a smoothing property of a hyperbolic system and boundary controllability abstract we investigate a method with which one can deduce controllability results from smoothing properties previous applications of the method were for partial differential equations like the euler bernoulli beam equation petrowski hyperbolic in this paper we study the method s applicability to a strictly hyperbolic system by considering the boundary controllability of a vibrating timoshenko beam with physical characteristics that may vary along the length of the beam two cases are considered a beam which is clamped at one end the other end being controlled by a torque and transverse force and a beam which is hinged at one end where a control torque is applied and free at the other end where a control force is applied

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

rapid stabilisation of multi dimensional schrodinger equation with the internal delay control abstractin this paper we are concerned with the controller design for multi dimensional schrodinger equation with the internal delay control we introduce a new approach to design the feedback con

the eigenvalue problem for networks of beams abstract in this paper we consider the spectral analysis of different models of networks of euler bernoulli beams we first give the characteristic equation for the spectrum secondly in some particular situations we show that the spectrum depends only on the structure of the graph thirdly we investigate the asymptotic behaviour of the eigenvalues by proving the so called weyl s formula

boundary control of the timoshenko beam it is shown that the timoshenko beam can be uniformly stabilized by means of a boundary control a numerical study on the spectrum is also presented

global existence and energy decay result for a weak viscoelastic wave equations with a dynamic boundary and nonlinear delay term in this paper we consider the weak viscoelastic wave equation u t t u u t t 0 t g t s u s d s u p 2 u with dynamic boundary conditions and nonlinear delay term first we prove a local existence theorem by using the faedo galerkin approximations combined with a contraction mapping theorem secondly we show that under suitable conditions on the initial data and the relaxation function the solution exists globally in time in using the concept of stable sets finally by exploiting the perturbed lyapunov functionals we extend and improve the previous result from gerbi and said houari 2011

stabilization of distributed control systems with delay abstract in this paper the asymptotic stabilization of linear distributed parameter control systems with delay is considered specifically we are concerned with the class of control systems described by the equation x t a x t l x t b u t where a is the infinitesimal generator of a strongly continuous semigroup on a banach space x assuming appropriate conditions we will show that the usual spectral controllability assumption implies the feedback stabilization of the system applications to systems described by partial differential equations with delay are given

robust control with respect to coprime factors of infinite dimensional positive real systems it is shown that infinite dimensional positive real systems can be robustly stabilized with respect to coprime factor perturbations with a robustness margin of at least 1 square root 2 this result is applied to dissipative colocated systems which arise in pde models of flexible structures

a dynamic control law for the wave equation abstract we consider a system described by the one dimensional linear wave equation in a bounded domain with appropriate boundary conditions to stabilize the system we propose a dynamic boundary controller applied at the free end of the system the transfer function of the proposed controller is restricted to be a positive real function which could be strictly proper we then show that if the transfer function of the controller is strictly proper then the resulting closed loop system is asymptotically stable and if proper but not strictly proper then the resulting closed loop system is exponentially stable

sampled data observers for semilinear damped wave equations under spatially sampled state measurements abstract sampled data observers controllers under the sampled in space and time measurements were suggested in the past for parabolic systems in the present paper for the first time a sampled data observer is constructed for a hyperbolic system governed by 1d semilinear wave equation with either viscous or boundary damping the measurements are sampled in space and time sufficient conditions for the exponential stability of the estimation error are derived by using the time delay approach to sampled data control and appropriate lyapunov krasovskii functionals the dual sampled data controller problems are formulated numerical examples including observer design for unstable damped sine gordon equation illustrate the efficiency of the method

stability and instability results of the wave equation with a delay term in the boundary or internal feedbacks in this paper we consider in a bounded and smooth domain the wave equation with a delay term in the boundary condition we also consider the wave equation with a delayed velocity term and mixed dirichlet neumann boundary condition in both cases under suitable assumptions we prove exponential stability of the solution these results are obtained by introducing suitable energies and by using some observability inequalities if one of the above assumptions is not satisfied some instability results are also given by constructing some sequences of delays for which the energy of some solutions does not tend to zero

stabilization of an euler bernoulli beam with input delay in the boundary control abstract in this paper we consider a cantilever euler bernoulli beam with controller delay suppose that the output of the boundary controller is of the form u t u t where u t is the controller input it is well known that a system with a collocated feedback control law is exponentially stable if 0 and it is unstable with the same control law when 0 in the present paper we shall design a dynamic controller that makes the system stabilize exponentially for any and 0 furthermore we discuss the stability of the system for

riesz basis property of serially connected timoshenko beams in this paper we study the riesz basis property of serially connected timoshenko beams with joint and boundary feedback controls suppose that the left end of the whole beam is clamped and the right end is free at intermediate nodes the displacement and rotational angle of beams are continuous but the shearing force and bending moment could be discontinuous the collocated velocity feedback of the beams at intermediate nodes and the right end are used to stabilize the system we prove that the operator determined by the closed loop system has compact resolvent and generates a c 0 semigroup in an appropriate hilbert space we also show that there is a sequence of the generalized eigenvectors of the operator that forms a riesz basis with parentheses hence the spectrum determined growth condition holds therefore if the imaginary axis is not an asymptote of the spectrum then the closed loop system is exponentially stable finally we give a conclusion remark to explain that our result can be applied not

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

two examples of ill posedness with respect to small time delays in stabilized elastic systems two examples of elastic control systems that are uniformly stabilized by feedback controls on their boundaries for which divergence rates can be obtained when small time delays are introduced into their feedbacks are presented

stabilization of the variable coefficient structural acoustic model with curved middle surface and delay effects in the structural component abstract this paper is concerned with the uniform energy decay rates of a structural acoustic model which describes the interactions between the acoustic medium and the elastic structural in an acoustic chamber where one wall is flexible and curved the coupled system considered consists of a variable coefficient wave equation and a variable coefficient plate equation defined on the riemannian manifold with the coupling on the interface between the acoustic medium and the flexible wall both the components of the dynamics are subject to nonlinear boundary damping furthermore a nonlinear delay term acting in the boundary feedbacks of the structure component is considered the riemannian geometry method is applied to derive the energy estimates of the nonlinear coupled system with variable coefficients the uniform energy decay rates of the nonlinear variable coefficient structural acoustic system with delay effects on the riemannian manifold are quantified by a solution to a constructed nonlinear ode

distributed control of a class of flexible mechanical systems with global constraint in this paper the constrained problem is investigated for both flexible string model and euler bernoulli beam model with the tip payload based on an infinite dimensional generalisation of a distributed control method the control objectives are to develop the control law so that the motion of flexible mechanical systems can track a desired reference signal and ensure that the string or beam remain in a constrained space we prove that with the proposed control the tracking error is exponentially stable without violation of the constraint the proof of convergence is based on an integral barrier lyapunov function iblf and extensive simulations are provided to illustrate the performance of the control system

output feedback stabilization of a one dimensional schrodinger equation by boundary observation with time delay in this article we are concerned with the stabilization of a 1 d schrodinger equation with boundary control and observation the boundary observation is suffered from an arbitrary given time delay we first show that the proportional output feedback control that stabilizes exponentially the time delay free system can not stabilize the corresponding time delay system anymore we then use the observer and predictor to solve the stabilization problem of time delay system the state is estimated in the time span where the observation is available and the state is predicted in the time interval when the observation is not available it is shown that the estimated state feedback stabilizes exponentially the time delay system the numerical simulation is presented to illustrate the effect of the stabilizing controller

on the stabilization and stability robustness against small delays of some damped wave equations in this paper we consider a system which can be modeled by two different one dimensional damped wave equations in a bounded domain both parameterized by a nonnegative damping constant we assume that the system is axed at one end and is controlled by a boundary controller at the other end we consider two problems namely the stabilization and the stability robustness of the closed loop system against arbitrary small time delays in the feedback loop we propose a class of dynamic boundary controllers and show that these controllers solve the stabilization problem when the damping coefficient is nonnegative and the stability robustness problem when the damping coefficient is strictly positive

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

instabilities and patterns in coupled reaction diffusion layers we study instabilities and pattern formation in reaction diffusion layers that are diffusively coupled for two layer systems of identical two component reactions we analyze the stability of homogeneous steady states by exploiting the block symmetric structure of the linear problem there are eight possible primary bifurcation scenarios including a turing turing bifurcation that involves two disparate length scales whose ratio may be tuned via the interlayer coupling for systems of n component layers and nonidentical layers the linear problem s block form allows approximate decomposition into lower dimensional linear problems if the coupling is sufficiently weak as an example we apply these results to a two layer brusselator system the competing length scales engineered within the linear problem are readily apparent in numerical simulations of the full system selecting a sqrt 2 1 length scale ratio produces an unusual steady square pattern

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

dynamic feedback control and exponential stabilization of a compound system abstract we studied the exponential stabilization problem of a compounded system composed of a flow equation and an euler bernoulli beam which is equivalent to a cantilever euler bernoulli beam with a delay controller we designed a dynamic feedback controller that stabilizes exponentially the system provided that the eigenvalues of the free system are not the zeros of controller in this paper we described the design detail of the dynamic feedback controller and proved its stabilization property

not all feedback stabilized hyperbolic systems are robust with respect to small time delays in their feedbacks we present two examples of hyperbolic partial differential equations which are stabilized by boundary feedback controls and then destabilized by small delays in these controls we show that in a general case when the controls are distributed stabilized hyperbolic systems possess nontrivial periodic solutions if small time delays are introduced into their feedbacks we also indicate by means of an example that the general case of this phenomenon is harder to demonstrate for boundary control problems

rapid stabilisation of an euler bernoulli beam with the internal delay control in this paper we are concerned with rapid stabilisation of an euler bernoulli beam with internal delayed control herein we introduce a new approach of the feedback control design from the system

spatiotemporal pattern formation of a diffusive bimolecular model with autocatalysis and saturation law in this paper a reaction diffusion bimolecular model with autocatalysis and saturation law is investigated firstly we provide some conditions for the stability turing instability of the constant positive solution then we mainly consider hopf bifurcations and steady state bifurcations which bifurcate from the unique constant positive solution of the system our results suggest the existence of spatially non homogeneous periodic orbit and non constant positive steady state solutions which implies the possibility of rich spatiotemporal patterns in this diffusive bimolecular model numerical examples are presented to support our theoretical analysis furthermore non existence of non constant steady state is investigated in terms of parameters

control of planar networks of timoshenko beams the present study is concerned with the questions of controllability and stabilizability of planar networks of vibrating beams consisting of several timoshenko beams connected to each other by rigid joints at all interior nodes of the system some of the exterior nodes are either clamped or free controls may be applied at the remaining exterior nodes and or at interior joints in the form of forces and or bending moments for a given configuration is it at all possible to drive all vibrations to the rest configuration in a given finite time interval by means of controls acting at some or all of the available nonclamped nodes of the network and if so where should such controls be placed alternatively a control objective is to construct energy absorbing boundary feedback controls that will guarantee uniform energy decay it is demonstrated that if such a network does not contain closed loops and if at most one of the exterior nodes is clamped exact controllability and uniform stabilizability of the

general stability of a viscoelastic variable coefficients plate equation with time varying delay in localized nonlinear internal feedback abstract this paper is concerned with the decay properties of a memory type euler bernoulli plate equation with variable coefficients and time varying delay in localized nonlinear internal feedback by using piecewise multiplier method and riemannian geometric analysis we establish the explicit and general decay rates of system whose nonlinear internal feedbacks act on a suitable subregion

optimal control of an elastically connected rectangular plate membrane system the optimal control of an elastically connected rectangular plate membrane system by point wise actuators is considered problems of the type are of significant practical interest in most real mechanical structures widely used in aeronautical civil naval and mechanical engineering an index of performance is formulated which consists of a modified energy functional of the two coupled structure at a specified time and penalty functions involving the point control actuators necessary conditions of optimality are derived in the form of independent integral equations which lead to explicit expressions for the point wise actuators the results are applied to a specific problem and numerical results are given that reveal the effectiveness of the proposed control mechanism

exact stability chart of an elastic beam subjected to delayed feedback abstract the stability of an elastic beam is studied when the beam is subjected to a longitudinal force governed by a feedback loop the setup of the simplified mechanical model is motivated by a basic problem of electroacoustics the corresponding governing equation is the 1d wave equation with delayed boundary conditions by means of the d alembert solution the system can be transformed into a delay differential equation of neutral type that includes two time delays the intricate stability chart is constructed analytically in the parameter plane of the gain parameter and the ratio of the time delays the complete chart extends the numerical results of the literature while it also draws attention to the numerical difficulties of finite degree of freedom approximations and to the extreme sensitivity of the dynamics with respect to the time delay parameters of the system

velocity inversion a case study in infinite dimensional optimization the goal of seismic velocity inversion is the estimation of seismic wave velocities inside the earth by attempting to predict in a least error sense seismic waveforms measured at its surface we present velocity inversion as a case study in the various infinite dimensional pathologies which may afflict practically important problems of distributed parameter identification treated as optimization problems in function spaces these features differentiate various problem formulations far beyond the degree one would expect for finite small dimensional problems we illustrate this differentiation by comparing the characteristics of three different least squares formulations of velocity inversion

exact controllability stabilization and perturbations for distributed systems exact controllability is studied for distributed systems of hyperbolic type or for petrowsky systems like plate equations the control is a boundary control or a local distributed control exact controllability consists in trying to drive the system to rest in a given finite time the solution of the problems depends on the function spaces where the initial data are taken and also depends on the function space where the control can be chosen a systematic method named hum for hilbert uniqueness method is introduced as the terminology indicates it is based on uniqueness results classical or new and on hilbert spaces constructed in infinitely many ways by using uniqueness a number of applications are indicated having a general method for exact controllability implies having a general method for stabilization this leads to new and complicated nonlinear riccati s type pdes to be compared with direct methods when available in the last part of the paper we consider how all this behaves fo

stabilisation of timoshenko beam system with delay in the boundary control in this paper we consider the exponential stabilisation problem of a timoshenko beam with delay in boundary control suppose that the controller outputs of the forms 1u1 t 1u1 t and 2u2 t 2u2 t where u1 t and u2 t are the inputs of boundary controllers in the past most of the stabilisation results are required j j 0 j 1 2 in the present paper we shall give a new dynamic feedback control law that makes the system exponential stabilisation 0 provided that j j j 1 2 the exponential stabilisation result is proved via test of exact observability of the system

travel time like variables and the solution of velocity inverse problems it was demonstrated earlier that in the solution of 1 d inverse problems there is great advantage to changing the independent variable from say z depth to travel time dz c essentially the advantage comes from the fact that the acoustic wave equation in travel time has the unknown c z appearing in a less critical position the current paper takes a step toward applying these ideas to the much harder but more interesting inverse problem in three dimensions there is no simple 3 d analog of the above definition of however it is shown that a surprisingly effective way of decomposing travel time into x y z components is straightforward these are defined via line integrals from say 0 0 0 to an arbitrary point x y z along the straight line connecting the points thus approximating the more natural integrals along the unknown raypath these line integrals define the new coordinates and the associated wave equation is derived and then simplified by dropping less important terms the

non dissipative boundary feedback for rayleigh and timoshenko beams abstract we show that a non dissipative feedback that has been shown in the literature to exponentially stabilize an euler bernoulli beam makes a rayleigh beam and a timoshenko beam unstable

the exponential stability region of timoshenko beam with interior delays and boundary damping abstractin this paper we investigate the exponential stability of a timoshenko beam with interior time delays and boundary damping at first we show that the system is well posed by the semigroup method next we construct an appropriate functional to study the exponential stability we transform the exponential stability into the solvability of inequality equations and then by analysing the relationship between delays parameters 1 2 and damping parameters 1 2 we describe the 1 2 region for which the system is exponentially stable

on a conjecture about assigning jobs to processors of differing speeds a difficult control problem concerning jobs that arrive to a buffer in a poisson process and are to be assigned to m processors of different speeds is treated the processors operate in parallel and processing times are independent and exponentially distributed once a job is assigned to a free processor it occupies that processor until completed and may not be reassigned to a faster processor if one becomes free a reasonable conjecture that remains unproved for more than two processors is that the policy that minimizes the mean waiting time is of threshold type this conjecture is discussed and it is shown that whether or not a job should be assigned to a processor can depend not only on the number in the queue and the speed of the fastest available processor but also on whether slower processors are busy or idle a strengthened form of the conjecture is proposed

refinements to the linear velocity inversion theory the linear inversion method presented by cohen and bleistein in 1979 gives seriously degraded results when large reflectors are encountered obviously there is an irrecoverable loss of information when such a linear algorithm is applied to a nonlinear world however in many cases excellent results can be achieved by suitable postprocessing of the output of the basic linear inversion algorithm although a certain degree of helpful postprocessing can be and has been performed by straightforward consideration of the linearization process we present here a substantially improved postprocessing algorithm the basis for these improvements is a more accurate scattering model due to lahlou et al where among other things a wkb analysis of the wave equation led to a much more accurate accounting of the geometric spreading of the scattered wave these notions plus an effective use of traveltime are used in the new algorithm to improve both the estimate of the reflector locations and the estimate of amplitude v

boundary control of a timoshenko beam system with input dead zone in this paper boundary control is designed for a timoshenko beam system with the input dead zone by the hamilton s principle the dynamics of the timoshenko beam system is represented by a distributed parameter model with two partial differential equations and four ordinary differential equations the bounded part is separated from the input dead zone and then forms the disturbance like term together with the boundary disturbance which finally acts on the timoshenko beam system boundary control based on the lyapunov s direct method is proposed to ensure the timoshenko beam converge into a small neighbourhood of zero where stability of the system is also analysed besides the existence and uniqueness of the solution of the timoshenko beam system are proved simulations are provided to reveal the applicability and effectiveness of the proposed control scheme

asymptotic stability of a viscoelastic problem with balakrishnantaylor damping and time varying delay a viscoelastic problem with balakrishnantaylordamping and time varying delay of the form utt a bu2 u ut u 0tg ts u s ds 1f1 ut x t 2f2 ut x t t 0is considered we prove a general stability result for the equation without the condition 2 0 by establishing some lyapunov functionals which are equivalent to the energy of the equation instead of multiplier technique and using some properties of convex functions

stochastic boundary control design for timoshenko beams with large motions abstract this paper considers modeling and boundary control of timoshenko beams with large motions under both deterministic and stochastic external loads the original nonlinear partial differential equations governing motion of the beams are derived and used in the control design the control design is based on the lyapunov direct method the proposed controllers guarantee globally practically k exponentially p stability of the beam motions at the reference state well posedness and stability are analyzed based on a lyapunov type theorem developed to study well posedness and stability for a class of stochastic evolution systems in hilbert space simulation results are included to illustrate the effectiveness of the proposed control design

a stability result of a timoshenko system with a delay term in the internal feedback abstract in this paper we consider a timoshenko system with a delay term in the feedback and prove a stability result the beam is clamped at the endpoints and has in addition to an internal damping a feedback with a delay under an appropriate assumption on the weights of the two feedbacks we prove the well posedness of the system and establish an exponential decay result for the case of equal speed wave propagation

stabilization of exact nonlinear timoshenko beams in space by boundary feedback abstract boundary feedback controllers are designed to stabilize timoshenko beams with large translational and rotational motions in space under external disturbances the exact nonlinear partial differential equations governing motion of the beams are derived and used in the control design the designed controllers guarantee globally practically asymptotically and locally practically exponentially stability of the beam motions at the reference state the control design well posedness and stability analysis are based on various relationships between the earth fixed and body fixed coordinates sobolev embeddings and a lyapunov type theorem developed to study well posedness and stability for a class of evolution systems in hilbert space simulation results are included to illustrate the effectiveness of the proposed control design

existence and uniqueness results for a nonlinear caputo fractional boundary value problem on a star graph abstract in this paper we study a nonlinear caputo fractional boundary value problem on a star graph by means of transformation an equivalent system of fractional boundary value problem is obtained then we establish the existence and uniqueness results by fixed point theory in particular using banach s contraction principle and schaefer s fixed point theorem we also present some examples to illustrate the application of our results

two approaches for the stabilization of nonlinear kdv equation with boundary time delay feedback this paper concerns the nonlinear korteweg de vries equation with boundary time delay feedback under appropriate assumption on the coefficients of the feedbacks delayed or not we first prove that this nonlinear infinite dimensional system is well posed for small initial data the main results of our study are two theorems stating the exponential stability of the nonlinear time delay system two different methods are employed a lyapunov function approach allowing to have an estimation on the decay rate but with a restrictive assumption on the length of the spatial domain of the kdv equation and an observability inequality approach with a contradiction argument for any noncritical lengths but without estimation on the decay rate some numerical simulations are given to illustrate the results

optimal boundary control of one dimensional multi span vibrating systems a class of optimal control problems of one dimensional coupled vibrating systems with control applied at the coupled points is considered a maximum principle is developed for a class of such optimal problems governed by n linear hyperbolic partial differential equations of second order in time and fourth order in space with variable coefficients the maximum principle given involves a hamiltonian which contains an adjoint variable as well as an admissible boundary control function the proof of the maximum principle is given with the help of convexity arguments the uniqueness theory of the solution of the optimal control problem is given using convexity arguments

robustness with respect to small delays for exponential stability of non autonomous systems robustness of stability with respect to small delays e g motivated by feedback systems in control theory is of great theoretical and practical important but this property does not hold for many systems in this paper we introduce the conception of robustness with respect to small time varying delays for exponential stability of the non autonomous linear systems sufficient conditions are given for the non autonomous systems to be robust and examples are provided to illustrate that the conditions are satisfied for a large class of the non autonomous parabolic systems

two questions concerning the boundary control of certain elastic systems abstract we present two questions connected with the stabilization of certain hyperbolic partial differential equations which are controlled on their boundaries the uncontrolled versions of these systems are conservative and therefore represent only approximate realizations of the physical phenomena the first question concerns the qualitative behavior of a given stabilizing feedback for such a system vis a vis that of an appropriately damped realization using the same feedback the second question concerns the robustness of both the original system and a damped version when time delays occur in a given feedback stabilization scheme

well posedness and exponential decay estimates for a korteweg de vries burgers equation with time delay abstract we consider the kdv burgers equation and its linear version in presence of a delay feedback we prove well posedness of the models and exponential decay estimates under appropriate conditions on the damping coefficients our arguments rely on a lyapunov functional approach combined with a step by step procedure and semigroup theory

feedback stabilisation of an euler bernoulli beam with the boundary time delay disturbance in this paper we consider the feedback stabilisation of an euler bernoulli beam with the boundary time delay disturbance due to unknown time delay coefficient the system might be exponentially i

destabilizing effects of small time delays on feedback controlled descriptor systems abstract in the last 15 years the problem of stabilizability and stabilization of descriptor systems have received considerable attention in this paper it is shown that if a descriptor system e x ax bu exhibits impulsive behavior then the stability of the closed loop system is extremely sensitive to small delays more precisely if f is the feedback which leads to a stable and impulsive free closed loop system then there exist numbers ej 0 and sj c with limj ej 0 and limj re sj and such that the delayed closed loop system obtained by applying the feedback u t fx t ej has a pole at sj moreover if the open loop system does not have impulsive behavior the same phenomenon occurs provided that the spectral radius of the matrix lim s f se a 1b is greater than 1 if this spectral radius is smaller than 1 it is shown that the closed loop stability is robust with respect to small delays

a comparison between the born and rytov approximations for the inverse backscattering problem we compare the born and rytov approximations in solving the inverse acoustic backscattering problem i e determining medium properties from reflections for the one dimensional problem we show that the rytov approximation is generally better than the born approximation in predicting sound speed changes while both methods have the same error in determining the positions of reflectors this is shown analytically for simple models and numerically for more general models the performance of the rytov approximation is degraded when low velocity regions are present in the medium being probed the accuracy of the inversion depends on the manner in which the sound speed perturbation is linearized the location of the receiver affects the accuracy of the inversion and in the case of the rytov approximation best results are obtained when the receiver is at the interface between the known and unknown regions furthermore the rytov method is less sensitive to the choice of reference sound speed used in the in

stabilisation of timoshenko beam system with a tip payload under the unknown boundary external disturbances this paper is concerned with the boundary stabilisation of a timoshenko beam with a tip payload under the boundary external disturbances nonlinear feedback control laws are designed to reduce the effects of the external disturbances since the controlled system is nonlinear the well posedness of the nonlinear closed loop system is investigated using the theory of nonlinear maximal monotone operators and the variational principle in addition we show the exponential stability of the nonlinear controlled system using the lyapunov direct method in the end the numerical simulations are displayed to illustrate the effectiveness of the proposed boundary controls

uniform stability for thermoelastic systems with boundary time varying delay abstract in this paper we consider a thermoelastic system with boundary time varying delay using the energy method we show under suitable assumptions that the damping effect through heat conduction is still strong enough to uniformly stabilize the system even in the presence of boundary time varying delay our result improves earlier results existing in the literature

robustness with respect to delays for exponential stability of distributed parameter systems in this paper we address the question of whether the open loop exponential growth rate of a linear system can be improved by a feedback in such a way that this improvement is robust with respect to small delays in the feedback loop when the input operator is admissible and the class of possible feedbacks consists of compact operators we find that if a feedback can improve the exponential growth rate then it can do so robustly furthermore we find that if the control space is finite dimensional and a bounded feedback cannot be found to improve exponential stability then a large class of unbounded feedbacks cannot improve the exponential growth rate robustly even if such feedbacks can improve the exponential growth rate in the absence of delays

sensitivity to infinitesimal delays in neutral equations the stability of a steady state solution of a neutral functional differential equation can be sensitive to infinitesimal changes in the delays this phenomenon is caused by the behavior of the essential spectrum and is determined by the roots of an exponential polynomial avellar and hale j math anal appl 73 1980 pp 434 452 have considered the case of multiple fixed and nonzero delays in the first part of this paper their results are illustrated by means of spectral plots in the second part we extend the theory of avellar and hale to the limit case whereby some of the delays are brought to zero which may lead to characteristic roots with arbitrarily large real part necessary and sufficient conditions are provided using these results we show that the ratio of the delays plays a crucial role when several delays tend to zero simultaneously as an illustration of the theory we analyze the robustness of a boundary controlled pde in the presence of a small feedback delay

dynamic domain decomposition of optimal control problems for networks of strings and timoshenko beams we consider general networks of strings and or timoshenko beams we apply controls at boundary nodes of the network and want to minimize some cost function along part of the structure optimality systems for the entire structure are far too complex to compute in reasonable time in particular in real time applications one wants to reduce the size of the problem thus dynamic decomposition into its physical elements appears to be a natural approach we show how to iteratively decompose the global optimality system into a system related to a substructure then we interpret the local system as an optimality system corresponding to an optimal control problem for the substructure and finally we show convergence of the outer iteration

stabilizability and stability robustness of state derivative feedback controllers we study the stabilizability of a linear controllable system using state derivative feedback control as a special feature the stabilized system may be fragile in the sense that arbitrarily small modeling and implementation errors may destroy the asymptotic stability first we discuss the pole placement problem and illustrate the fragility of stability with examples of a different nature we also define a notion of stability called p stability which explicitly takes into account the effect of small modeling and implementation errors next we investigate the effect on the fragility of including a low pass filter in the control loop finally we completely characterize the stabilizability and p stabilizability of linear controllable systems using state derivative feedback in the stabilizability characterization the odd number limitation well known in the context of the stabilization of unstable periodic orbits using pyragas type time delayed feedback plays a crucial role

global bifurcation analysis and pattern formation in homogeneous diffusive predator prey systems abstract the dynamics of a general diffusive predator prey system is considered existence and nonexistence of non constant positive steady state solutions are shown to identify the ranges of parameters of spatial pattern formation bifurcations of spatially homogeneous and nonhomogeneous periodic solutions as well as non constant steady state solutions are studied

boundary feedback exponential stabilization of a timoshenko beam with both ends free in the present paper we consider the boundary feedback stabilization of a timoshenko beam with both ends free we propose boundary feedback control law that makes the closed loop system dissipative using asymptotic analysis techniques we give explicit asymptotic formula of eigenvalues of the closed loop system and prove the riesz basis property of eigenvectors and generalized eigenvectors by a detailed analysis of spectrum of the closed loop system we show that the closed system is exponentially stable

a rank one perturbation result on the spectra of certain operators on considere l equation differentielle d ordre 2 x ax x a est un operateur symetrique non borne dans un espace de suites h

global existence asymptotic stability and uniform attractors for non autonomous thermoelastic systems with constant time delay in this paper we first consider a non autonomous thermoelastic system with a boundary delay and obtain the asymptotic behavior then using the contractive function method and multiplier techniques we establish the asymptotic behavior and the existence of a uniform attractor of the system with a boundary time delay the main advantage of this method is that we only need to verify compactness condition with the type of energy estimates same as those for establishing the absorbing set moreover we investigate an alternative result of solutions to semilinear thermoelastic systems by virtue of the semigroup method

a note on stabilization of locally damped wave equations with time delay abstract in this paper we consider the wave equation with internal distributed time delay and local damping in a bounded and smooth domain r n when the local damping acts on a neighborhood of a suitable part of the boundary of we show that an exponential stability result holds if the coefficient of the delay term is sufficiently small

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

general decay of the solution for a viscoelastic wave equation with a time varying delay term in the internal feedback in this paper we consider a viscoelastic wave equation with a time varying delay term the coefficient of which is not necessarily positive by introducing suitable energy and lyapunov functionals under suitable assumptions we establish a general energy decay result from which the exponential and polynomial types of decay are only special cases