on generalized convexity of fuzzy variables maps in this paper we investigate the convexity and quasiconvexity of fuzzy functions by use the interval analysis some properties of convex and quasiconvex fuzzy functions are introduced applications of fuzzy convexity and quasiconvexity to optimality are discussed

non iterative computation of infimum in discrete time h optimization and solvability conditions for the discrete time disturbance decoupling problem a non iterative method for the computation of the infimum for a class of discrete time h optimal control problems and the solvability conditions for the general discrete time disturbance decoupling problem are given in this paper the method for the computation of the infimum is applicable to systems where the transfer functions from the disturbance input to the measurement output and from the control input to the controlled output are free of unit circle invariant zeros and satisfy certain geometric conditions the solvability conditions we obtained for the general discrete time disturbance decoupling problem are also necessary and sufficient conditions

a weakly equivalent condition of convex fuzzy sets abstract in this short communication we first introduce inner straight line g x y on the subset g in the euclidean space rn and define the concept of the weakly quasi convex fuzzy sets second we will give a weak equivalent condition that a fuzzy closed set is a convex fuzzy set

riccati differential equation in optimal filtering of periodic non stabilizable systems this paper discusses the periodic solutions of the matrix riccati differential equation in the optimal filtering of periodic systems special emphasis is given to non stabilizable systems and the question addressed is the existence and uniqueness of a steady state periodic non negative definite solution of the periodic riccati differential equation which gives rise to an asymptotically stable steady state filter the results presented show that the stabilizability is not a necessary condition for the existence of such a periodic solution the convergence of the general solution of the periodic riccati differential equation to a periodic equilibrium solution is also investigated the results are extensions of existing time invariant systems results to the case of periodic systems

robust stabilization of discrete time linear systems with norm bounded time varying uncertainty abstract this paper presents an algorithm for the stabilization of a class of discrete time uncertain systems suffering from uncertainty of the norm bounded time varying type the stabilizing control gain matrix is obtained by solving a certain discrete riccati equation the solution of this riccati equation is also a lyapunov matrix which is used to establish the stability of closed loop system the results presented in this paper generalize those obtained in previous works for continuous time uncertain systems

brief constrained linear state estimation a moving horizon approach this article considers moving horizon strategies for constrained linear state estimation additional information for estimating state variables from output measurements is often available in the form of inequality constraints on states noise and other variables formulating a linear state estimation problem with inequality constraints however prevents recursive solutions such as kalman filtering and consequently the estimation problem grows with time as more measurements become available to bound the problem size we explore moving horizon strategies for constrained linear state estimation in this work we discuss some practical and theoretical properties of moving horizon estimation we derive sufficient conditions for the stability of moving horizon state estimation with linear models subject to constraints on the estimate we also discuss smoothing strategies for moving horizon estimation our framework is solely deterministic

comments on kalman filtering methods for computing information matrices for time invariant periodic and generally time varying varma models and samples abstract this paper discusses some results contained in a paper by zadrozny and mittnik 1 in relation to the work developed by terceiro 2 it also considers several issues concerning the efficiency of the algorithm and the state space formulation of varma models

numerical j spectral factorization of general para hermitian matrices a numerical algorithm for j spectral factorization of para hermitian rational matrices is presented based on a generalization of the notion of separated realization of a para hermitian matrix the transformations used preserve the para hermitian matrix pencil structure

the set of positive semidefinite solutions of the algebraic riccati equation of discrete time optimal control in this paper the algebraic riccati equation are of the discrete time linear quadratic lq optimal control problem and its set of positive semidefinite solutions is studied under the most general assumption which is output stabilizability with respect to an appropriate basis the discrete time algebraic riccati equation dare decomposes into a lyapunov equation and an irreducible riccati equation the focus is on the riccati part which amounts to studying a dare where all unimodular modes are controllable a bijection between positive semidefinite solutions and certain well defined sets of f invariant subspaces is established which together with its inverse is order reversing as an application issues concerning positive definite or strong solutions are clarified analogous results for negative semidefinite solutions are valid only under an additional assumption on the unobservable subspace

linear optimal unbiased filter for time variant systems without apriori information on initial conditions in this technical note an optimal unbiased filter ouf is derived for time variant systems to relax the initial condition assumption in kalman filter kf by minimizing the mean square errors subject to the unbiasedness condition a solution is derived in a batch computation form first to facilitate the on line application a recursive realization is further developed the effect of removing the initial condition assumption on the estimation performance is analysed and we show that the proposed algorithm converges to the kf asymptotically two state harmonic model and four state moving target tracking model are employed to demonstrate that the ouf can improve transient estimation performance significantly and can be used in place of the kf when the apriori information about the initial state values is not available

a successive optimal construction procedure for state feedback gains abstract this paper studies a successive optimal construction procedure of state feedback gains this topic was first studied in the context of the pole assignment problem for lq linear quadratic regulators but the selection of weighting matrices in each successive step was restricted in previous researches in this paper we consider more general selections of weighting matrices and give extended results in both the continuous time and the discrete time cases

some properties of weakly convex fuzzy mappings in this paper we introduce the concepts of weakly convex fuzzy sets weakly convex fuzzy mappings and weakly quasi convex fuzzy mappings and then give characterization theorems for these fuzzy sets and fuzzy mappings

brief extension of minimum variance estimation for systems with unknown inputs in this paper we address the problem of minimum variance estimation for discrete time time varying stochastic systems with unknown inputs the objective is to construct an optimal filter in the general case where the unknown inputs affect both the stochastic model and the outputs it extends the results of darouach and zasadzinski automatica 33 1997 717 where the unknown inputs are only present in the model the main difficulty in treating this problem lies in the fact that the estimation error is correlated with the systems noises this fact leads generally to suboptimal filters necessary and sufficient conditions for the unbiasedness of this filter are established then conditions under which the estimation error and the system noises are uncorrelated are presented and an optimal estimator and a predictor filters are derived sufficient conditions for the existence of these filters are given and sufficient conditions for their stability are obtained for the time invariant case a numerical example is given in order to illustrate the proposed method

lattice properties of sets of semidefinite solutions of continuous time algebraic riccati equations the set of negative semidefinite solutions of the algebraic riccati equation a x xa xbb x c c 0 is studied under the most general hypothesis namely that a b is stabilizable modulo the undetectable subspace of a c if is a lattice then is isomorphic to 0 s where t0 is the direct sum of copies of the set of nonnegative real numbers and is a closure of which is order isomorphic to a system of well defined a invariant subspaces necessary and sufficient conditions are given such that or is a lattice

convergence properties of the riccati difference equation in optimal filtering of nonstabilizable systems this paper studies the convergence and properties of the solutions of the riccati difference equation special emphasis is given to systems which are not necessarily stabilizable in the filtering sense particularly those having uncontrollable roots on the unit circle besides generalizing and unifying previous work the results have application to a number of important problems including filtering and control of systems with purely deterministic disturbances such as sinusoids and drift components

on properties of convex fuzzy mappings the objective of this paper is to obtain some important properties about convex fuzzy mappings based on a linear ordering of fuzzy numbers proposed by goetschel and voxman firstly a new kind of fuzzy mapping termed semistrictly convex fuzzy mapping is defined through this linear ordering note that semistrict convexity does not imply convexity and the interrelationships among convex strictly convex and semistrictly convex mappings are established under certain conditions furthermore this paper obtains several characterizations for the above three classes of fuzzy mappings under the conditions of upper or lower semicontinuity finally some further characteristic properties for semistrictly convex fuzzy mappings are derived

mixed problem for some semi linear wave equation with a nonhomogeneous condition on considere le probleme aux valeurs limites et initiales suivant u tt u xx u t sign u t 0 x t 0 1 0 t u x 0 t g t u 1 t 0 u x 0 u 0 x u t x 0 u 1 x avec 0 1 avec u 0 h 1 0 1 u 1 dans l 2 0 1 et g t dans l 2 0 t un theoreme d existence globale et d unicite est demontre

normal forms of symplectic pencils and the discrete time algebraic riccati equation abstract the solution of the discrete time algebraic riccati equation leads to symplectic pencils of matrices normal forms of such pencils under symplectic equivalence are determined special attention is given to characteristic roots of modulus 1 and their corresponding elementary divisors and inertial invariants

on positive definite solutions to the algebraic riccati equation abstract complete necessary and sufficient conditions for the existence of a positive definite solution to the algebraic riccati equation are given it is also shown that when a positive definite solution exists it is either unique or else there are uncountably many such solutions

riccati equations in optimal filtering of nonstabilizable systems having singular state transition matrices until recently it was believed that a necessary and sufficient condition for convergence of the riccati difference equation of optimal filtering was that the system be both delectable and stabilizable recently it has been shown that the stabilizability condition can be removed but convergence has only established under restrictive assumptions including the requirement that the state transition matrix be nonsingular the present paper generalizes these results in several directions first properties of the algebraic riccati equation are established for the case of singular state transition matrix second several assumptions previously imposed in establishing convergence of the riccati difference equation for systems with unreachable modes on the unit circle are relaxed including replacing observability by detectability weakening the conditions on the initial covariance and allowing the state transition matrix to be singular third results on the convergence and properties of the riccati equations are expressed as both necessary and sufficient conditions whereas previous results were only sufficient these extensions mean that the results have wider applicability including fixed lag smoothing problems and filtering for systems with time delays the implications of the results in the dual problem of optimal control are also studied

criterion for the convergence of the solution of the riccati differential equation the optimal control problem for a linear system with a quadratic cost function leads to the matrix riccati differential equation the convergence of the solution of this equation for increasing time interval is investigated as a function of the final state penalty matrix a necessary and sufficient condition for convergence is derived for stabilizable systems even if the output in the cost function is not detectable an algorithm is developed to determine the limiting value of the solution which is one of the symmetric positive semidefinite solutions of the algebraic riccati equation examples for convergence and nonconvergence are given a discussion is also included of the convergence properties of the solution of the riccati differential equation to any real symmetric not necessarily positive semidefinite solution of the algebraic riccati equation

a non iterative method for computing the infimum in h optimization this paper presents a simple and non iterative procedure for the computation of the exact value of the infimum in the singular h optimization problem and is an extension of our earlier work the problem formulation is general and does not place any restriction on the direct feedthrough terms between the control input and the controlled output variables and between the disturbance input and the measurement output variables our method is applicable to a class of singular h optimization problems for which the transfer functions from the control input to the controlled output and from the disturbance input to the measurement output have no invariant zeros on the jw axis and also satisfy certain geometric conditions the computation of the infimum in our method involves solving two well defined riccati and two lyapunov equations

convexity of n dimensional fuzzy number valued functions and its applications the aim of this study is to generalize convexity from vector valued maps to n dimensional fuzzy number valued functions and to investigate some relations among the convexity and generalized convexity of n dimensional fuzzy number valued functions which are based on a new ordering of n dimensional fuzzy numbers proposed in this study furthermore some criteria are obtained for the convexity and generalized convexity under the conditions of lower and upper semicontinuity respectively finally we study the local global minimum properties of the convex fuzzy number valued functions

closed and convex fuzzy sets in this paper we establish a characterization theorem for closed fuzzy sets and give two weak conditions that a closed fuzzy set is a convex fuzzy set we also present some results for convex fuzzy sets strictly convex fuzzy sets and closed fuzzy sets

on convex and concave fuzzy mappings abstract in this paper we introduce the concepts of convex subsets of f 0 the set of all fuzzy numbers and monotonic fuzzy mappings on r2 and show that a monotonic fuzzy mapping f on a convex set c r1 or r2 is quasi convex and quasi concave we establish two characterizations for convex fuzzy mappings and two characterizations for concave fuzzy mappings we also prove the least upper bound property

asymptotic stability and energy decay rates for solutions of the wave equation with memory in a star shaped domain we study the asymptotic stability and give the energy decay rates for solutions of the wave equation with boundary dissipation of the memory type

a step toward a unified treatment of continuous and discrete time control problems in this paper we introduce a new approach for a unified theory for continuous and discrete time optimal control problems based on the generalized cayley transformation we also relate the associated discrete and continuous generalized algebraic riccati equations we demonstrate the potential of this new approach by proving a new result for discrete algebraic riccati equations but we also discuss where this new approach as well as all other approaches still is nonsatisfactory we explain a discrepancy observed between the discrete and continuous case and show that this discrepancy is partly due to the consideration of the wrong analogues we also present an idea for an implication scheme that relates general theorems for discrete and continuous control problems

on existence and asymptotic stability of solutions of the degenerate wave equation with nonlinear boundary conditions abstract we study the global existence of solutions of the nonlinear degenerate wave equation 0 x y y 0 in 0 y 0 on 1 0 y y f y g y 0 on 0 0 y x 0 y 0 y x 0 y 1 x in where y denotes the derivative of y with respect to parameter t f s c0 s s and g is a nondecreasing c1 function such that k1 s 2 g s s k2 s 2 for some k1 k2 0 with 0 0 if n 1 2 the existence of solutions is proved by means of the faedo galerkin method furthermore when 0 the uniform decay is obtained by making use of the perturbed energy method

an adaptive control algorithm for linear systems having unknown time delay abstract this paper presents an algorithm for adaptive control of linear systems having unknown time delay a rational approximation is used for the delay and it is argued that within this framework the analysis of the properties of the corresponding adaptive control algorithm essentially reduces to the issue of robustness to unmodelled dynamics a global convergence theory is presented using recent methods for analyzing robustness properties of adaptive control algorithms the analysis is supported by simulation results

existence conditions and properties for the maximal periodic solution of periodic riccati difference equations the existence and properties of the maximal symmetric periodic solution of the periodic riccati difference equation is analysed for the optimal filtering problem of linear periodic discrete time systems special emphasis is given to systems not necessarily reversible and subject only to a detectability assumption necessary and sufficient conditions for the existence and uniqueness of periodic non negative definite solutions of the periodic riccati difference equation which gives rise to a stable filter are also established furthermore the convergence of non negative definite solutions of the riccati equation is investigated

existence and uniform decay rates of solutions to a degenerate system with memory conditions at the boundary in this article we study the degenerate system r 1 r 2 0 subject to memory conditions on the boundary given email protected 1 x u t email protected email protected u v email protected 0 r 2 x v t email protected a u v email protected 0 email protected 0 email protected 0 tg 1 t s email protected email protected s email protected 1x 0 email protected 0 email protected 0 tg 2 t s email protected email protected s email protected 1x 0 u 0 v 0 u 0 v 0 r 1u t 0 r 2v t 0 r 1u 1 r 2v 1 email protected where w is a bounded region in r n whose boundary is partitioned into disjoint sets c 0 c 1 we prove that the dissipations given by the memory terms are strong enough to guarantee exponential or polynomial decay provided the relaxation functions also decay exponentially or polynomially and with the same rate of decay

convergence of the dre solution to the are strong solution in this paper we use the boundary solutions to a linear matrix inequality lmi associated with kalman filtering to investigate the convergence of the solution of a differential riccati equation dre to the so called strong solution of an algebraic riccati equation are we furthermore extend our results to kalman filtering with indefinite input noise covariances

technical communique reduced order kalman filter with unknown inputs this paper presents an optimal reduced order kalman filter for discrete time dynamic stochastic linear systems with unknown inputs the problem is to estimate a part of the state vector in the case where none of the observations are assumed to be noise free the proposed filter is obtained by minimizing the trace of the estimation error covariance matrix with respect to the remaining degrees of freedom after noninteresting state and unknown inputs decoupling the necessary and sufficient conditions for stability and convergence of the filter are established

a semilinear wave equation with space time dependent coefficients and a memory boundarylike antiperiodic condition a low frequency asymptotic expansion this paper studies a low frequency asymptotic expansion for a unique strong solution to an initial boundary value problem of a semilinear wave equation this equation admits space time dependent coefficients and a memory boundarylike antiperiodic condition for some small parameters from coefficients of this semilinear wave equation and of boundary conditions we approximate a unique strong solution to this problem by a polynomial of these parameters and coefficients of this polynomial are strong solutions of a sequence of well defined linear initial boundary value problems

bounds on the solution of the algebraic riccati equation under perturbations in the coefficients abstract this paper is concerned with bounds on symmetric solutions of the continuous algebraic matrix riccati equation under perturbations on its coefficients special emphasis is given to the question of estimating the size of the perturbations on the stabilizing solution of the riccati equation when one or all its coefficients are subject to small perturbations upper bounds on the norm of the perturbations on the stabilizing solution are presented moreover it is shown that these perturbations can be determined as a single valued continuous function of the perturbations on the coefficient of the riccati equation

geometric aspects of the riccati difference equation in the nonsymmetric case abstract this paper provides a collection of geometric results concerning the nonsymmetric riccati difference equation it gives representation formulas which express all the solutions in terms of a suitable number of known ones further results include geometric properties of the difference of two solutions and the generalization of some of the author s earlier results to the nonsymmetric case

a necessary and sufficient condition for solvability of the linear quadratic control problem without stabilty in this short paper a necessary and sufficient condition is given for the existence of a minimizing control for the regular non negative definite linear quadratic control problem without stability

convergence of the kalman filter gain for a class of nondetectable signal extraction problems convergence of the filter gain is proved for a class of problems with undetectable modes on the unit circle this situation arises when the signal is an unstable arma process corrupted by arma noise with the same unstable modes since modes common to signal and noise are unobservable

an algebraic riccati equation for the discrete time periodic prediction problem abstract in this paper the periodic problem is reformulated as a prediction problem relative to a suitable time invariant system this enables one to establish a one to one correspondence between the solutions of the discrete time periodic riccati equation dpre and the solutions of a suitable discrete time and time invariant riccati equation in particular the constant solutions of this last equation are the periodic generators of the original periodic riccati equation this enables one to easily derive existence uniqueness and convergence results for the drpe from known results relative to the time invariant case

convexity and semicontinuity of fuzzy mappings in this paper a criterion for the convex fuzzy mapping is obtained under the condition of upper and lower semicontinuity respectively an upper lower semicontinuous fuzzy mapping is proved which convexity is equivalent to weak convexity or b vexity satisfying a special condition

brief monotonicity of the optimal cost in the discrete time regulator problem and schur complements this paper deals with the monotonicity of the optimal rather than the more usual stabilising cost of the discrete time regulator problem the approach relies on a monotonicity result on riccati operators and on a formula for the difference of schur complements

existence uniqueness and stability of solutions to singular linear quadratic optimal control problems we consider general continuous and discrete time linear quadratic optimal control problems where the dynamics of the system is a linear differential or difference algebraic equation with constant coefficient matrices and the cost functionals are defined by infinite integrals or sums these problems occur in numerous applications in many different fields such as economics operations research electrical engineering model and system design biology and chemistry since they form two of the simplest optimal control problems and they are also used as linear approximations for many nonlinear problems which are much harder to solve we extend some of the known results to these general problems

closed form solutions to a class of h optimization problems a closed form solution is presented to the h sub optimal control problem via state or output feedback the problem formulation is general and does not impose any restrictions on feedthrough terms between the control input and the controlled output or between the disturbance input and the measurement output variables it is however required that both the transfer function from the disturbance input to the measurement output and the transfer function from the control input to the controlled output have no invariant zeros on the jw axis and that they satisfy certain geometric conditions for the same class of systems the conditions under which the h optimal control problem via state feedback has a solution are given moreover explicit expressions for the optimal solutions are provided finally the pole zero cancellations in the closed loop system resulting from the h optimal or sub optimal state or output feedback are examined

receding horizon recursive state estimation describes a receding horizon discrete time state observer using the deterministic least squares framework the state estimation horizon which determines the number of past measurement samples used to reconstruct the state vector is introduced as a tuning parameter for the proposed state observer a stability result concerning the choice of the state estimation horizon is established it is also shown that the fixed memory receding horizon state observer can be related to the standard dynamic observer by using an appropriate end point state weighting on the estimator cost function

state feedback h optimal control problems for non detectable systems abstract this paper considers an h optimal control problem via state feedback with special emphasis on non detectable systems the solution to this problem involves iteratively solving one algebraic riccati equation the results completely solve the state feedback h control problems for non detectable systems and they have been derived under relatively weaker assumptions similar to those needed for lqg optimal control

continuous and discrete time riccati theory a popov function approach abstract necessary and sufficient conditions for the existence of the stabilizing solution of the algebraic riccati equation are derived for both the continuous and the discrete time case under the weakest possible assumptions imposed on the initial data both frequency domain conditions involving an associated popov function and time domain conditions involving an associated matrix pencil are investigated

lmi based minimax estimation and filtering under unknown covariances in this paper we consider a minimax approach to the estimation and filtering problems in the stochastic framework where covariances of the random factors are completely unknown the term random factors refers either to unknown parameters and measurement noise in the estimation problem or to disturbance process and the initial state of a linear discrete time dynamic system in the filtering problem we introduce a notion of the attenuation level of random factors as a performance measure for both a linear unbiased estimate and a filter this is the worst case variance of the estimation error normalised by the sum of variances of all random factors over all nonzero covariance matrices it is shown that this performance measure is equal to the spectral norm of the transfer matrix and therefore the minimax estimate and filter can be computed in terms of linear matrix inequalities lmis moreover the explicit formulae for both the minimax estimate and the minimal value of the attenuation level are prese

exact computation of infimum for a class of continuous time h optimal control problem with a nonzero direct feedthrough term from the disturbance input to the controlled output a noniterative method for the computation of infimum for a class of continuous time h optimal control problem is considered in this paper the problem formulation is fairly general and does not place any restrictions on any direct feedthrough terms of the given systems the method is applicable to systems where i the transfer function from the disturbance input to the measurement output is free of imaginary axis invariant zeros and left invertible and ii the transfer function from the control input to the controlled output of the given system is free of imaginary axis invariant zeros and right invertible the result presented in this paper is a continuation of the previous work of the author and his co workers chen et al 1992 in which the direct feedthrough term from the disturbance input to the measurement output of the given system are required to be zero

on the approximate solution of a mathematical model of a viscoelastic bar abstract the mathematical model expressing the shock between a solid body and a linear viscoelastic bar is considered within the framework of the mikusinski calculus the existence of the solution of the corresponding problem in the field of mikusinski operators is proved moreover an approximate solution of the corresponding problem is constructed and the error of approximation is estimated

a note on the maximal solution of the periodic riccati equation the periodic symmetric solutions of the periodic riccati differential equation associated with the filtering problem are considered by the authors it is proven that under the sole assumption of detectability there exists a maximal solution moreover such a solution turns out to be strong i e the characteristic multipliers of the associated closed loop system belong to the closed unit disk the proof relies on an iterative linearization technique which calls for a sequence of periodic lyapunov equations similar results are given for the minimal solution

difference and differential riccati equations a note on the convergence to the strong solution the convergence of the solutions of the differential difference riccati equations to the strong solution of the corresponding algebraic riccati equation are is addressed detectability only is required in the analysis and no assumption is made on the eigenvalues on the real imaginary axis on the unit circle in the discrete time case in particular from the results it follows that under the sole assumption of detectability a positive definite initial condition guarantees convergence to the strong solution even in the presence of unreachable eigenvalues on the imaginary axis or on the unit circle

on a shock problem involving a linear viscoelastic bar abstract the paper deals with the initial boundary value problem for the linear wave equation 1 u tt t u xx ku u t f x t 0 x 1 0 t t u 0 t 0 t u x 1 t q t u x 0 u 0 x u t x 0 u 1 x where k are given constants and u 0 u 1 f are given functions the unknown function u x t and the unknown boundary value q t satisfy the following linear integral equation 2 q t k 1 t u 1 t 1 t u t 1 t g t 0 t k t s u 1 s d s where g k k 1 1 are given functions the paper consists of four parts in part 1 we prove a theorem of global existence and uniqueness of a weak solution u q of problem 1 2 the proof is based on a galerkin type approximation associated to various energy estimates type bounds weak convergence and compactness arguments in part 2 it is devoted to the study of the regularity of the solution u q with respect to the functions 1 f g k k 1 in part 3 we prove that the solution u q of this problem is stable with respect to the data k 1 f g k k 1 finally in part 4 we obtain an asymptotic expansion of the solution u q of this problem up to order n 1 in k for k sufficiently small

global existence and stability for wave equation of kirchhoff type with memory condition at the boundary abstract we consider a nonlinear wave equation of kirchhoff type with memory condition at the boundary and we study the asymptotic behavior of the corresponding solutions we proved that the energy decay with the same rate of decay of the relaxation function that is the energy decays exponentially when the relaxation function decay exponentially and polynomially when the relaxation function decay polynomially

singular riccati equations stabilizing large scale systems in this paper we discuss the convergence of a stabilization algorithm based on a singular version of the discrete riccati difference equation this method is particularly appealing for large scale linear time invariant dynamical systems since one can nicely exploit the sparsity of such systems in order to reduce the complexity of the algorithm

mean square stabilizing solutions for discrete time coupled algebraic riccati equations in this paper we present new sufficient conditions for the existence of a mean square stabilizing solution for a set of coupled algebraic riccati equations which arises from the study of quadratic optimal control of discrete time linear systems with markov switching parameters the conditions are derived under the assumptions of mean square stabilizability and on the unobservable modes of the system and compared with existing results

direct computation of infimum in discrete time h optimization using measurement feedback a direct and non iterative method for the computation of the infimum for a class of discrete time h optimal control problem is considered in this paper the problem formulation is fairly general and does not place any restrictions on any direct feedthrough terms of the given systems the method is applicable to systems where i the transfer function from the disturbance input to the measurement output is free of unit circle invariant zeros and left invertible and ii the transfer function from the control input to the controlled output of the given system is free of the unit circle invariant zeros and right invertible

deadbeat control and tracking of discrete time systems a new approach for forcing the state of a linear discrete time system to zero in a minimum number of steps is discussed the problem is formulated as the solution to a steady state optimal control problem with no cost on the control this problem in turn is set up as the solution to an associated eigenvalue problem no special assumption on the open loop system matrix and or the ratio of the number of states to controls is required stable numerical techniques are presented for solving for the feedback gain robust deadbeat tracking is also discussed

comments on existence conditions of positive definite solutions for algebraic matrix riccati equations abstract it is pointed out that the main results in a recent paper by kano 1987 have previously been published in the literature

existence of positive definite and semidefinite solutions of discrete time algebraic riccati equations the discrete time algebraic riccati equation is studied necessary and sufficient conditions for the existence of positive definite and positive semidefinite solutions are given

existence of unmixed solutions of the discrete time algebraic riccati equation and a nonstrictly bounded real lemma abstract the existence of a solution of the discrete time algebraic riccati equation is established assuming modulus controllability and positive semidefiniteness on the unit circle of the popov function as an application a nonstrictly bounded real lemma is obtained

on fuzzy convexity and parametric fuzzy optimization abstract in this paper some different types of convexity and generalized convexity of fuzzy sets are defined and their properties are studied a general fuzzy nonlinear programming problem is formulated with application of the concept of convexity

periodic strong solution for the optimal filtering problem of linear discrete time periodic systems the periodic riccati difference equation prde for the optimal filtering problem of linear periodic discrete time systems is addressed specifically the author provides a number of results on the existence uniqueness and stability properties of symmetric periodic nonnegative definite solutions of the periodic riccati difference equation in the case of nonreversible and nonstabilizable periodic systems the convergence of symmetric periodic nonnegative definite solutions of the periodic riccati difference equation is also analyzed the results have been established under weaker assumptions and include both necessary and sufficient conditions the existence and properties of symmetric periodic nonnegative definite solutions of the prde are established directly from the prde

nonnegative solutions of algebraic riccati equations abstract nonnegative hermitian solutions of various types of continuous and discrete algebraic riccati equations are studied the hamiltonian is considered with respect to two different indefinite scalar products for the set of nonnegative solutions the order structure and the topology of the set and the stability of solutions is treated for general hermitian solutions a method to compute the inertia is given although most attention is payed to the classical types arising from lq optimal control theory the case where the quadratic term has an indefinite coefficient is studied as well

a semilinear wave equation with space time dependent coefficients and a memory boundarylike antiperiodic condition regularity and stability this paper deals with regularity and stability of solutions to an initial boundary value problem of a semilinear wave equation this equation admits space time dependent coefficients and a memory boundarylike antiperiodic condition for regularity or existence of a unique strong solution the faedo galerkin method and the energy method associated with the maximal solution of a nonlinear volterra integral equation are applied then as an application of the regularity result stability of this unique strong solution is obtained by the energy method

stability of a random riccati equation with markovian binary switching this paper is concerned with the boundedness of the solution of a random riccati difference equation arising from kalman filtering with observation losses characterized by a markovian binary jump parameter a new sufficient condition for stability in the peak covariance sense is obtained which has a simpler form and is shown to be less conservative for systems with the observability index of two than existing works meanwhile we give some conditions under which the covariance matrix is bounded or unbounded in the usual sense then the equivalence between the peak covariance stability and the usual covariance stability is established for systems with the observability index of one and independent and identically distributed i i d observation losses

computationally efficient optimal output decentralized estimation this paper presents decentralized computational architectures for the optimal state estimation in stochastic large scale linear systems the main feature of the proposed architectures lies on elaborating each subsystem s decision not only by processing its own local data but also by adjusting this decision with all other related subsystem s local data this adjustment procedure ensures the optimality of the decentralized filter it is emphasized that the kalman filter algorithm operates more efficiently when measurements are processed into low order subsets especially when they are processed one at a time thus using this feature in a decentralized scheme significantly increases computational savings and numerical stability architectures presented in this paper for the mechanization of decentralized estimators allow a high degree of parallelism and can be implemented on a wide range of computer networks

on the optimal unbiased functional filtering presents a simple solution to the optimal unbiased reduced order or functional filtering problem for linear time varying systems necessary and sufficient conditions for the existence of the obtained filter are given stability and convergence conditions are developed for the time invariant systems both continuous and discrete time cases are considered

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

h sub infinity optimal one step ahead output feedback control of discrete time systems the discrete time one step ahead standard four blocks h sub infinity optimal control problem is considered the output feedback problem is transformed into a one step ahead h sub infinity optimal state estimation problem and the existing solution is used to derive the controller it is assumed that only previous measurements are available for control two results are obtained the first requires the solutions of two coupled riccati equations where the necessary and sufficient condition for the existence of the h sub infinity optimal result requires only the positive semidefiniteness of these solutions the second result applies two decoupled riccati equations with a coupling constraint as in the continuous time case and two additional conditions the derivation procedure is most simple and may thus provide considerable insight into the solution of the discrete time standard problem a similar procedure can also be used to obtain a solution to problems where the current measurement is available

an exact multivariate model based structural decomposition we propose a simple and structured procedure for decomposing a vector of time series into trend cycle seasonal and irregular components contrary to common practice we do not assume these components to be orthogonal conditional on their past however the state space representation employed ensures that their estimates converge to values with null variances and covariances null variances are very important as they ensure that the components do not change when the sample increases this lack of revisions is the most important feature of our method in comparison with most alternative procedures on the other hand null covariances provide a solid statistical foundation for the decomposition as it ensures that a given component can be analyzed and interpreted independently of any other component s other convenient properties of our method derive from the use of a state space approach first defining the problem in state space avoids dependence on particular model specifications so the same proc

on the solution of discrete time markovian jump linear quadratic control problems abstract a necessary and sufficient condition for the existence of a positive semidefinite solution of the coupled algebraic discrete time riccati like equation occurring in markovian jump control problems is derived by verifying a simple matrix inequality it is shown that such a solution exists and can be obtained as a limit of a monotonic sequence this leads to a straightforward numerical algorithm for the computation of the solution an example is given to illustrate the proposed method

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

hermitian solutions of the discrete time algebraic riccati equation this paper deals with the existence and uniqueness of unmixed solutions of the discrete time algebraic riccati equation dare sets of solutions of the dare are parametrized by invariant subspaces of the state transition matrix

monotonicity and stabilizability properties of solutions of the riccati difference equation propositions lemmas theorems fallacious conjectures and counterexamples abstract the problem considered is that of selecting an initial covariance matrix for the kalman filter to ensure that the closed loop filter at every subsequent time instant is exponentially asymptotically stable as a time invariant filter sufficient conditions are derived based on monotonicity properties of the solution of the riccati difference equation the results have application in observer design and the cases of filtering for nonstabilizable systems and systems with singular system matrices are included

convex fuzzy mappings abstract in this note the concept of convexity and logarithmic convexity for fuzzy mappings are introduced and some applications to optimization are discussed

necessary and sufficient conditions for fuzzy optimality problems in this paper we define a new minimum concept for fuzzy optimization problems more general than those that exist in the literature we find necessary optimality conditions based on a new fuzzy stationary point definition and we prove that these conditions are also sufficient under new fuzzy generalized convexity notions