parity space based fault detection for linear discrete time varying systems with unknown input in this paper a new approach to parity space based fault detection fd is put forward for linear discrete time varying ldtv systems the focus of our study is on solving the problem with heavy online computational burden the main contributions are two folds firstly the problem of parity space based fd is formulated as finding a minimum of quadratic form of unknown input secondly by applying projection in krein space a solution of optimal parity space based fd is obtained via recursively computing innovations it is shown that the reduction of computation cost is achievable especially with the increase of parity space order finally a numerical example is given to demonstrate the application of the proposed method

on l1 gain control of 2 d positive roesser systems with directional delays necessary and sufficient conditions abstract in this paper the problem of l 1 gain control is addressed for two dimensional 2 d positive roesser systems with directional delays a complete solution to the design problem is presented for the first time specifically by exploiting a new approach based on 2 d z transform an exact value of l 1 induced norm of the input output operator is obtained this analytical result is utilized to derive necessary and sufficient conditions under which a 2 d positive system with delays is asymptotically stable with a prescribed l 1 gain performance then by utilizing a vertex optimization approach necessary and sufficient conditions are established for the existence of a state feedback controller sfc that makes the closed loop system positive and stable subject to l 1 induced performance the proposed synthesis conditions are formulated in terms of linear programming lp which can be effectively solved by various convex algorithms to minimize the l 1 performance index

recursive state estimation for two dimensional shift varying systems with random parameter perturbation and dynamical bias abstract in this paper the state estimation problem is investigated for a class of two dimensional 2 d stochastic systems with shift varying parameters the stochasticity with the underlying system comes from three sources namely random parameter perturbations dynamical biases and additive white noises the measurement output is subject to the uniform quantization as a result of communication constraints on the sensors the purpose of the addressed problem is to recursively estimate the system states with prescribed estimation performance in spite of the stochastic disturbances and the uniform quantizations an augmented model is first constructed to combine the information about the state and the bias and the dynamical evolution is subsequently discussed furthermore through stochastic analysis and mathematical induction the estimator design algorithm is developed to acquire certain upper bound on the estimation error variance and such an upper bound is then minimized in the matrix trace sense moreover the boundedness issue of the estimation errors is investigated via matrix inversion lemma and inductive analysis technique finally the effectiveness of the proposed state estimation algorithm is validated on a typical 2 d system modeled by the well known darboux equation with extensive application potentials in industrial processes

the existence and design of functional observers for two dimensional systems abstract this paper is concerned with functional observers for two dimensional 2d systems described by the fornasini marchesini local state space second model a necessary and sufficient condition is given for the existence of asymptotic functional observers a more tractable necessary condition for the existence of asymptotic functional observers is also presented as it helps exclude those 2d systems for which there is no asymptotic functional observer a constructive design method is then proposed for the design of asymptotic functional observers using a rank condition on the given system matrices and a linear matrix inequality lmi technique two illustrative examples are provided to demonstrate the feasibility and effectiveness of the proposed method

absorption semigroups their generators and schrodinger semigroups on presente des resultats de perturbations pour des c 0 semi groupes on considere le probleme aux valeurs initiales pour l equation de la chaleur avec absorption avec une solution dans l p r v avec une mauvaise fonction v r r on considere le meme probleme dans l 2 r pour l equation de schrodinger

unknown input observers for 2d state space models in this paper dead beat unknown input observers uios for two dimensional 2d state space models are investigated dead beat uios are observers which produce an exact estimate of the original system state trajectory after a finite number of evolution steps independently of the system and observer initial conditions and of the unknown disturbances that affect the system functioning necessary and sufficient conditions for the existence of dead beat uios are provided as well as a parameterization of all dead beat uio transfer matrices comparisons with luenberger type uios are also carried out and the extension of the paper results to the case of asymptotic uios with a given rate of convergence and to roesser models are finally discussed

finite frequency model reduction of two dimensional digital filters this technical note is concerned with the model reduction problem of two dimensional 2 d digital filters over finite frequency ranges the 2 d digital filter is described by the fornasini marchesini local state space fm lss model with the aid of the generalized kalman yakubovich popov gkyp lemma for 2 d systems sufficient conditions for the finite frequency model reduction problem are derived compared with full frequency methods the proposed finite frequency method can get a better approximation performance over finite frequency ranges an example is given to demonstrate the effectiveness of the proposed method

a new scheme of fault detection for linear discrete time varying systems in this note a new scheme of fault detection fd is proposed for linear discrete time varying ldtv systems subject to l 2 norm bounded unknown inputs the basic idea is to find an optimal estimation of the l 2 norm of the unknown inputs including the unknown initial state variables this leads to a natural design of the fd system with the l 2 norm boundedness of the unknown inputs as a threshold and the l 2 norm of the unknown input estimate as the evaluation function to avoid heavy computational burden projection technique in krein space is applied which allows a recursive computation of the evaluation function it is shown that the achieved fd system satisfies both the worst case and best case sensitivity robustness ratio criteria and further applications to observer based fd lead to an alternative design of h infty h infty and or h h infty fault detection filter

support theorem for the fundamental solution to the schrodinger equation on certain compact symmetric spaces abstract in this paper we construct the fundamental solution to the schodinger equation on a compact symmetric space with even root multiplicities using shift operators of heckman and opdam next we prove that the support of the fundamental solution becomes a lower dimensional subset at a rational time whereas its support and its singular support coincide with the whole symmetric space at an irrational time moreover we also show that generalized gauss sums appear in the expression of the fundamental solution

robust h_ infty filtering for two dimensional uncertain linear discrete time varying systems a krein space based method a robust h infty filtering algorithm is proposed for two dimensional 2 d linear uncertain time varying systems in this study the considered 2 d systems are subject to unknown inputs measurement noises and time varying modeling uncertainties to appropriately deal with the system uncertainties a new problem formulation of robust h infty filter design for 2 d uncertain systems is first presented by introducing an alternative indefinite quadratic performance function in lieu of the standard h infty performance index then the robust 2 d h infty filter design is converted to an optimization problem of finding the positive minimum of the new indefinite quadratic performance function under certain conditions by relating this quadratic form to a specific 2 d state space model in krein space the krein space estimation theory is used to solve the reformulated optimization problem a recursive robust 2 d time varying h infty filter and its explicit condition for the existence are obtained through projection techniques in 2 d krein space one thermal process plant is used to illustrate the effectiveness of the proposed filter

brief paper unbiased minimum variance input and state estimation for linear discrete time systems this paper addresses the problem of simultaneously estimating the state and the input of a linear discrete time system a recursive filter optimal in the minimum variance unbiased sense is developed where the estimation of the state and the input are interconnected the input estimate is obtained from the innovation by least squares estimation and the state estimation problem is transformed into a standard kalman filtering problem necessary and sufficient conditions for the existence of the filter are given and relations to earlier results are discussed

generalized kalman yakubovich popov lemma for 2 d fm lss model this paper is concerned with the generalized kalman yakubovich popov kyp lemma for 2 d fornasini marchesini local state space fm lss systems by carefully analyzing the feature of the states in 2 d fm lss models a linear matrix inequality lmi characterization for a rectangular finite frequency region is constructed and then by combining this characterization with s procedure a generalized kyp lemma is proposed for 2 d fm lss models as applications of the developed kyp lemma new conditions are further derived for designing controllers guaranteeing finite frequency positive realness of the closed loop systems where both state feedback and dynamic output feedback control laws are considered finally two illustrative examples clearly show the effectiveness of the proposed results the main contribution of the paper is trifold 1 a novel characterization for a finite frequency region has been developed 2 a generalized kyp lemma has been proposed including the existing bounded realness and positive realness results as special cases and 3 systematic methods for finite frequency positive real control of 2 d systems have been presented

state estimation for stochastic discrete time systems with multiplicative noises and unknown inputs over fading channels abstract this paper deals with robust state estimation problem for a class of stochastic discrete time systems with multiplicative noises and unknown inputs over fading channels an unbiased unknown input insensitive filter is designed such that the variance of the estimation error is minimized in the sense of the so called p estimation the filter gain matrix is derived through solving a recursive riccati equation and a generalized lyapunov equation a necessary and sufficient condition that guarantees the existence of the filter is given which establishes a fundamental limit on the mean square capacity of each fading channel unknown input estimation and finite horizon stability of the proposed filter are also discussed to illustrate the effectiveness of the proposed approach the proposed algorithm is applied to a faulty remote controlled uninterruptible power system where both the state and the fault are estimated

a dominated type convergence theorem for the feynman integral a dominated type convergence theorem is proved for the operator valued feynman integral defined via the trotter product formula this definition is intimately related to the one of feynman and the physical setting is the same as in his original paper the convergence result given here provides the final piece of a unifying and rather satisfactory picture of three approaches to the feynman integral

the fornasini marchesini and the roesser models algebraic methods for recasting this paper is devoted to giving a new method for recasting the fornasini marchesini model of the two dimensional system to the roesser form endowed with an important feature that the dimensions of both models are the same the two dimensional similarity transformation and spectral transformations of the transfer function variables are used for this purpose both the standard and singular cases are considered

a sufficient condition on the exponential stability of two dimensional 2 d shift variant systems in this paper we consider a class of two dimensional 2 d shift variant systems based on the bound on the deviation of parameters a sufficient condition is derived which ensures exponential stability with different decaying rates along the two directions an example is presented to illustrate the result

filtering design for two dimensional markovian jump systems with state delays and deficient mode information this paper is concerned with the problem of h filtering for a class of two dimensional markovian jump linear systems described by the fornasini marchesini local state space model the systems under consideration are subject to state delays and deficient mode information in the markov chain the description of deficient mode information is comprehensive that simultaneously includes the exactly known partially unknown and uncertain transition probabilities by invoking the properties of the transition probability matrix together with the convexification of uncertain domains a new h performance analysis criterion for the filtering error system is firstly derived then via some matrix inequality linearisation procedures two approaches for the filter synthesis are proposed it is shown that both the full order and reduced order filters can be constructed by solving a set of linear matrix inequalities finally simulation studies are provided to illustrate the effectiveness of the proposed design methods

dominated semigroups with singular complex potentials abstract we develop the perturbation and approximation theory for dominated c 0 semigroups on l p 1 p

scattering theory for the laplacian on symmetric spaces of noncompact type and its application to a conjecture of strichartz abstract in this paper we develop the scattering theory for the laplacian on symmetric spaces of noncompact type we study the asymptotic properties of the resolvent in the framework of the agmon hormander space our approach is based on a detailed analysis of the helgason fourier transform and generalized spherical functions on symmetric spaces of noncompact type as an application of our scattering theory we prove a conjecture by strichartz concerning a characterization of a family of generalized eigenfunctions of the laplacian

unbiased minimum variance estimation for systems with unknown exogenous inputs a new method is developed for the state estimation of linear discrete time stochastic systems in the presence of an unknown disturbance the filter obtained is optimal in the unbiased minimum variance sense the necessary and sufficient conditions for the existence and the stability of the filter are given

near optimal control for time varying linear discrete systems with additive nonlinearities and random gains in this technical note the near optimal control problem is investigated for a class of time varying linear discrete systems subject to additive nonlinearities and random gains first certain upper bound on the cost function is proposed to quantify the control performance subsequently in virtue of the time varying discrete riccati like recursions drlrs the near optimal control strategy is designed such that this upper bound is minimized over the finite horizon to reflect the steady state behavior of the dynamic system the upper bound of the derived time varying drlrs is also analyzed over the infinite horizon by resorting to the semidefinite programming method finally a numerical example is provided to verify the validity and advantages of the proposed methodology

detectability and stabilizability of time varying discrete time linear systems the concepts of detectability and stabilizability are explored for time varying systems we study duality invariance under feedback an extended version of the lemma of lyapunov existence of stabilizing feedback laws linear quadratic filtering and control and the existence of approximate canonical forms

product formula for imaginary resolvents with application to a modified feynman integral abstract an abstract product formula for imaginary resolvents is proved for a pair of self adjoint operators a b of a complex hilbert space here a is assumed to be nonnegative and the positive part of b is arbitrary while its negative part is small with respect to a in the sense of quadratic forms the proof is somewhat simpler than the author s original one which required both a and b to be nonnegative when specialized this theorem establishes the convergence of the modified feynman integral recently introduced by the author in the most general case for which the schrodinger equation can be solved without ambiguity

unbiased minimum variance fault and state estimation for linear discrete time varying two dimensional systems the fault and state estimation problem is addressed for a class of linear discrete time varying two dimensional systems subject to state and measurement noises two estimators are proposed to compute the estimation of the system state and or fault recursively both of which are unbiased with minimum variance through formulating the estimation problem as the solvability problem of the corresponding matrix equations of estimator gains and system constraint the necessary and sufficient condition of the existence and the solution for the proposed estimators are given an example is used to demonstrate the effectiveness of the proposed estimators