extended fast fixed order rls adaptive filters the existing derivations of conventional fast rls adaptive filters are intrinsically dependent on the shift structure in the input regression vectors this structure arises when a tapped delay line fir filter is used as a modeling filter we show unlike what original derivations may suggest that fast fixed order rls adaptive algorithms are not limited to fir filter structures we show that fast recursions in both explicit and array forms exist for more general data structures such as orthonormally based models one of the benefits of working with orthonormal bases is that fewer parameters can be used to model long impulse responses

laguerre domain adaptive filters using a tapped delay line as an adaptive fitter the complexity of the filter increases with increasing correlation length of input and reference signal the author seeks simple adaptive filter structures such that for a long correlation length only a minor complexity of the filter is needed he considers adaptive mechanisms governed by an exponentially weighted squared error criterion laguerre domain adaptive filters are introduced which lead to a tapped iir filter line these filters contain a discount factor as a free variable which makes it possible to set the memory and the number of adaptive coefficients independently convergence properties of the proposed adaptive filters are discussed

on a backward parabolic problem with local lipschitz source abstract we consider the regularization of the backward in time problem for a nonlinear parabolic equation in the form u t a u t f u t t u 1 where a is a positive self adjoint unbounded operator and f is a local lipschitz function as known it is ill posed and occurs in applied mathematics e g in neurophysiological modeling of large nerve cell systems with action potential f in mathematical biology a new version of quasi reversibility method is described we show that the regularized problem with a regularization parameter 0 is well posed and that its solution u t converges on 0 1 to the exact solution u t as 0 these results extend some earlier works on the nonlinear backward problem

the exact analytic solutions of a nonlinear differential iterative equation abstract this paper is concerned with a second order nonlinear iterated differential equation of the form c 0 x z c 1 x z c 2 x z x p z b x z h z by constructing a convergent power series solution of an auxiliary equation analytic solutions of the original equation are obtained we discuss not only the general case 1 but also the critical case 1 especially when is a root of unity furthermore the exact and explicit analytic solution of the original equation is investigated for the first time such equations are important in both applications and the theory of iterations

stability radius and internal versus external stability in banach spaces an evolution semigroup approach in this paper the theory of evolution semigroups is developed and used to provide a framework to study the stability of general linear control systems these include autonomous and nonautonomous systems modeled with unbounded state space operators acting on banach spaces this approach allows one to apply the classical theory of strongly continuous semigroups to time varying systems in particular the complex stability radius may be expressed explicitly in terms of the generator of an evolution semigroup examples are given to show that classical formulas for the stability radius of an autonomous hilbert space system fail in more general settings upper and lower bounds on the stability radius are proven for banach space systems in addition it is shown that the theory of evolution semigroups allows for a straightforward operator theoretic analysis of internal stability as determined by classical frequency domain and input output operators even for nonautonomous banach space systems in particular for the nonautonomous setting internal stability is shown to be equivalent to input output stability for stabilizable and detectable systems for the autonomous setting an explicit formula for the norm of input output operator is given

exponential stability of laminated timoshenko beams with boundary internal controls abstract for a laminated timoshenko system with slip along the interface we study existence and boundary interior stabilization of solutions our first main result using resolvent estimates in the frequency domain is to show that interior damping created by the interfacial slip in companion with boundary feedback controls acting on the complementary displacements traverse and rotation angle drives the solution to zero with exponential decay rate we impose neither conditions on the physical parameters of the model nor on the damping coefficients our second main result is to investigate the asymptotic behavior of solutions for partially dissipative problems assuming the condition that the waves travel at the same speed we prove the decay of solutions with exponential rate finally the same condition allows us to show that dissipative effect created by the interfacial slip is strong enough to exponentially stabilizes the solutions to zero

analytic solutions of a second order iterative functional differential equation abstract this paper is concerned with a second order iterative functional differential equation x x r z c 0 z c 1 x z c m x m z where r and m are nonnegative integers x 0 z z x 1 z x z x 2 z x x z etc are the iterates of the function x z by constructing a convergent power series solution y z of a companion equation of form 2 y r 1 z y r z y r 1 z y r z y r z 3 i 0 m c i y i z analytic solutions of the form y y 1 z for the original differential equation are obtained

blind input initial state and system identification of simo laguerre systems laguerre filters have infinite impulse responses iirs but with finite tapped delay line parameterizations this paper investigates subspace based blind identification of laguerre filter tap coefficients the internal filter state and the input given only noisy observations of the output this paper deals only with single input multiple output simo laguerre models a state space model for the simo laguerre system is derived from which blind estimation algorithms are developed as in the finite impulse response fir case the laguerre filter taps coefficients can be estimated from the column space of a certain hankel matrix constructed from noisy output observations whereas the internal state and input can be estimated from the row space by exploiting state space structure while not exactly uniquely identifiable conditions are given for which the tap coefficients the internal state and the input can be determined to within a multiplicative scalar factor

the lack of exponential stability in certain transmission problems with localized kelvin voigt dissipation in this paper we consider the transmission problem of a material composed of three components one of them is a kelvin voigt viscoelastic material the second is an elastic material no dissipation and the third is an elastic material inserted with a frictional damping mechanism the main result of this paper is that the rate of decay will depend on the position of each component when the viscoelastic component is not in the middle of the material then there exists exponential stability of the solution instead when the viscoelastic part is in the middle of the material there is not exponential stability in this case we show that the corresponding solution decays polynomially as 1 t 2 moreover we show that the rate of decay is optimal over the domain of the infinitesimal generator finally using a second order scheme that ensures the decay of energy newmark beta method we give some numerical examples which demonstrate this asymptotic behavior

order recursive rls laguerre adaptive filtering this paper solves the problem of designing recursive least squares rls lattice or order recursive algorithms for adaptive filters that do not involve tapped delay line structures in particular an rls laguerre lattice filter is obtained

regularization and convergence for ill posed backward evolution equations in banach spaces abstract this work is concerned with a mathematical study of ill posed backward evolution equations associated with densely defined linear differential operators in banach spaces a general approach is presented to investigate the convergence and stability of a class of regularized solutions for ill posed backward evolution equations associated with sectorial or half strip operators generalized concepts of qualification pairs and index functions are introduced to characterize the explicit convergence rates of the concerned regularized solutions applications of our results to general backward evolution equations are also investigated

classifications and existence of positive solutions of higher order nonlinear iterative functional differential equations classification schemes for eventually positive solutions of a class of higher order nonlinear iterative functional differential equations of the form r t x m 1 t f t x t x t x t 0 in the case when ds r s are given in terms of their magnitudes and necessary as well as sufficient conditions for the existence of these positive solutions are also provided

decay rates for 1 d mixed type ii and type iii thermoelastic system with localized viscous damping abstract this work is devoted to discussing that how the locations of the thermal and viscous damping affect the stability of the 1 d elastic systems the spatial domain of the 1 d thermoelastic system under consideration can be divided into three sub intervals that is the thermoelastic region of type ii the one of type ii with viscous damping and the one of type iii the following two kinds of energy decay rates for the system are obtained 1 if the thermoelastic region of type iii includes one exterior point of the spatial domain of the system the energy of the system decays exponentially 2 if not that is the thermoelastic region of type iii is strictly inside the spatial domain the system always lacks of exponential decay however the optimal polynomial decay rate is further estimated for this system with smooth initial states finally some numerical simulations are presented to verify the stability results obtained in this work

local analytic solutions of a functional differential equation αz βx z x az bx z in this paper we are concerned with the existence of analytic solution of a functional differential equation email protected z x az bx z where a b a b are four complex numbers we first discuss the existence of analytic solutions for some special cases of the above equation then by reducing the equation with the schroder transformation to the another functional equation with proportional delay an existence theorem is established for analytic solutions of the original equation for the constant l given in the schroder transformation we discuss the case 0 l 1 and l on the unit circle s 1 i e l 1 we study l is at resonance i e at a root of the unity and l is near resonance under the brjuno condition

local analytic solutions of a functional differential equation with a deviating argument depending on the state derivative near resonance this paper is concerned with a functional differential equation x n z 1x az bx z with a deviating argument depending on the state derivative where a b are two complex numbers we first discuss the existence of analytic solutions for some special cases of the above equation then by reducing the equation with the schroder transformation to another functional differential equation with proportional delay an existence theorem is established for analytic solutions of the original equation for the constant l given in the schroder transformation besides the case 0 l 1 we focus on those l on the unit circle s 1 i e l 1 we discuss not only those l s at resonance i e at a root of the unity but also those l near resonance under the brjuno condition

conditional stability of unstable viscous shock waves in compressible gas dynamics and mhd extending our previous work in the strictly parabolic case we show that a linearly unstable lax type viscous shock solution of a general quasilinear hyperbolic parabolic system of conservation laws possesses a translation invariant center stable manifold within which it is nonlinearly orbitally stable with respect to small l 1 h 3 perturbations converging time asymptotically to a translate of the unperturbed wave that is for a shock with p unstable eigenvalues we establish conditional stability on a codimension p manifold of initial data with sharp rates of decay in all l p for p 0 we recover the result of unconditional stability obtained by mascia and zumbrun the main new difficulty in the hyperbolic parabolic case is to construct an invariant manifold in the absence of parabolic smoothing

analytic solutions of a class of iterative functional differential equations analytic solutions are obtained for iterative functional differential equations that are natural extensions of x 1 x x we make use of neutral functional differential equations with proportional delays as well as neutral differential difference equations for achieving our purposes

on uniform decay of a nonsimple thermoelastic bar with memory abstract in this paper we investigate the asymptotic behavior of a one dimensional problem of linear theory of nonsimple thermoelasticity with hereditary heat conduction we show that the corresponding semigroup is exponentially stable when the thermal memory kernel decays exponentially for large time but not analytic we conclude by showing the impossibility of localization in time of the solutions

approximation of stable systems by laguerre filters laguerre methods are used to develop concrete techniques and results for approximating stable infinite dimensional systems both hankel norm and l approximation by laguerre filters are studied the infimum of the hankel norm approximation error when the system is approximated by laguerre filters of given maximum order is given by the norm of a certain shifted hankel operator and the best laguerre filter to approximate the system is obtained essentially from the associated eigenproblem for the shifted hankel operator hankel optimal laguerre filters are here called cf laguerre filters as there is a certain connection to the caratheodory fejer interpolation problem and typically provide near best solutions to related l approximation problems a time domain compressed laguerre shift method for solving certain nehari problems for delay systems is used to determine analytically the achievable hankel error norms and thus also to obtain bounds for the achievable l error norm for delay systems a result on a laguerre filter approximation problem in the hilbert schmidt norm is given as well

on pid controller tuning using orthonormal series identification abstract the step response of a closed loop system is identified by means of a laguerre expansion this offers certain advantages over arma models namely lack of bias in the estimates structural flexibility and the ability to precompute the regressors the laguerre coefficients of the retuned system are calculated in terms of the tuning constants and a quadratic performance index is optimized results from simulations and from industrial trials are given

stability of post fertilization traveling waves article history this paper studies the stability of a family of traveling wave solutions to the system proposed by lane et al d c lane j d murray v s manoranjan analysis of wave phenomena in a morphogenetic mechanochemical model and an application to post fertilization waves on eggs ima j math appl med biol 4 4 1987 309 331 to model a pair of mechanochemical phenomena known as post fertilization waves on eggs the waves consist of an elastic deformation pulse on the egg s surface and a free calcium concentration front the family is indexed by a coupling parameter measuring contraction stress effects on the calcium concentration this work establishes the spectral linear and nonlinear orbital stability of these post fertilization waves for small values of the coupling parameter the usual methods for the spectral and evolution equations cannot be applied because of the presence of mixed partial derivatives in the elastic equation nonetheless exponential decay of the directly constructed semigroup on the complement of the zero eigenspace is established we show that small perturbations of the waves yield solutions to the nonlinear equations decaying exponentially to a phase modulated traveling

local analytic solution of a second order functional differential equation with a state derivative dependent delay abstract this paper is concerned with a second order functional differential equation x z 1 x az bx z with a state derivative dependent delay by reducing the equation to another functional differential equation with proportional delay an existence theorem is established for analytic solutions of the original equation and systematic methods for deriving explicit solutions are also given we not only prove the convergence of the formal solution under the diophantine condition i e eigenvalues is far from unit roots but also make progresses without the diophantine condition i e the convergence is equivalent to the well known small divisor problems

on the energy decay of the linear thermoelastic plate with memory abstract we analyze the longterm properties of a c 0 semigroup describing the solutions to a linear evolution system that models a thermoelastic thin plate with memory effects in the heat flux law under reasonably general assumptions on the memory kernel all single trajectories are shown to decay to zero in spite of that the semigroup is not exponentially stable

calculation of the local cross correlation function on the basis of the laguerre transform a simple and computationally efficient mechanism for calculating a running or local cross correlation function of two time domain signals is presented in order to obtain a running cross correlation function the signals must be windowed it is argued that an appropriate window for a local cross correlation is an exponential function to obtain a computationally efficient mechanism the windowed functions are decomposed in a series of orthogonal functions the set or orthogonal functions is matched to the chosen window and is a laguerre fourier series the cross correlation of the windowed functions is equal to a weighted summation of cross correlated pattern functions the weights are determined by cross correlating the laguerre coefficients

the functional differential equation x t x x t abstract a classification of the solutions of the functional differential equation x t x x t is given and it is proved that every solution either vanishes identically or is strictly monotonie for monotonically increasing solutions existence and uniqueness of the solution x are proved with the condition x t0 x0 where t0 x0 is any given pair of reals in some specified subset of r 2 every monotonically increasing solution is thus obtained it is analytic and depends analytically on t0 and x0 only for t0 x0 1 is the question of analyticity still open

frequency domain analysis of tracking and noise performance of adaptive algorithms in this paper an analysis of the tracking and noise performance of several adaptive algorithms is carried out for the case of model structures with fixed pole positions such structures have previously been proposed as an efficient generalization of the common fir model structure the focus of this work is to analyze the associated tradeoff between noise sensitivity and tracking ability in the frequency domain by illustrating how it is influenced by such things as input and noise spectral densities step size and in particular the choice of the fixed pole locations the latter influence is not described by preexisting analysis but is shown here to be amenable to attack by a particular class of orthonormal bases

existence of solutions for a mixed type differential equation with state dependence abstract in this paper we study a general n dimensional mixed type differential equation with state dependence many known works give the existence of solutions with the so called return condition in this paper without requiring the return condition we prove a non local existence of solutions by using a technique of compactification and the dependence of the maximum of functions on the size of their domains we apply our result to differential equations with iterates

modified quasi reversibility method for final value problems in banach spaces this paper is concerned with the final value problem associated with a linear operator a in a banach space where a is the generator of a uniformly bounded analytic semigroup based on the delaubenfels functional calculus we use new quasi reversibility method introduced by boussetila and rebbani recently to form an approximate problem we obtain some results in a banach space similar to those in a hilbert space

exact and explicit solutions for a nonlinear extended iterative differential equation abstract this paper is concerned with a nonlinear iterative functional differential equation x z 1 x p z bx z by constructing a convergent power series solution of an auxiliary equation analytic solutions of the original equation are obtained we discuss not only in the general case but also in critical cases especially for given in schroder transformation is a root of the unity and in case h4 we dealt with the equation under the brjuno condition which is weaker than the diophantine condition moreover the exact and explicit solution of the original equation has been investigated for the first time such equations are important in both applications and the theory of iterations

analytic solutions of an iterative functional differential equation this paper is concerned with a functional differential equation x z 1 x az bx z where a b are two complex numbers by constructing a convergent power series solution y z of a auxiliary equation of the form b 2y z y m 2z ay mz my mz ay z analytic solutions of the form 1b y my 1 z az for the original differential equation are obtained

exponential stability in thermoviscoelastic mixtures of solids in this paper we investigate the asymptotic behavior of solutions to the initial boundary value problem for a one dimensional mixture of thermoviscoelastic solids our main result is to establish the exponential stability of the corresponding semigroup and the lack of exponential stability of the corresponding semigroup

analytic solutions of a second order iterative functional differential equation abstract this paper is concerned with a second order iterative functional differential equation x z x m z 2 its analytic solutions are discussed by locally reducing the equation to another functional differential equation with proportional delays 2 y z y z y z y z y z 3 y m z 2 and by constructing a convergent power series solutions for the latter equation

smooth solutions of a nonhomogeneous iterative functional differential equation with variable coefficients using the fixed point theorems of banach and schauder in this paper we discuss the existence uniqueness and stability of smooth solutions of a nonhomogeneous iterative functional differential equation with variable coefficients

spectral conditions for admissibility of evolution equations in hilbert space abstract we study properties of solutions of the evolution equation u t b u t f t where b is a closable operator on the space ap r h of almost periodic functions with values in a hilbert space h such that b commutes with translations the operator b generates a family b of closed operators on h such that b e i t x e i t b x whenever e i t x d b for a closed subset r we prove that the following properties i and ii are equivalent i for every function f ap r h such that f there exists a unique mild solution u ap r h of eq such that u ii b i is invertible for all and sup b i 1

system identification using laguerre models the traditional approach of expanding transfer functions and noise models in the delay operator to obtain linear in the parameters predictor models leads to approximations of very high order in cases of rapid sampling and or dispersion in time constants by using prior information about the time constants of the system more appropriate expansions related to laguerre networks are introduced and analyzed it is shown that the model order can be reduced compared to arx fir ar modeling by using laguerre models furthermore the numerical accuracy of the corresponding linear regression estimation problem is improved by a suitable choice of the laguerre parameter consistency error bounds persistence of excitation conditions and asymptotic statistical properties are investigated this analysis is based on the result that the covariance matrix of the regression vector of a laguerre model has a toeplitz structure

stability of bright solitary wave solutions to perturbed nonlinear schrodinger equations abstract the propagation of pulses in ideal nonlinear optical fibers without loss is governed by the nonlinear schrodinger equation nls when considering realistic fibers one must examine perturbed nls equations with the particular perturbation depending on the physical situation that is being modeled a common example is the complex ginzburg landau equation cgl which is a dissipative perturbation it is known that some of the stable bright solitons of the nls survive a dissipative perturbation such as the cgl given that a wave persists it is then important to determine its stability with respect to the perturbed nls a major difficulty in analyzing the stability of solitary waves upon adding dissipative terms is that eigenvalues may bifurcate out of the essential spectrum since the essential spectrum of the nls is located on the imaginary axis such eigenvalues may lead to an unstable wave in fact eigenvalues can pop out of the essential spectrum even if the unperturbed problem has no eigenvalue embedded in the essential spectrum here we present a technique which can be used to track these bifurcating eigenvalues as a consequence we are able to locate the spectrum for bright solitary wave solutions to various perturbed nonlinear schrodinger equations and determine precise conditions on parameters for which the waves are stable in addition we show that a particular perturbation the parametrically forced nls equation supports stable multi bump solitary waves the technique for tracking eigenvalues which bifurcate from the essential spectrum is very general and should therefore be applicable to a larger class of problems than those presented here

analytic solutions of a second order iterative functional differential equation this paper is concerned with an iterative functional differential equationc 1x z c 2x z c 3x z x az bx z with the delay depends on the argument of the unknown function and the state derivative by reducing the equation with the schroder transformation to another functional differential equation without iteration of the unknown function we give existence of its local analytic solutions which extend the known results in related literature

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

logarithmic well posed approximation of the backward heat equation in banach space abstract in this paper we apply a logarithmic approximation introduced by boussetila and rebbani in order to study an ill posed cauchy problem in banach space the proposed method induces a well posed problem whose approximation parameter yields continuous dependence on modeling throughout properties of holomorphic semigroups are utilized culminating in the motivating application which is the backward heat equation in l p r 1 p

frequency domain approach for the polynomial stability of a system of partially damped wave equations in this paper we study the stability of a system of wave equations which are weakly coupled and partially damped using a frequency domain approach based on the growth of the resolvent on the imaginary axis we establish the polynomial energy decay rate for smooth initial data we show that the behavior of the system is sensitive to the arithmetic property of the ratio of the wave propagation speeds of the two equations

extended rls lattice adaptive filters this paper solves the problem of developing exact fast weighted rls lattice adaptive filters for input signals induced by general orthonormal filter models the resulting algorithm can be viewed as a counterpart of the extended fast fixed order rls adaptive filters previously derived

the operator valued marcinkiewicz multiplier theorem and maximal regularity given a closed linear operator on a umd space we characterize maximal regularity of the non homogeneous problem

ill posed problems associated with sectorial operators in banach space abstract ill posed problems of the form u t a u h 0 t t u 0 are studied in banach space under two related scenarios both of which consider a well posed logarithmic approximation in the first scenario a generates a bounded holomorphic semigroup of angle 2 and so a is sectorial of angle 0 in the second where may be relaxed to any value in 0 2 we impose an additional assumption that e a is sectorial regularization results for the original ill posed problem are then established in the linear case where h h t and subsequently extended to nonlinear problems where h is replaced by h t u t we compare the two cases in terms of regularization convergence rates and apply our results to backward heat equations both linear and nonlinear in l p r n 1 p

unbounded holomorphic functional calculus and abstract cauchy problems for operators with polynomially bounded resolvents abstract we consider linear unbounded operators b on a banach space x whose spectrum is contained in an open set v such that the resolvent w b 1 exists and is o 1 w for w v for some 1 we will call this an operator of type v for such operators we construct a functional calculus b defined for functions holomorphic on v whose real part is bounded above such that b generates an exponentially bounded b m semigroup where m 2 v this map is a continuous algebra homomorphism in a sense that is made precise later we give best possible spectral mapping theorems applications of this construction include the following we characterize subsets v of the complex plane with the property that whenever a is densely defined and of type v then the abstract cauchy problem has a solution for all initial data in a dense set we show that when b is of a type v then there exists a ranach subspace y such that d b m y x and there exists an h v functional calculus for b y on this interpolating space the imaginary powers of b form a c 0 group and we have spectral decompositions of b when v is disconnected our construction produces solutions for all initial data in dense sets of wide classes of first and second order cauchy problems including the schrodinger equation the backwards heat equation and the laplace equation on l p r n or l p i p where is a region in r n with smooth boundary we also consider incomplete cauchy problems of arbitrarily high order we emphasize that in our construction of b we do not assume that is meromorphic at this allows us to define exponentials cosines and logarithms of b directly for large classes of operators b for example we may define the exponential e 5 of an operator b with real spectrum

analytic solutions of an iterative functional differential equation abstract this paper is concerned with an iterative functional differential equation x x r z c 0 z c 1 x z c 2 x x z c m x m z where r and m are nonnegative integers x 0 z z x 1 z x z x 3 z x x x z etc are the iterates of the function x z and j 0 m c j 0 by constructing a convergent power series solution y z of a companion equation of the form y r 1 z y r z j 0 m c j y j z analytic solutions of the form y y 1 z for the original differential equation are obtained

analytic solutions of a second order nonautonomous iterative functional differential equation abstract in this paper a second order nonautonomous iterative functional differential equation is considered by reducing the equation with the schroder transformation to another functional differential equation without iteration of the unknown function we give existence of its local analytic solutions we first discuss the case that the constant given in the schroder transformation does not lie on the unit circle in c and the case that the constant lies on the circle but fulfills the diophantine condition then we further study the case that the constant is a unit root in c but the diophantine condition is offended finally we investigate analytic solutions of the form of power functions

evolutionary semigroups and dichotomy of linear skew product flows on locally compact spaces with banach fibers abstract we study evolutionary semigroups generated by a strongly continuous semi cocycle over a locally compact metric space acting on banach fibers this setting simultaneously covers evolutionary semigroups arising from non autonomous abstract cauchy problems and c 0 semigroups and linear skew product flows the spectral mapping theorem for these semigroups is proved the hyperbolicity of the semigroup is related to the exponential dichotomy of the corresponding linear skew product flow to this end a banach algebra of weighted composition operators is studied the results are applied in the study of roughness of the dichotomy dichotomy and solutions of nonhomogeneous equations green s function for a linear skew product flow pointwise dichotomy versus global dichotomy and evolutionary semigroups along trajectories of the flow

asymptotic stability of semigroups associated with linear weak dissipative systems with memory we study the asymptotic behavior of the solutions of a class of linear dissipative integral differential equations we show in the abstract setting a necessary and sufficient condition to get an exponential decay of the solution in the case of the lack of exponential decay we find the polynomial rate of decay of the solution some examples are given

analytic solutions of an iterative functional differential equation abstract this paper is concerned with an iterative functional differential equation x z x m z where x m z x x x z is the m th iterate of the function x z by constructing a convergent power series solution y z of a companion equation of the form y z y z y m z analytic solutions of the form y y 1 z for the original differential equation are obtained

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

continuous dependence on modeling for nonlinear ill posed problems abstract the nonlinear ill posed cauchy problem d u d t a u t h t u t u 0 where a is a positive self adjoint operator on a hilbert space h h and h 0 t h h is a uniformly lipschitz function is studied in order to establish continuous dependence results for solutions to approximate well posed problems the authors show here that solutions of the problem if they exist depend continuously on solutions to corresponding approximate well posed problems if certain stabilizing conditions are imposed the approximate problem is given by d v d t f a v t h t v t v 0 for suitable functions f the main result is that u t v t c 1 t t m t t where c and m are computable constants independent of and 0 1 this work extends to the nonlinear case earlier results by the authors and by ames and hughes

least squares design of higher order nonrecursive differentiators a method is described that can be used to design non recursive linear phase higher order differentiators that can perform differentiation over any frequency range the method is based on formulating the absolute mean square error between the amplitude responses of the practical and ideal differentiator as a quadratic function the coefficients of the differentiators are obtained by solving a set of linear equations this method leads to a lower mean square error and is computationally more efficient than both the eigenfilter method and the method based on the remez exchange algorithm design of differentiators based on minimization of the relative mean square error is also carried out finally the method is extended to the design of frequency selective higher order differentiators

local invertible analytic solution of a functional differential equation with deviating arguments depending on the state derivative abstract this paper is concerned with a functional differential equation of the form x z 1 x a z b x z with the distinctive feature that the argument of the unknown function depends on the state derivative where a b are two complex numbers by reducing the equation with the schroder transformation to another functional differential equation with proportional delay we give existence of its local invertible analytic solutions we discuss not only that the constant given in schroder transformation at resonance i e at a root of the unity but also those near resonance near a root of the unity under the brjuno condition

indirect stabilization of weakly coupled kirchhoff plate and wave equations with frictional damping abstract we investigate the indirect stabilization of a weakly coupled system consisting of a kirchhoff plate equation involving free boundary conditions and the wave equation with dirichlet boundary conditions in a bounded domain the distributed damping is frictional and appears in one of the equations only first we consider the case where the damping occurs in the wave equation and using the frequency domain method combined with an interpolation inequality we derive a polynomial decay estimate for the associated semigroup afterwards we consider the case where the frictional damping occurs in the kirchhoff plate equation and we use the same technique to derive a polynomial decay estimate for the underlying semigroup that latter polynomial decay estimate is similar to the one obtained earlier by different authors in the case of a coupling between a frictionally damped euler bernoulli plate equation and an undamped wave equation which is quite surprising since the operator defining the damping in the kirchhoff plate equation is compact

stability of perturbed linear distributed parameter systems we present an estimate for a class of unbounded perturbations of the generator of an exponentially stable semigroup when this estimate is satisfied then the perturbed operator still generates an exponentially stable semigroup for generators of holomorhic semigroups the class of allowed perturbations contains unbounded operators of the form ha with the estimate is given in terms of the norm of the solution of the lyapunov equation which corresponds to the unperturbed system