delayless observers for systems with delay the design of minimal order observers for linear systems having a time delay in the state variables is considered necessary and sufficient conditons are established for the existence of delayless observers for these systems

the optimal projection equations for reduced order state estimation the singular measurement noise case the optimal projection equations for reduced order state estimation are generalized to allow for singular i e colored measurement noise the noisy and noise free measurements serve as inputs to dynamic and static estimators respectively the optimal solution is characterized by necessary conditions which involve a pair of oblique projections corresponding to reduced estimator order and singular measurement noise intensity

comments on an asymptotic modal observer for linear autonomous time lag systems this note first shows that the proof of theorem1 in the above mentioned paper is incomplete and that the state observer scheme results in steady state error alternatively a memoryless state observer for linear time delay systems is provided

finite spectrum assignment problem for systems with delay in state variables this correspondence is concerned with the finite spectrum assignment problem for linear systems with delay in state variables a systematic procedure for constructing the feedback law is presented on the basis of advanced elementary row operations on matrices with two variables s and z e sh

an observer of systems with delays in state variables the paper is concerned with the design of an observer of systems with delays in state variables and control it is shown on the basis of the finite spectrum assignment theory that if the system is spectrally observable there exists an observer which can estimate the state variables of the system as fast as desired a systematic design procedure of the observer is presented the advantage of the proposed method is that the observer is constructed without preliminary knowledge of the open loop spectrum in contrast with the design method based on the spectral decomposition

comments on two recent papers on reduced order optimal state estimation for linear systems with partially noise corrupted measurement two recent correspondence on the optimal singular state estimation problem are shown to be in error optimal linear least squares estimators based on an innovations approach 9 10 are presented an important outcome is the clarification and hopeful elimination of some current misconceptions in relation to stochastic observer theory

an observer design for linear systems with unknown inputs a method is presented for designing an observer for the state of a linear time invariant system with unknown inputs the structure algorithm developed by silverman is applied to obtain the observer which estimates the maximum estimable subspace of the state it is shown that the observer equation can be derived from the maximum uncontrollable subspace of the original system with the aid of a left inverse for a transposed linear system this leads us to the necessary and sufficient condition for the existence of a state observer an application to the insensitivity observer synthesis is also included

multi stage solvers optimized for damping and propagation explicit multi stage solvers are routinely used to solve the semi discretized equations that arise in computational fluid dynamics cfd problems often they are used in combination with multi grid methods in that case the role of the multi stage solver is to efficiently reduce the high frequency modes on the current grid and is called a smoother in the past when optimizing the coefficients of the scheme only the damping characteristics of the smoother were taken into account and the interaction with the remainder of the multi grid cycle was neglected recently it had been found that coefficients that result in less damping but allow for a higher courant friedrichs lewy cfl number are often superior to schemes that try to optimize damping alone while this is certainly true for multi stage schemes used as a stand alone solver we investigate in this paper if using higher cfl numbers also yields better results in a multi grid setting we compare the results with a previous study we conducted and where a more accurate model of the multi grid cycle was used to optimize the various parameters of the solver we show that the use of the more accurate model results in better coefficients and that in a multi grid setting propagation is of little importance we also look into the gains to be made when we allow the parameters to be different for the pre and post smoother and show that even better coefficients can be found in this way

lqg optimal control of multirate sampled data systems an lqg control synthesis technique for multirate sampled data systems where each input has its own frequency of updating and each output has its own frequency of measurement is presented the skew of the output sampling mechanism renders the prediction problem singular for the lack of measures at some time instants an ad hoc prediction algorithm is derived by enlarging the dimension of the state vector to be estimated and feeding the state filter with a combination of measured outputs over a past and finite interval of time the constraints on the input updating mechanism are dealt with by inserting a dynamical system corresponding to a zero order hold into the loop

full order observer design for linear systems with unknown inputs in this article a full order observer without unknown inputs reconstruction is suggested in order to achieve finite time reconstruction of the state vector for a class of linear systems with unknown inputs the observer is a simple one its derivation being direct and easy it will be shown that the problem of full order observers for linear systems with unknown inputs can be reduced in this case to a standard one the unknown input vector will not interfere in the observer equations the effectiveness of the suggested design algorithm is illustrated by a numerical example aircraft longitudinal motion and for the same aircraft dynamics we make a comparison between our new observer and other already existing observers from the existence conditions and dynamic characteristics point of view the superiority of the new designed observer is demonstrated

closed loop state and input observer for systems with unknown inputs a closed loop observer that can identify states and inputs simultaneously is developed for linear time invariant systems with unknown inputs the necessary and sufficient conditions for the existence of the observer are derived and proved parameter identification of a system with a few unknown or time varying parameters is investigated by applying the observer technique developed in this paper potential usage in machine monitoring machine diagnostics appears promising

the unified structure of unbiased minimum variance reduced order filters a unified two stage functional filter utsff is proposed serving as a unified structure of unbiased minimum variance reduced order filters for linear time varying discrete time systems the utsff includes two parts one is for the main functional estimate which defines the main computing structure of the filter and the other is for the complementary functional estimate which is added to the former in order to further enhance the filtering performance the relationships between the utsff and existing reduced order filters are explored through the utsff a general procedure for applying a suitable unbiased minimum variance reduced order filter is given simulation examples are also given to illustrate the proposed results

design of observers for linear systems with unknown inputs with a straightforward treatment a design of reduced order observers is presented for linear systems with unknown inputs the observers are derived with a physical meaning some explanations are given within the framework of descriptor system observer design principles the conditions for the existence of the observers are presented some illustrative examples are included

general two stage extended kalman filters a general two stage extended kalman filter gtsekf which extends the linear general two stage kalman filter to nonlinear systems is further proposed a new nonlinear two stage transformation is introduced to facilitate achieving this extension as in the linear one the gtsekf is derived mainly by applying the nonlinear two stage transformation to the well known extended kalman filter ekf and is shown to be equivalent to the ekf with a decoupled computing structure a nonlinear filter for estimating constant parameters in dynamic systems is presented to illustrate one application of the proposed gtsekf a literature example is also given to demonstrate the correctness and usefulness of the proposed results

brief analysis of nonlinear time delay systems using modules over non commutative rings the theory of non commutative rings is introduced to provide a basis for the study of nonlinear control systems with time delays the left ore ring of non commutative polynomials defined over the field of meromorphic function is suggested as the framework for such a study this approach is then generalized to a broader class of nonlinear systems with delays that are called generalized roesser systems finally the theory is applied to analyze nonlinear time delay systems a weak observability is defined and characterized generalizing the well known linear result properties of closed submodules are then developed to obtain a result on the accessibility of such systems

a generalization of the runge kutta iteration iterative solvers in combination with multi grid have been used extensively to solve large algebraic systems one of the best known is the runge kutta iteration we show that a generally used formulation a jameson numerical solution of the euler equations for compressible inviscid fluids in f angrand a dervieux j a desideri r glowinski eds numerical methods for the euler equations of fluid dynamics siam philadelphia 1985 pp 199 245 does not allow to form all possible polynomial transmittance functions and we propose a new formulation to remedy this without using an excessive number of coefficients after having converted the optimal parameters found in previous studies e g b van leer c h tai k g powell design of optimally smoothing multi stage schemes for the euler equations aiaa paper 89 1923 1989 we compare them with those that we obtain when we optimize for an integrated 2 grid v cycle and show that this results in superior performance using a low number of stages we also propose a variant of our new formulation that roughly follows the idea of the martinelli jameson scheme a jameson analysis and design of numerical schemes for gas dynamics 1 artificial diffusion upwind biasing limiter and their effect on multigrid convergence int j comput fluid dyn 4 1995 171 218 j v lassaline optimal multistage relaxation coefficients for multigrid flow solvers http www ryerson ca jvl papers cfd2005 pdf used on the advection diffusion equation which that can be extended to other types gains in the order of 30 50 have been shown with respect to classical iterative schemes on the advection equation better results were also obtained on the advection diffusion equation than with the martinelli jameson coefficients but with less than half the number of matrix vector multiplications

a note on interval observer design for unknown input estimation this paper addresses the problem of interval observer design for unknown input estimation in linear time invariant systems although the problem of unknown input estimation has been widely studied in the literature the design of joint state and unknown input observers has not been considered within a set membership context while conventional interval observers could be used to propagate with some additional conservatism unknown inputs by considering them as disturbances the proposed approach allows their estimation under the assumption that the measurement noise and the disturbances are bounded lower and upper bounds for the unmeasured state and unknown inputs are computed numerical simulations are presented to show the efficiency of the proposed approach

brief paper adaptive observers for time delay nonlinear systems in triangular form a simple nonlinear observer with a dynamic gain is proposed for a class of bounded state nonlinear systems subject to state delay by saturating the states of the observer nonlinearities with either symmetric or non symmetric saturation functions we show that the observer exists whatever the delay is furthermore it will be highlighted that the observer design is free from any preliminary analysis of the time delay system such as estimating the lipschitz constants of nonlinearities the proposed design encompasses a wide class of nonlinear and time delay systems written in triangular form and generalizes previous results on delayless nonlinear systems

optimization of the runge kutta iteration with residual smoothing iterative solvers in combination with multi grid have been used extensively to solve large algebraic systems one of the best known is the runge kutta iteration previously haelterman et al 2009 3 we reformulated the runge kutta scheme and established a model of a complete v cycle which was used to optimize the coefficients of the multi stage scheme and resulted in a better overall performance we now look into aspects of central and upwind residual smoothing within the same optimization framework we consider explicit and implicit residual smoothing and either apply it within the runge kutta time steps as a filter for restriction or as a preconditioner for the discretized equations we also shed a different light on the very high cfl numbers obtained by upwind residual smoothing and point out that damping the high frequencies by residual smoothing is not necessarily a good idea

adaptive control scheme for uncertain time delay systems the paper exposes some of the potential of a recently introduced backstepping transformation for linear uncertain time delay systems to address the classic problems of equilibrium regulation under partial measurements disturbance rejection parameter or delay adaptation for each of these problems an implementable control strategy is proposed it is analyzed through a convergence analysis of infinite dimensional dynamics based on a transport partial differential equation representation of the estimated input delay and the mentioned backstepping transformation the considered controllers contain this representation of the system under the form of a distributed parameter system and use it to determine relevant adaptation strategies an illustration example is proposed

finite spectrum assignment and observer for multivariable systems with commensurate delays this paper is concerned with control of multivariable systems with commensurate delays the purpose of this paper is to enlarge the class of finite spectrum assignable systems to spectrally controllable multivariable systems with commensurate delays by overcoming an infinite number of eigenvalues which are contained in the system and make control very complex it is proved that if the system is spectrally controllable there is a delayed feedback matrix such that the closed loop system is spectrally controllable through a single input combining this result with previous ones about single input systems it is verified that spectral controllability is equivalent to finite spectrum assignability for multivariable systems with commensurate delays an observer for the system with delayed outputs is presented by using these results the multivariable system can be regulated as desired without preliminary knowledge of open loop eigenvalues and a stability test of transcendental functions whenever the system is spectrally controllable and spectrally observable

e bounded state estimation for time delay systems with bounded disturbances a new problem on e bounded functional state estimation for time delay systems with unknown bounded disturbances is studied in this paper in the presence of unknown bounded disturbances the common assumption regarding the observer s matching condition is no longer required in this regard instead of achieving asymptotic convergence for the observer error the error is now required to converge exponentially within a ball with a small radius e 0 this means that the estimate converges exponentially within an e bound of the true value a general observer that utilises multiple delayed output and input information is proposed sufficient conditions for the existence of the proposed observer are first given we then employ an extended lyapunov krasovskii functional which combines the delay decomposition technique with a triple integral term to study the e convergence problem of the observer error system moreover the obtained results are shown to be more effective than the existing results for the cases w

linear systems with commensurate time delays stability and stabilization independent of delay notions of exponential stability independent of delay and stabilizability independent of delay are developed for the class of delay differential systems of the retarded type with commensurate time delays various criteria for exponential stability independent of delay with a given order are specified in terms of matrices whose entries are functions of a single real parameter and polynomials in one variable whose coefficients are functions of a single real parameter sufficient conditions and a necessary condition based on local stabilizability are given for stabilizability independent of delay using state feedback with commensurate time delays constructive methods for determining a stabilizing feedback are also presented the last part of the paper deals with a standard type of observer and regulator with the requirement that the closed loop system be stable independent of delay

optimizing a multigrid runge kutta smoother for variable coefficient convection diffusion equations abstract the theory of generally locally toeplitz or glt for short sequences of matrices is proposed in the analysis of a multigrid solver for the linear systems generated by finite volume finite difference approximations of variable coefficients linear convection diffusion equations in 1d proposed by birken in 2012 and extended here to 2d problems the multigrid solver is used with a runge kutta smoother optimal coefficients for the smoother are found by considering the unsteady linear advection equation and using optimization algorithms in particular in order to reduce the issues of having multiple local minima the sequential quadratic programming sqp mixed with genetic and particle swarm optimization algorithms are proposed numerical results show that our proposals are competitive with respect to other multigrid implementations

unknown inputs functional observers designs for delay descriptor systems new time and frequency domain designs of unknown inputs functional observers uifo for a class of descriptor systems with a constant time delay are investigated in this paper the unknown inputs are present in both the state and the measurement equations the time procedure design is based on the unbiasedness of the estimation error and the lyapunov krasovskii stability theory after given the existence condition of such observers the gain implemented in the functional observer with internal delay design is obtained in terms of linear matrix inequalities the particular cases where the observer is independent of internal delay and where it is independent of delay are also investigated a design algorithm that summarises the different steps of the uifo design is proposed then the frequency procedure design is derived from time domain results by applying the factorisation approach where we define some useful matrix fraction descriptions note that the order of this unknown input observers is equal to

an asymptotic modal observer for linear autonomous time lag systems a full state vector observer is derived for a class of linear autonomous time lag systems represented by differential equations the major features of the approach are 1 an observer is constructed just for the set of unstable or poorly damped modes of the delayed system once they have been determined and 2 the design is accomplished by using a partial fraction expansion separating the unstable part from the system and then applying well known finite dimensional state vector techniques a procedure for the construction is given along with some numerical results to illustrate the simplicity of the observer

disturbance localization and pole shifting by dynamic compensation this paper concerns the problem of disturbance localization and pole shifting by dynamic compensation in multivariable linear systems with inaccessible state vector a necessary and sufficient condition for the solvability of the problem is given two synthesis procedures of the compensator are presented one is based on an observer and the other is based on a dual observer the observer designed by the proposed procedure acts as as unknown input observer for a linear function an improved procedure of designing a reduced order unknown input observer is also given the result may be applicable to reducing the compensator order

stabilization of linear distributed control systems with unbounded delay in this paper we study the asymptotic stabilization of linear distributed parameter control systems with unbounded delay assuming that the semigroup of operators associated with the uncontrolled and nondelayed equation is compact and that the phase space is a uniform fading memory space we characterize those systems that can be stabilized using a feedback control as consequence we conclude that every system of this type is stabilizable with an appropriated finite dimensional control

disturbance decoupled observer design a unified viewpoint this paper is concerned with the observer design for linear systems with unknown inputs an equivalent system which is free of unknown inputs is derived for the purpose of the observer design based on the equivalent system description one can design an observer full order reduced order minimal order or functional for linear systems with unknown inputs using well known techniques it is shown that the equivalent system exists as long as there exists a disturbance decoupled observer two sets of the known existence conditions of disturbance decoupled observers are proved to be equivalent

characterization of the law of the iterated logarithm in banach spaces on utilise une technique de randomisation gaussienne pour demontrer qu une variable aleatoire a valeurs dans un espace de banach satisfait la loi du logarithme itere sous une certaine condition necessaire et suffisante

almost sure behaviour of f valued random fields letx n n d be a field of independent random variables taking values in a semi normed measurable vector spacef for a broad class of fields n d of positive numbers the almost sure behaviour of k nxk n n d is studied the main result allows us to deduce some new and well known theorems for fields of independentf random variables from related results for fields of independent real random variables

h synthesis of unknown input observers for non linear lipschitz systems the problem of unknown input observer design for non linear lipschitz systems is considered a new dynamic framework which is a generalization of previously used linear unknown input observers is introduced the additional degrees of freedom offered by this dynamic framework are used to deal with the lipschitz non linearity the necessary and sufficient condition that ensures asymptotic convergence of the new observer is presented and the equivalence between this condition and an h optimal control problem which satisfies the standard regularity assumptions in the h optimization theory is shown based on these results a design procedure that is solvable using commercially available software is presented a simulation example is given to illustrate the proposed design

optimal minimal order least squares estimators via the general two stage kalman filter a direct derivation of the optimal minimal order least squares estimator is presented using the general two stage kalman filter using this new result the reduced order estimators of o reilly 1982 and fairman and luk 1985 are readily shown to be equivalent a practical implementation issue to consider these two estimators is also addressed

brief paper observer based control of a class of time delay nonlinear systems having triangular structure time delay systems constitute a special class of dynamical systems that are frequently present in many fields of engineering it has been shown in the literature that the existence of a stabilizing observer based controller is related to delay dependent conditions that are generally satisfied for a small time delay motivating works towards reducing the conservatism of the results are among the on going research topics especially when partial state measurements are imposed this paper investigates the problem of observer based stabilization of a class of time delay nonlinear systems written in triangular form first we show that a delay nonlinear observer is globally convergent under the global lipschitz condition of the system nonlinearity then it is shown that a parameterized linear feedback that uses the observer states can stabilize the system whatever the size of the delay an illustrative example is provided to approve the theoretical results

feedback stabilization of linear autonomous time lag systems a stabilization theory which employs well established finite dimensional control system tools is developed for the stabilization of linear autonomous time lag systems the main ideas include 1 a set whose elements are matrices each of which is a left zero of the system characteristic quasi polynomial matrix and 2 a linear transformation which reduces the delay system to a delay free system whose state matrix is a direct sum of n elements of the matrix set where n is some positive integer from the definition of this matrix set it is shown that each of its elements inherits its spectrum from that of the delay system so that by design the system unstable poles may be embedded in the spectrum of the delay free system under the assumption of spectral stabilizability it is then shown how to obtain a stabilizing feedback control law on the basis of the delay free system numerical examples are presented to confirm the theory

linear functional state observer for time delay systems a new linear functional state observer for time delay systems is introduced in this paper it is shown that the observer converges with any prescribed stability margin to any number of linear functionals when some conditions are met the design procedure is simple and can be easily implemented numerical examples are given to illustrate the properties of the new observer and its advantages over existing observer design techniques in the literature

a necessary condition for spectral controllability of delay systems on the basis of finite laplace transforms abstract this paper is concerned with spectral controllability of systems with multiple commensurate delays in the state variables a necessary condition for spectral controllability is presented on the basis of finite laplace transforms it is closely related to the finite spectrum assignment problem physical meanings of it are also discussed

linear functional observers for systems with delays in state variables the discrete time case this note extends to the discrete time case the design of linear functional state observers recently developed for continuous time delay systems sufficient conditions for the stability dependent of delays and stability independent of delays are derived using linear and bilinear matrix inequalities lmis and bmis formulations

reduced order kalman filter for a continuous time fractional order system using fractional order average derivative abstract this paper investigates two kinds of reduced order kalman filters for a continuous time fractional order system with uncorrelated and correlated process and measurement noises the fractional order average derivative is adopted to enhance the discretization accuracy for the investigated continuous time fractional order system the uncorrelated and correlated cases for the process and measurement noises are treated by the reduced order kalman filters to achieve the robust estimation for a part of states of a fractional order system the truncation issue is considered to implement the practical application of the proposed state estimation algorithm finally two examples for uncorrelated and correlated noises are offered to verify the effectiveness of the proposed reduced order kalman filters

an observer for time lag systems a full state vector observer is derived for a class of linear differential state delayed control systems the approach dualizes a feedback stabilization theory based on the reducing transformation technique a major feature of the approach is that the observer or the combined controller observer can be designed by well known finite dimensional state vector methods once the set of unstable and poorly damped modes of the system has been determined

linear functional observers for systems with delays in state variables this paper is concerned with the design of linear functional state observers for systems with delays in state variables in particular the necessary and sufficient conditions for the existence of the rth order observers are given sufficient conditions for the stability dependent of delays and stability independent of delays are derived using linear matrix in equality formulation a systematic design method of these observers is presented numerical examples are given to illustrate this method

disturbance decoupled observer design via singular value decomposition singular value decomposition is used to formulate a technique for the design of luenberger observers when there are completely unknown system inputs

time delay systems design of delay free and low order observers this note provides a comprehensive treatment on the design of functional observers for linear systems having a time varying delay in the state variables the designed observers possess attractive features of being low order and delay free and hence they are cost effective and easy to implement existence conditions are derived and a design procedure for finding low order observers is given

enthalpy based modelling and design of asymptotic observers for chemical reactors this article proposes to consider the basic thermodynamics based formulation of the energy balance equation for chemical systems with a limited number of simplifying assumptions the objective is to show via the design of one typical mass and energy balance state observer how such design can be modified by considering the proposed thermodynamically based model formulation the objective is also to emphasise the difference and the links between the energy balance based temperature equation largely used in process control the design of the asymptotic observer is illustrated with two examples one cstr in liquid phase and another one in gaseous phase

on reducing the order of kalman filters for discrete time stochastic systems having singular measurement noise a reduced order least squares state estimator is developed for estimating the states of a linear discrete time stochastic system having some outputs which are noise free

stabilization of hereditary distributed parameter control systems abstract in this paper we study the asymptotic stabilization of semilinear distributed parameter control systems with delay assuming that the semigroup of operators associated with the uncontrolled and undelayed equation is compact we prove that a well known rank condition which implies the feedback stabilization for lumped systems can be extended to this type of systems

full order observers for linear systems with unknown inputs this note presents a simple method to design a full order observer for linear systems with unknown inputs the necessary and sufficient conditions for the existence of the observer are given

approximation of rectangular sums of b valued random variables given independent identically distributed random variables xn n q indexed by q tuples of positive integers and taking values in a separable banach space b we approximate the rectangular sums sum limits m leqq n x m n in mathbb n q by a brownian sheet we obtain the corresponding result for random variables with values in a separable hilbert space h while assuming an optimal moment condition generalized versions of the functional law of the iterated logarithm are thus derived

an observer design for linear time delay systems an observer design is proposed for linear systems with time delays the key to the design is to find a generalized coordinate change such that in the new coordinates all the time delay terms are injected by the system s output the existence of such a coordinate change is guaranteed by a rank condition on the observability matrix the novelty of the proposed design is clearly reflected in the multiple output case where a dimensional expansion in the coordinate change could become necessary and hence is allowed

on the spectral controllability of delay differential equations a computable necessary and sufficient condition is proved for the spectral controllability of a class of linear hereditary systems and a counterexample is given to a previously published result

finite dimensional observers for delay systems a finite dimensional observer theory is formulated for a class of point delayed systems the observer is characterized by the fact that it directly generates a finite dimensional feedback controller for this class of systems the theory is based on a preliminary approximation theory which allows the delay system to be exponentially approximated by a system of ordinary differential equations

existence and design of functional observers for linear systems this paper presents straightforward derivations of the functional observers design for linear time invariant multivariable systems the order of these observers is equal to the dimension spl tau of the vector to be estimated necessary and sufficient conditions for the existence and stability of these observers are given illustrative examples are included

remarks concerning the asymptotic stability and stabilization of linear delay differential equations abstract this note concerns the asymptotic stability for all values of the delays of controlled and uncontrolled linear delay differential equations in the case of uncontrolled systems it is shown by example that structural considerations must be accounted for in the controlled case although arbitrary pole placement may not be possible there is an algorithm which sometimes reduces the spectrum of the feedback system to one which is finite and is contained in the left half plane