrices plan x d est tel que x d x d est une matrice bloc ayant une structure de blocs specifiees alors x d est a optimal dans d n n on trouve que dans certains cas le plan a optimal dans d n n n est pas unique une plus grande classe de plans de pesage de bilan chimique est d o n n ou x d peut avoir certains elements egaux a zero il est observe que les plans qui sont a optimaux dans d n n ne le sont pas necessairement dans d o n n

the regularity of the wave equation with partial dirichlet control and colocated observation in this paper we analyze a multidimensional controlled wave equation on a bounded domain subject to partial dirichlet control and colocated observation by means of a partial fourier transform it is shown that the system is well posed and regular in the sense of d salamon and g weiss the corresponding feedthrough operator is found to be the identity operator on the input space

unbounded extensions and operator moment problems abstract extension results expressed in terms of complete boundedness leading to necessary and sufficient conditions for the solvability of power moment problems with unbounded operator data are given as an application necessary and sufficient conditions for the existence of selfadjoint and normal extensions for some classes of commuting tuples of unbounded linear operators are obtained

uniform tube based stabilization of switched linear systems with mode dependent persistent dwell time in this note the stabilization problem for a class of discrete time switched linear systems with additive disturbances is investigated the considered switching signals are of mode dependent persistent dwell time mpdt property and the disturbances are assumed to be amplitude bounded by constructing a quasi time varying qtv lyapunov function a qtv stabilizing controller is designed for the nominal system such that the resulting closed loop system is globally uniformly asymptotically stable in the presence of bounded additive disturbances a mpdt robust positive invariant set is determined for the error system between the nominal system and disturbed system a concept of generalized robust positive invariant grpi set under admissible mpdt switching is further proposed for the error system it is demonstrated that the disturbed system is also asymptotically stable in the sense of converging to the mpdt grpi set that can be regarded as the cross section of a uniform tube of the disturbed system a numerical example is provided to verify the theoretical findings

controllability and stability of a second order hyperbolic system with collocated sensor actuator a second order hyperbolic system with collocated sensor actuator is considered the semigroup generation is shown for the closed loop system under the feedback of a generic unbounded observation operator the equivalence between the exponential stability of the closed loop system and exact controllability of the open loop system is established in the general framework of well posed linear systems finally the conditions are weakened for the diagonal semigroups with finite dimensional inputs example of beam equation is presented to display the application

on the ϰth root of a stieltjes moment sequence abstract stieltjes moment sequences a n n 0 whose th roots a n n 0 are stieltjes moment sequences are studied is a fixed integer greater than or equal to 2 a formula connecting the closed supports of representing measures of a n n 0 and a n n 0 is established the relationship between the holes of the supports of these measures is investigated the set of all pairs m n of positive integers for which there exists a stieltjes moment sequence whose square root is a stieltjes moment sequence and both of them have representing measures supported on subsets of 0 of cardinality m and n respectively is described

analysis designs and behavior of dissipative joints for coupled beams in the construction of modern large flexible space structures active and passive damping devices are commonly installed at joints of coupled beams to achieve the suppression of vibration in order to successfully control such dynamic structures the function and behavior of dissipative joints must be carefully studied these dissipative joints are analyzed by first classifying them into types according to the discontinuities of physical variables across a joint the four important physical variables for beams are displacement y rotation theta bending moment m and shear v dissipative joints can be classified into the following four types 1 m and v are continuous y and theta are discontinuous 2 y and m are continuous theta and v are discontinuous 3 y and theta are continuous m and v are discontinuous 4 theta and v are continuous y and m are discontinuous according to the conjugacy of these variables mechanical designs have been achieved for all t

brief paper lyapunov tools for predictor feedbacks for delay systems inverse optimality and robustness to delay mismatch we consider lti finite dimensional completely controllable but possibly open loop unstable plants with arbitrarily long actuator delay and the corresponding predictor based feedback for delay compensation we study the problem of inverse optimal re design of the predictor based feedback law we obtain a simple modification of the basic predictor based controller which employs a low pass filter and has been proposed previously by mondie and michiels for achieving robustness to discretization of the integral term in the predictor feedback law the key element in our work is the employment of an infinite dimensional backstepping transformation and the resulting lyapunov function for the infinite dimensional systems consisting of the state of the ode plant and the delay state the lyapunov function allows us to quantify the lyapunov stability properties under the modified feedback the inverse optimality of the feedback and its disturbance attenuation properties for the basic predictor feedback the availability of the lyapunov function also allows us to prove robustness to small delay mismatch in both positive and negative directions

a multiplicative property characterizes quasinormal composition operators in l2 spaces abstract a densely defined composition operator in an l 2 space induced by a measurable transformation is shown to be quasinormal if and only if the radon nikodym derivatives h n attached to powers n of have the multiplicative property h n h n almost everywhere for n 0 1 2

stabilization of bernoulli euler beams by means of a pointwise feedback force we study the energy decay of a bernoulli euler beam which is subject to a pointwise feedback force we show that both uniform and nonuniform energy decay may occur the uniform or nonuniform decay depends on the boundary conditions in the case of nonuniform decay in the energy space we give explicit polynomial decay estimates valid for regular initial data our method consists of deducing the decay estimates from observability inequalities for the associated undamped problem via sharp trace regularity results

on the optimality of finite williams ii a designs on considere des plans de type ii a de williams et on s interesse a l autoregression du premier ordre stationnaire avec 0

robustness of optimal designs for correlated random variables abstract suppose that y y i is a normal random vector with mean xb and covariance 2 i n where b is a p dimensional vector b j x x ij is an n p matrix with x ij 1 1 this corresponds to a factorial design with 1 1 representing low or high level respectively or corresponds to a weighing design with 1 1 representing an object j with weight b j placed on the left and right of a chemical balance respectively e optimal designs z are chosen that are robust in the sense that they remain e optimal when the covariance of y i y i is 0 for i i within a smaller class of designs similar results are obtained with respect to a general class of optimality criteria which include the a and d criteria

exponential stabilization of a rayleigh beam using collocated control we consider a hinged elastic beam described by the rayleigh beam equation on the interval 0 pi we assume the presence of two sensors one measures the angular velocity of the beam at a point xi epsiv 0 pi and the other measures the bending curvature of the beam at the same point if xi 0 or xi pi then the second output is not needed the corresponding operator semigroup is unitary on a suitable hilbert state space these two measurements are advantageous because they make the open loop system exactly observable regardless of the point xi we design the actuators and the feedback law in order to exponentially stabilize this system using the theory of collocated static output feedback developed in our recent paper we design the actuators such that they are collocated meaning that b c where b is the control operator and c is the observation operator it turns out that if xi epsiv 0 pi then the actuators cause a discontinuity of the bending exactly at this is the price in this example of having collocated actuators and sensors this obliges us to use an extension of to define the output signal in terms of the left and right limit of the bending at xi we prove that for all static output feedback gains in a suitable finite range the closed loop system is well posed and exponentially stable this follows from the general theory in our paper whose main points are recalled here

the moment problem on compact semi algebraic sets in this chapter we begin the study of the multidimensional moment problem the passage to dimensions d 2 brings new difficulties and unexpected phenomena in sect 3 2 we derived solvability criteria of the moment problem on intervals in terms of positivity conditions it seems to be natural to look for similar characterizations in higher dimensions as well this leads us immediately into the realm of real algebraic geometry and to descriptions of positive polynomials on semi algebraic sets in this chapter we treat this approach for basic closed compact semi algebraic subsets of mathbb r d it turns out that for such sets there is a close interaction between the moment problem and positivstellensatze for strictly positive polynomials

largest j simplices in d cubes some relatives of the hadamard maximum determinant problem abstract this paper studies the computationally difficult problem of finding a largest j dimensional simplex in a given d dimensional cube the case in which j d is of special interest for it is equivalent to the hadamard maximum determinant problem it has been solved for infinitely many values of d but not for d 14 the subcase in which j d 3 mod 4 subsumes the famous problem on the existence of hadamard matrices the known results for the case j d are here summarized and used but the main focus is on fixed small values of j when j 1 the problem is trivial and when j 2 or j 3 it is here solved completely i e for all d beyond that the results are fragmentary but numerous and they lead to several attractive conjectures some other problems involving simplices in cubes are mentioned and the relationship of largest simplices to d optimal weighing designs is discussed

wave equation stabilization by delays equal to even multiples of the wave propagation time for a string equation with time delays in the output feedback loop we study stability and show that the system is a riesz spectral system and prove that the spectrum determined growth condition holds for all delays when the delay is equal to the even multiples of the wave propagation time we develop the necessary and sufficient conditions for the feedback gain and time delay which guarantee the exponential stability of the closed loop system in particular we show that as the delay of even multiples is increasing to infinity the stability bound on the feedback gain decays to zero we also show that whenever the delay is an odd multiple of the wave propagation time the closed loop system is unstable the lack of robustness to a small perturbation in time delay is specifically discussed for the delay equal to two a numerical simulation for the case of the delay equal to two is presented to illustrate the convergence finally an alternative stability analysis is conducted within the framework of well posed infinite dimensional systems

extending positive definiteness the main result of this paper gives criteria for extendibility of mappings defined on symmetric subsets of semigroups to positive definite ones by specifying the mappings in question we obtain new solutions of relevant issues in harmonic analysis concerning truncations of some important multivariate moment problems like complex two sided complex and multidimensional trigonometric moment problems in addition unbounded subnormality and existence of unitary power dilation of several contractions is treated as an application of our general scheme

uniquely e optimal designs with n 2 mod4 correlated observations abstract in this paper we consider uniquely e optimal and highly e efficient designs described by a linear model with design matrices with elements in 1 0 1 the errors are assumed to be equally positively correlated and to have equal variances these designs correspond to chemical balance weighing designs or to three level factorial designs designs that satisfy certain conditions are proved to be uniquely e optimal designs when the number of observations n 2 mod 4 constructions of such designs are presented given the existence of an s n matrix and a hadamard matrix it is also proved that the constructed uniquely e optimal designs are not in general a or d optimal finally the high e efficiency of the designs of masaro and wong 2008 11 12 and certain other designs is shown these designs can be a good substitute for unknown e optimal designs in some cases

linear systems with delayed controls a reduction linear systems with delayed control action are transformed into systems without delays under an absolute continuity condition the new system is an ordinary differential control equation in the general case the new system is a measure differential control system it is shown how the controllability stabilization and various optimization problems can be analyzed via the reduced systems

a subnormal weighted shift on a directed tree whose nth power has trivial domain abstract it is shown that for any positive integer n there exists a subnormal weighted shift on a directed tree whose nth power is closed and densely defined while its n 1 th power has trivial domain similar result for composition operators in l 2 spaces is established

robustness of a optimal designs abstract suppose that y y i is a normal random vector with mean xb and covariance 2 i n where b is a p dimensional vector b j x x ij is an n p matrix a optimal designs x are chosen from the traditional set d of a optimal designs for 0 such that x is still a optimal in d when the components y i are dependent i e for i i the covariance of y i y i is with 0 such designs depend on the sign of the general results are applied to x x ij where x ij 1 1 this corresponds to a factorial design with 1 1 representing low level or high level respectively or corresponds to a weighing design with 1 1 representing an object j with weight b j being weighed on the left and right of a chemical balance respectively

delay robustness of linear predictor feedback without restriction on delay rate robustness is established for the predictor feedback for linear time invariant systems with respect to possibly time varying perturbations of the input delay with a constant nominal delay the prior results have addressed qualitatively constant delay perturbations robustness of stability in l 2 norm of actuator state and delay perturbations with restricted rate of change robustness of stability in h 1 norm of actuator state the present work provides simple formulas that allow direct and accurate computation of the least upper bound of the magnitude of the delay perturbation for which the exponential stability in supremum norm on the actuator state is preserved while the prior work has employed lyapunov krasovskii functionals constructed via backstepping the present work employs a particular form of small gain analysis two cases are considered the case of measurable possibly discontinuous time varying perturbations and the case of constant perturbations

a optimization of exact first order saturated designs for n 1 mod 4 observations abstract the case of exact first order saturated designs with n 1 mod 4 observations n 2 s s 1 1 s 1 2 is considered conditions are found for the a optimality of such designs when the first r rows of the corresponding design matrix have a known structure by modifying the method of sathe and shenoy 1989 for the case n 1 mod 4 the structure of the information matrix of the a optimal design is found then by exhaustive search it is proved that the known d optimal saturated design for n 9 ehlich 1964 is also a optimal

on the optimality of a class of designs with three concurrences abstract in the present paper we consider a class of unequally replicated designs having concurrence range 2 and spectrum of the form 1 2 v 3 3 now jacroux s some sufficient conditions for the type i optimality of block designs j statist plann inference 11 1985 385 396 proposition 2 4 says that a design with spectrum of the above form if satisfies some further conditions is type 1 optimal unfortunately this proposition does not apply to our designs since they have a poor status regarding e optimality yet we are able to prove the a optimality in the general class of these designs using majorisation technique a method of construction of an infinite series of our a optimal designs has also been given the first and only known infinite series of examples of designs satisfying jacroux s conditions appears to be the first one in section 4 1 of morgan and srivastav on the type 1 optimality of nearly balanced incomplete block designs with small concurrence range statist sinica 10 2000 1091 1116 hitherto referred to as ms in this paper we use majorisation technique to prove stronger optimality properties of the above mentioned designs of ms as well as to present simpler proof of another optimality result in ms

optimal supersaturated designs we consider screening experiments where an investigator wishes to study many factors using fewer observations our focus is on experiments with two level factors and a main effects model with intercept since the number of parameters is larger than the number of observations traditional methods of inference and design are unavailable in 1959 box suggested the use of supersaturated designs and in 1962 booth and cox introduced measures for efficiency of these designs including e s2 which is the average of squares of the off diagonal entries of the information matrix ignoring the intercept for a design to be e s2 optimal the main effect of every factor must be orthogonal to the intercept factors are balanced and among all designs that satisfy this condition it should minimize e s2 this is a natural approach since it identifies the most nearly orthogonal design and orthogonal designs enjoy many desirable properties including efficient parameter estimation factor balance in an e s2 optimal d

the classical moment problem as a self adjoint finite difference operator abstract this is a comprehensive exposition of the classical moment problem using methods from the theory of finite difference operators among the advantages of this approach is that the nevanlinna functions appear as elements of a transfer matrix and convergence of pade approximants appears as the strong resolvent convergence of finite matrix approximations to a jacobi matrix as a bonus of this we obtain new results on the convergence of certain pade approximants for series of hamburger

modeling stabilization and control of serially connected beams many flexible structures consist of a large number of components coupled end to end in the form of a chain in this paper we consider the simplest type of such structures which is formed by n seri

brief paper dynamic stabilization of an euler bernoulli beam equation with time delay in boundary observation an euler bernoulli beam equation under boundary control and delayed observation is considered an observer predictor based scheme is developed to stabilize the equation on a time interval where the observation is available the state is tracked by the observer when the observation is not available due to the delay the state is estimated by the predictor the estimation is then used in proportional feedback it is shown that the state of closed loop system decays exponentially for smooth initial values

an example on the effect of time delays in boundary feedback stabilization of wave equations this note is concerned with the erect of time delays in boundary feedback stabilization schemes for wave equations the question to be addressed is whether such delays can destabilize a system which is uniformly asymptotically stable in the absence of delays

seminormal composition operators on l2 spaces induced by matrices the laplace density case abstract bounded composition operators with matrix symbols on l 2 where is a positive borel measure with a laplace type density function on the d dimensional euclidean space are studied hyponormality and subnormality of adjoints of such operators are characterized explicitly in terms of their symbols

the complex moment problem and subnormality a polar decomposition approach abstract it has been known that positive definiteness does not guarantee a bisequence to be a complex moment however it turns out that positive definite extendibility does theorems 1 and 22 and this is the main theme of this paper the main tool is generally understood polar decomposition to strengthen applicability of our approach we work out a criterion for positive definite extendibility in a fairly wide context theorems 9 and 29 all this enables us to prove characterizations of subnormality of unbounded operators having invariant domain theorems 37 and 39 and their further applications theorems 41 and 43 and a description of the complex moment problem on real algebraic curves theorems 52 and 56 the latter question is completed in the appendix in which we relate the complex moment problem to the two dimensional real one with emphasis on real algebraic sets

pointwise stabilisation of a string with time delay in the observation abstractpointwise stabilisation is proposed in this paper for a string equation where the observation signal is subject to a time delay different from the boundary control the feedback stabiliser is acting at the middle joint of the string well posedness of the open loop system and solvability of the observer are shown first an observer system is then designed to estimate the state at the time interval when the observation is available and a predictor system is designed to predict the state at the time interval when the observation is not available pointwise output feedback controller is introduced to make the closed loop system asymptotically stable for the non smooth initial values and exponentially stable for the smooth initial values respectively simulation results demonstrate that the output feedback based on the observer and predictor effectively stabilises the pointwise control system with time delay