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

on the quadratic spans of debruijn sequences the quadratic span of a periodic binary sequence is defined to be the length of the shortest quadratic feedback shift register fsr that generates it an algorithm for computing the quadratic span of a binary sequence is described the required increase in quadratic span is determined for the special case of when a discrepancy occurs in a linear fsr that generates an initial portion of a sequence the quadratic spans of binary debruijn sequences are investigated an upper bound for the quadratic span of a debruijn sequence of span n is given this bound is attained by the class of debruijn sequences obtained from m sequences it is easy to see that a lower bound is n 1 but a lower bound of n 2 is conjectured the distributions of quadratic spans of debruijn sequences of span 3 4 5 and 6 are presented

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

a simple derivation of the berlekamp massey algorithm and some applications corresp another viewpoint is presented on the derivation of the berlekamp massey algorithm our approach differs from previous ones in the following manner the properties of the shortest linear feedback shift register that generates a given sequence are first derived without reference to the berlekamp massey algorithm the berlekamp massey algorithm is then derived using these properties our approach has the advantage of being easier to understand

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

the linear algebra of the generalized pascal matrix abstract this paper discusses three kinds of generalized pascal matrix and generalizes the results of r brawer and m pirovino

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

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

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

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

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

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

results on the nonlinear span of binary sequences the problem of finding the length of a shortest feedback shift register that generates a given finite length sequence is considered an efficient algorithm for the determination of the span is proposed that takes advantage of the special block structure of the associated system of linear equations the span distribution of finite length binary sequences is also studied

the algebraic properties of the generalized pascal functional matrices associated with the exponential families abstract in this paper pascal matrices are generalized to functional matrices by using the exponential families and the restricted sequences of polynomials of binomial type some algebraic properties of the pascal functional matrices are presented and proved in addition several important combinatorial identities are obtained

stirling matrix via pascal matrix abstract the pascal type matrices obtained from the stirling numbers of the first kind s n k and of the second kind s n k are studied respectively it is shown that these matrices can be factorized by the pascal matrices also the ldu factorization of a vandermonde matrix of the form v n x x 1 x n 1 for any real number x is obtained furthermore some well known combinatorial identities are obtained from the matrix representation of the stirling numbers and these matrices are generalized in one or two variables

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

an extended berlekamp massey algorithm for the inversion of toeplitz matrices the berlekamp massey algorithm bma which solves special toeplitz systems of linear equations is extended to an algorithm for inverting toeplitz matrices the original bma itself leads to one row of the inverse of the corresponding toeplitz matrix the other rows are derived using the same operations that are central to the original bma two alternatives for the extended bma are presented the first includes the usual bma without any changes and the second simplifies the structure by some modifications also in the original bma part both versions follow a tree like structure if the branches of the tree are implemented in parallel the time demand would be nearly the same as for the usual bma in contrast to other toeplitz algorithms only slight modifications must be incorporated to handle singular submatrices

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

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

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

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

a view of gaussian elimination applied to early stopped berklekamp massey algorithm in this paper we adopt a restricted gaussian elimination on the hankel structured augmented syndrome matrix to reinterpret an early stopped version of the berlekamp massey algorithm in which only t e iterations need to be performed for the decoding of bch codes up to t errors where e is the number of errors actually occurring with e leq t instead of the 2t iterations required in the conventional berklekamp massey algorithm the minimality of t e iterations in this early stopped berklekamp massey esbm algorithm is justified and related to the subject of simultaneous error correction and detection in this paper we show that the multiplicative complexity of the esbm algorithm is upper bounded by te e 2 1 forall e leq t and except for a trivial case the esbm algorithm is the most efficient algorithm for finding the error locator polynomial

a variation of constants formula for abstract functional differential equations in the phase space abstract for linear functional differential equations with infinite delay in a banach space a variation of constants formula is established in the phase space as an application one applies it to study the admissibility of some spaces of functions whose spectra are contained in a closed subset of the real line

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

control of linear systems with fixed noncommensurate point delays the first solution is given to the fundamental open problem of stabilizability and detectability necessary sufficient conditions for internal stabilization by feedback of retarded and a large class of neutral delay differential systems with several fixed noncommensurate point delays using causal compensators observers and state feedback or dynamic output feedback which are also the same type of neutral or retarded delay differential systems with fixed point delays only our results are rank conditions on the system matrices zi f g and zif t h t evaluated at points in the complex plane and are the weakest possible generally applicable sufficient such rank conditions for stabilization of neutral systems in the light of what is known on the stability of such systems these conditions are necessary for most practical purposes the class of systems we consider includes all retarded delay differential systems with noncommensurate fixed point delays in the case of retarded systems these rank conditions are necessary and sufficient conditions for stabilization via compensators which are causal retarded delay differential systems with fixed point delays only these constitute the first full solution of these previously unsolved problems of stabilizability and detectability which together are necessary and sufficient conditions for internal stabilization by feedback for delay differential systems even in the retarded single fixed point delay case an application of our results to a problem of practical importance in control of linear systems with no delays provides a stabilization criterion interesting in itself

finite spectrum assignment for multivariable delay systems in the frequency domain a frequency domain approach to arbitrary finite spectrum assignment for multivariable delay systems is developed and a practical example is presented for illustration

schur algorithms for hermitian toeplitz and hankel matrices with singular leading principal submatrices it is shown how a simple matrix algebra procedure can be used to induce schur type algorithms for the solution of certain toeplitz and hankel linear systems of equations when given levinson durbin algorithms for such problems the algorithm of p delsarte et al 1985 for hermitian toeplitz matrices in the singular case is used to induce a schur algorithm for such matrices an algorithm due to g heinig and k rost 1984 for hankel matrices in the singular case is used to induce a schur algorithm for such matrices the berlekamp massey algorithm is viewed as a kind of levinson durbin algorithm and so is used to induce a schur algorithm for the minimal partial realization problem the schur algorithm for hermitian toeplitz matrices in the singular case is shown to be amenable to implementation on a linearly connected parallel processor array of the sort considered by kung and hu 1983 and in fact generalizes their result to the singular case

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

the linear algebra of the generalized pascal functional matrix abstract in this paper we generalize pascal s matrix by defining the polynomials factorial binomial then using this generalization we introduce a two variable pascal s matrix and state its related theorems and prove them finally we introduce pascal s functional matrix associated with a sequence a a n n 0 and obtain several important combinatorial identities

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

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

voronoi regions of lattices second moments of polytopes and quantization if a point is picked at random inside a regular simplex octahedron 600 cell or other polytope what is its average squared distance from the centroid in n dimensional space what is the average squared distance of a random point from the closest point of the lattice a n or d n e n a n ast or d n ast the answers are given here together with a description of the voronoi or nearest neighbor regions of these lattices the results have applications to quantization and to the design of signals for the gaussian channel for example a quantizer based on the eight dimensional lattice e8 has a mean squared error per symbol of 0 0717 cdots when applied to uniformly distributed data compared with 0 08333 cdots for the best one dimensional quantizer

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

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

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

an extension of the generalized pascal matrix and its algebraic properties abstract the extended generalized pascal matrix can be represented in two different ways as a lower triangular matrix n x y or as a symmetric n x y these matrices generalize p n x q n x and r n x which are defined by zhang and by call and velleman a product formula for n x y has been found which generalizes the result of call and velleman it is shown that not only can n x y be factorized by special summation but also n x y as q n xy s t y 1 x or n x y p n t y x finally the inverse of n x y and the values of det n x y det n 1 x y det n x y and det n 1 x y are given

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

generalized pascal functional matrix and its applications in this paper we introduce the generalized pascal functional matrix and show that the existing variations of pascal matrices are special cases of this generalization we study some algebraic properties of such generalized pascal functional matrices in addition we demonstrate a direct application of these properties by deriving several novel combinatorial identities and a nontraditional approach for lu decompositions of some well known matrices such as symmetric pascal matrices

extended bernoulli and stirling matrices and related combinatorial identities abstract in this paper we establish plenty of number theoretic and combinatoric identities involving generalized bernoulli polynomials and stirling numbers of both kinds which generalize various known identities these formulas are deduced from pascal type matrix representations of bernoulli and stirling numbers for this we define and factorize a modified pascal matrix corresponding to bernoulli and stirling cases

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

generalized higher order bernoulli number pairs and generalized stirling number pairs abstract from a delta series f t and its compositional inverse g t hsu defined the generalized stirling number pair s n k s n k in this paper we further define from f t and g t the generalized higher order bernoulli number pair b n z b n z making use of the bell polynomials the potential polynomials as well as the lagrange inversion formula we give some explicit expressions and recurrences of the generalized higher order bernoulli numbers present the relations between the generalized higher order bernoulli numbers of both kinds and the corresponding generalized stirling numbers of both kinds and study the relations between any two generalized higher order bernoulli numbers moreover we apply the general results to some special number pairs and obtain series of combinatorial identities it can be found that the introduction of generalized bernoulli number pair and generalized stirling number pair provides a unified approach to lots of sequences in mathematics and as a consequence many known results are special cases of ours

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

factorial stirling matrix and related combinatorial sequences abstract in this paper some relationships between the stirling matrix the vandermonde matrix the benoulli numbers and the eulerian numbers are studied from a matrix representation of k s n k which will be called the factorial stirling matrix where s n k are the stirling numbers of the second kind as a consequence a number of interesting and useful identities are obtained

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

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

a simple hankel interpretation of the berlekamp massey algorithm abstract a simple interpretation of the berlekamp massey algorithm in the light of the hankel matrix is presented the salient result is that the jump of the linear feedback shift register lfsr length is derived almost trivially from the so called iohvidov index of the hankel matrix prior to making any reference to the berlekamp massey algorithm itself next the hankel system of equations that yields the updated connection polynomial is solved via the natural lu factorization of the hankel matrix which itself leads to the berlekamp massey algorithm in a simple and transparent manner

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