decentralized finite time h filtering for interconnected markovian jump system with interval mode dependent delays this paper concerns with the problem of finite time h filtering for a class of interconnected markovian jump system with mode dependent delays in the interconnection sufficient conditions guaranteeing the interconnected markovian jump systems to be finite time bounded are established by constructing an augmented lyapunov krasovskii functional the obtained conditions are delay range dependent and mode dependent based on the results the decentralized filter is proposed to guarantee the finite time bounded and h performance of the resulting augmented system for admissible disturbances the desired filter parameters can be obtained via solving a group of linear matrix inequalities lmis finally a numerical example is employed to illustrate the effectiveness of the proposed methods

essential pseudospectra and essential norms of band dominated operators abstract an operator a on an l p space is called band dominated if it can be approximated in the operator norm by operators with a banded matrix representation the coset of a in the calkin algebra determines for example the fredholmness of a the fredholm index the essential spectrum the essential norm and the so called essential pseudospectrum of a this coset can be identified with the collection of all so called limit operators of a it is known that this identification preserves invertibility hence spectra we now show that it also preserves norms and in particular resolvent norms hence pseudospectra in fact we work with a generalization of the ideal of compact operators so called p compact operators allowing for a more flexible framework that naturally extends to l p spaces with p 1 and or vector valued l p spaces

brief estimation and detection of unknown inputs using optimal fir filter the optimal finite impulse response fir filter is applied to systems with both unknown inputs and noise in order to obtain noise suppressed estimates of the unknown inputs the unknown inputs are modeled as random walk processes and estimated together with the state using the optimal fir filtering algorithm the estimate for each unknown input is shown to be independent of the window initial state and also of other unknown inputs a detection scheme for an unknown input is developed utilizing a test variable independently of other unknown inputs finally numerical examples are given to show the performance of the proposed estimation and detection method

parity equations based unknown input reconstruction for mimo stochastic systems with an application in this paper an approach for reconstructing an unknown input for multiple input multiple output systems is presented it is assumed that the system is affected by process noise whereas the available system inputs are contaminated by measurement noise the novel approach is based on a parity equations concept and forms an extension of the idea developed previously by the authors a modification of the algorithm is also provided which allows the approach to deal with systems whose zero is close to unity the order of the parity space can be treated as a tuning parameter allowing for a trade off between the smoothness of the reconstructed unknown input and a phase lag an analytical solution of the overall problem is obtained by making use of a lagrange multiplier method the utility of the scheme is demonstrated when applied to a practical hydrological system

fuzzy closure spaces abstract fuzzy topological spaces do not constitute a natural boundary for the validity of theorems but many results can be extended to what are called fuzzy closure spaces or fcs s for short the notions of a subspace a sum and a product are extended to fcs s the hereditary additivity and productivity behaviour of compactness in fcs s is investigated and some weak forms of compactness and fuzzy continuous functions in fcs s are introduced the interaction between fuzzy proximity spaces and fcs s is investigated a necessary background is included for completeness

unbiased h filtering for neutral markov jump systems abstract the unbiased h filtering problem is studied for stochastic markov jump system with constant and neutral time delays by re constructing the system the dynamic filtering error characteristics of unknown inputs and time delays are obtained a sufficient condition is initially established on the existence of mode dependent unbiased h filter of constant time delay system using stochastic lyapunov krasovskii function then the unbiased h filter is also designed for the jump system with constant and neutral time delays the design criterions are presented in the form of linear matrix inequality finally the unbiased h filtering problems are described as optimization algorithms numerical examples illustrate the effectiveness of the developed techniques

some additive l fuzzy topological properties abstract the notion of sum for crisp topological spaces have extended to fuzzy topology by ghanim et al 1984 the concept of sum of l fuzzy topological spaces is introduced and its basic properties are discussed by the author 1993 in this paper the additivity of three kinds of l fuzzy topological properties strong separation properties countability and weakly n compactness are studied

limit operators compactness and essential spectra on bounded symmetric domains abstract this paper is a follow up to a recent article about the essential spectrum of toeplitz operators acting on the bergman space over the unit ball as mentioned in the said article some of the arguments can be carried over to the case of bounded symmetric domains and some cannot the aim of this paper is to close the gaps to obtain comparable results for general bounded symmetric domains in particular we show that a toeplitz operator on the bergman space a p is fredholm if and only if all of its limit operators are invertible even more generally we show that this is in fact true for all band dominated operators an algebra that contains the toeplitz algebra moreover we characterize compactness and explain how the berezin transform comes into play in particular we show that a bounded linear operator is compact if and only if it is band dominated and its berezin transform vanishes at the boundary for p 2 band dominated can be replaced by contained in the toeplitz algebra

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

quasi banded operators convolutions with almost periodic or quasi continuous data and their approximations abstract we study the stability and fredholm property of the finite sections of quasi banded operators acting on l p spaces over the real line this family is significantly larger than the set of band dominated operators but still permits to derive criteria for the stability and results on the splitting property as well as an index formula in the form as it is known for the classical cases in particular this class covers convolution type operators with semi almost periodic and quasi continuous symbols and operators of multiplication by slowly oscillating almost periodic or even more general coefficients

topological modification of a fuzzy closure space abstract fuzzy topological spaces do not constitute a natural boundary for the validity of theorems and many results can be extended to what are called fuzzy closure spaces fuzzy closure spaces have been introduced in 6 as a generalization of closure spaces 1 in the present paper we introduce the concept of topological modification of a fuzzy closure operator we prove that the topological modification of a fuzzy closure operator u on x is the finest topological fuzzy closure operator on x coarser than u the interaction between the concepts of a subspace and the topological modification of a fuzzy closure operator is also examined

some strong separation in fuzzy topological spaces abstract recently macho stadler et al fuzzy sets and systems 43 1991 95 116 introduced the notion of fuzzy separation using the family of its level topologies lt t t i1 the present work deals with introducing and studying the operations on ri fuzzy topological spaces i 0 1 moreover the notion of fuzzy separation which is well defined as a fuzzy topological concept is described a comparison between the above notions with the analogous fuzzy ones are discussed an acceptable clue which indicates that these notions are equivalent is offered

sums of l fuzzy topological spaces it follows from l ftop being topological over set that there is l fuzzy topological sum in l ftop in this paper we use the final topologies constructed in section 3 of rodabaugh powerset operator foundations of variable basis fuzzy topology in u hohle s e rodabaugh eds mathematics of fuzzy sets logic topology and measure theory the handbooks of fuzzy sets series vol 3 kluwer academic publishers boston dordrecht london 1999 pp 91 116 to characterize l fuzzy topological sum internally and establish connections between l fuzzy topological sum and its factor spaces we create a functor w from l fys the category of l fuzzifying topological space to l ftop and show that w has a right adjoint hence there exists an adjunction from l fys to l ftop moreover w preserves l fuzzy topological sums that already exists in both l fys and l ftop finally we examine certain additivity property of l fuzzy topological spaces these results imply that the topological sum in l ftop a necessary consequence of l ftop being a topological construct is now better understood

a quasi local characterisation of lp roe algebras abstract very recently spakula and tikuisis provide a new characterisation of uniform roe algebras via quasi locality when the underlying metric spaces have straight finite decomposition complexity in this paper we improve their method to deal with the l p version of uniform roe algebras for any p 1 due to the lack of reflexivity on l 1 spaces some extra work is required for the case of p 1

regularly open sets in fuzzy topological spaces abstract this paper is devoted to the study of the role of fuzzy regularly open sets we prove some properties of fuzzy almost continuous mappings and define fuzzy almost open mappings we prove that under a fuzzy almost continuous and fuzzy almost open map the inverse image of a fuzzy regularly open set is fuzzy regularly open further we define a new type of fuzzy separation axioms fuzzy almost separation axioms it is interesting that there are some deviations in the behaviour of these axioms as compared to those in general topology for example in a fuzzy almost t1 space not every fuzzy singleton is closed also a fuzzy space which is fuzzy almost t 2 1 2 as well as fuzzy almost t0 is fuzzy almost regular while in general topology we have to take an almost t2 space in place of almost t0 space

a kalman filtering derivation of simultaneous input and state estimation abstract simultaneous input and state estimation algorithms are studied as particular limits of kalman filtering problems this admits interpretation of the algorithm properties and critical analysis of their claims to being partly model free and to providing unbiased estimates a disturbance model white noise of unbounded variance is provided and the bias feature is shown to be a geometric projection property rather than probabilistic in nature as a consequence of this analysis the algorithm is connected in the stationary case to algebraic riccati equation computations for the gains estimate covariances and filter frequency response

brief paper unbiased minimum variance state estimation for linear systems with unknown input the problem of state estimation for a linear system with unknown input which affects both the system and the output is discussed in this paper a recursive optimal filter with global optimality in the sense of unbiased minimum variance over all linear unbiased estimators is provided the necessary and sufficient condition for the convergence and stability is also given which is milder than existing approaches

an affirmative answer to a core issue on limit operators abstract an operator on an l p space is called band dominated if it can be approximated in the operator norm by operators with a banded matrix representation it is known that a rich band dominated operator is p fredholm which is a generalization of the classical fredholm property if and only if all of its so called limit operators are invertible and their inverses are uniformly bounded we show that the condition on uniform boundedness is redundant in this statement

semi induced fuzzy topologies abstract induced fuzzy topologies were first introduced by wong 15 and weiss 14 they were studied by lowen who called them topologically generated fuzzy topologies 7 an induced fuzzy topology includes its modification topology we generalize induced fuzzy topologies to semi induced fuzzy topologies viz those which include their modification topologies the yet more general fuzzy topologies of structure c are also introduced the fully stratified fuzzy topological spaces of structure c are precisely the fuzzy neighbourhood spaces of lowen 4 in subsequent papers this relationship will be established and benefited from the two axioms of semi induction and structure c hold trivially for crisp fuzzy topologies we call such axioms fuzzy structural axioms in fuzzy topology in this paper we analyze the axioms of structure c semi induction and induction in this context we show how these axioms are linked to the three structural asioms of structures a b and d introduced by us in 11 the basic notions and results pertaining to structures a b and d are compiled in the first section the behaviour of warren s fuzzy boundary in semi induced fuzzy topological spaces fts s for short is also explained

simultaneous input and state estimation for nonlinear systems with applications to flow field estimation this paper studies the problem of simultaneous input and state estimation sise for nonlinear dynamical systems with and without direct input output feedthrough we take a bayesian perspective to develop a sequential joint input and state estimation approach our scheme gives rise to a nonlinear maximum a posteriori optimization problem which we solve using the classical gauss newton method the proposed approach generalizes a number of sise methods presented in the literature we illustrate the effectiveness of the proposed scheme for nonlinear systems with direct feedthrough in an oceanographic flow field estimation problem involving submersible drogues that measure position intermittently and acceleration continuously

semi open sets and semi continuity in fuzzy bitopological spaces abstract in this paper the concepts of fuzzy semi open sets and fuzzy semi continuous mappings due to azad 1981 have been generalized to fuzzy bitopological spaces and some of their properties are studied

technical communique on the asymptotic stability of minimum variance unbiased input and state estimation in this note we investigate the asymptotic stability of the filter for minimum variance unbiased input and state estimation developed by gillijns and de moor sufficient conditions for the stability are proposed and proven with inspiration from the kalman filter stability analysis

optimal filtering for systems with unknown inputs an optimal filtering formula is derived for linear time varying discrete systems with unknown inputs by making use of the well known innovations filtering technique the derivation is an extension of a new observer design method for time invariant deterministic systems with unknown inputs the systems under consideration have the most general form the derived optimal filter has a similar form to the standard kalman filter with some modified covariance and gain matrices

state estimation for descriptor systems via the unknown input filtering method this paper addresses the optimal unbiased minimum variance state estimation of descriptor systems in the framework of unknown input filtering it is shown that any descriptor system can be equivalently transformed into a standard state space system with unknown inputs the existing globally optimal state estimators can then be readily used to facilitate the optimal filter design this research highlights the relationship between descriptor state estimation and unknown input filtering for standard state space systems with unknown inputs a direct application to the state estimation of descriptor systems with unknown inputs via the proposed results is also addressed an illustrative example is given to show the novelty of the proposed results

on smooth topological spaces ii separation axioms in the present paper we introduce the notions of smooth separation axioms in several ways and investigate some of their properties and the relations between them in the general framework of smooth topological spaces

fuzzy alpha sets and alpha continuous maps abstract in this paper we generalize the notion of sets to fuzzy spaces we also introduce the concepts of fuzzy continuous and fuzzy open mappings and discuss their relations with fuzzy continuous and other weaker forms of fuzzy continuous mappings counterexamples are given to show the non coincidence of these mappings

almost compactness and near compactness in smooth topological spaces abstract this paper discusses almost compactness in fuzzy topology and we introduce near compactness for fuzzy topological spaces we give some characterizations of almost compactness in terms of regular open or regular closed fuzzy sets we show that the weakly continuous image of a compact fuzzy topological space is almost compact and that the fuzzy strongly continuous image of an almost compact fuzzy topological space is compact moreover nearly compact fuzzy topological spaces are defined and we characterize near compactness we show that the almost continuous and almost open image of a nearly compact space is nearly compact

discrete sets in fuzzy topological spaces abstract we introduce the notion of discrete set in fuzzy topological spaces and prove that a fuzzy hausdorif topological space x has an infinite discrete set if the set x is infinite

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

fuzzy preopen sets and fuzzy preseparation axioms abstract in this paper the concept of preopen sets due to a s mashhour m e abd el monsef and s n el debb 7 has been generalised to the fuzzy setting further fuzzy separation axioms have been introduced and investigated with the help of fuzzy preopen sets

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

framework for state and unknown input estimation of linear time varying systems the design of unknown input decoupled observers and filters requires the assumption of an existence condition in the literature this paper addresses an unknown input filtering problem where the existence condition is not satisfied instead of designing a traditional unknown input decoupled filter a double model adaptive estimation approach is extended to solve the unknown input filtering problem it is proved that the state and the unknown inputs can be estimated and decoupled using the extended double model adaptive estimation approach without satisfying the existence condition numerical examples are presented in which the performance of the proposed approach is compared to methods from literature

simultaneous input and state estimation for stochastic nonlinear systems with additive unknown inputs abstract this paper investigates simultaneous input and state estimation for a class of nonlinear stochastic systems we propose a recursive filter to concurrently estimate system states and unknown inputs we show that the estimation errors of the proposed filter are practically exponentially stable in probability and the estimation error covariance matrices are uniformly bounded

a call for crispness in fuzzy set theory abstract this paper is a reflection of some rather negative experiences i have had during the preparation of lecture notes for a general course on fuzzy set theory the lack of standard definitions for fundamental concepts many fundamental concepts are not expanded fully enough and several proofs of important properties are incorrect

a unified filter for simultaneous input and state estimation of linear discrete time stochastic systems in this paper we present a unified optimal and exponentially stable filter for linear discrete time stochastic systems that simultaneously estimates the states and unknown inputs in an unbiased minimum variance sense without making any assumptions on the direct feedthrough matrix we also provide the connection between the stability of the estimator and a system property known as strong detectability and discuss the global optimality of the proposed filter finally an illustrative example is given to demonstrate the performance of the unified unbiased minimum variance filter

technical communique extension of unbiased minimum variance input and state estimation for systems with unknown inputs this paper extends the existing results on joint input and state estimation to systems with arbitrary unknown inputs the objective is to derive an optimal filter in the general case where not only unknown inputs affect both the system state and the output but also the direct feedthrough matrix has arbitrary rank the paper extends both the results of gillijns and de moor gillijns s de moor b 2007b unbiased minimum variance input and state estimation for linear discrete time systems with direct feedthrough automatica 43 934 937 and darouach zasadzinski and boutayeb darouach m zasadzinski m boutayeb m 2003 extension of minimum variance estimation for systems with unknown inputs automatica 39 867 876 the resulting filter is an extension of the recursive three step filter ertsf and serves as a unified solution to the addressed unknown input filtering problem the relationship between the ertsf and the existing literature results is also addressed

optimal filtering for systems with unknown inputs via the descriptor kalman filtering method this paper addresses globally optimal unbiased minimum variance state estimation for systems with unknown inputs that affect both the system and the output with the descriptor kalman filtering method it is shown that directly applying the conventional descriptor kalman filter dkf to the considered problem may not yield the globally optimal solution because the unknown input vector may not be estimable to remedy this problem three approaches are proposed to facilitate optimal filter design the transformed approach uses some input and output transformations the untrammeled approach does not require any transformations and the augmented approach reconstructs the unknown input dynamics then three 5 block forms of the extended dkf 5 block edkf are derived as globally optimal state estimators in the sense that the first two filters are equivalent to the recently developed extended recursive three step filter and the third is equivalent to the conventional augmented state kalman filter the relationship between the proposed edkfs and the existing results in the literature is addressed simulation results are given to illustrate the usefulness of the proposed filters

smooth topological spaces abstract in 1986 badard introduced the concept of a smooth topological space in this paper we give some links between smooth topological spaces and the corresponding results in chang s fuzzy topological spaces the concepts of subspace continuity and compactness are studied

unbiased minimum variance linear state estimation abstract a method is developed for linear estimation in the presence of unknown or highly non gaussian system inputs the state update is determined so that it is unaffected by the unknown inputs the filter may not be globally optimum in the mean square error sense however it performs well when the unknown inputs take extreme or unexpected values in many geophysical and environmental applications it is performance during these periods which counts the most the application of the filter is illustrated in the real time estimation of mean areal precipitation

gain constrained kalman filtering for linear and nonlinear systems this paper considers the state estimation problem with a constraint on the data injection gain special cases of this problem include the enforcing of a linear equality constraint in the state vector the enforcing of unbiased estimation for systems with unknown inputs and simplification of the estimator structure for large scale systems both the one step gain constrained kalman predictor and the two step gain constrained kalman filter are presented the latter is extended to the nonlinear case yielding the gain constrained unscented kalman filter two illustrative examples are presented

a metric approach to limit operators we extend the limit operator machinery of rabinovich roch and silbermann from z n to bounded geometry strongly discrete metric spaces we do not assume the presence of any group structure or action on our metric spaces using this machinery and recent ideas of lindner and seidel we show that if a metric space x has yu s property a then a band dominated operator on x is fredholm if and only if all of its limit operators are invertible we also show that this always fails for metric spaces without property a

on fuzzy d continuity and a near compactness in fuzzy topological spaces abstract the concept of fuzzy continuity was introduced by saha 18 mashhour et al have introduced the concept of near compactness in fuzzy setting in this paper we give a characterization of fuzzy continuity and fuzzy nearly compactness also we investigate the image of fuzzy nearly compact spaces under some types of functions finally a refinement is made to some results in 15 17

fuzzy topological properties and hereditariness some known compactness notions and separation axioms already given in chang fuzzy topological spaces are extended to a more general context of categories where i topological spaces on arbitrary i sets are defined the invariance under morphisms in these categories and the usual hereditary conditions of the considered topological properties in such a context are investigated

fredholm theory for band dominated and related operators a survey abstract this paper presents the fredholm theory on l p spaces for band dominated operators and important subclasses such as operators in the wiener algebra it particularly closes several gaps in the previously known results for the case p and addresses the open questions raised by chandler wilde and lindner in s n chandler wilde m lindner limit operators collective compactness and the spectral theory of infinite matrices mem amer math soc 210 989 2011 the main tools are provided by the limit operator method and an algebraic framework for the description and adaption of fredholmness and convergence a comprehensive overview of this approach is given

epimorphisms in categories of separated fuzzy topological spaces abstract the categorical theory of closure operators is used to characterize the epimorphisms in certain categories of separated fuzzy topological spaces in the sense of lowen these include the 0 t 0 spaces of wuyts and lowen the ft s spaces of ghanim kerre and mashhour and the t 2 spaces of rodabaugh

kalman filter for discrete time stochastic linear systems subject to intermittent unknown inputs state estimation of stochastic discrete time linear systems subject to persistent unknown inputs has been widely studied but only few works have been dedicated to the case where unknown inputs may be simultaneously or sequentially active or inactive in this technical note a kalman filter approach is proposed for state estimation of systems with unknown intermittent inputs the design is based on the minimisation of the trace of the state estimation error covariance matrix under the constraint that the state estimation error is decoupled from the unknown inputs corrupting the system at the current time the necessary and sufficient stability conditions are established considering the upper bound of the prediction error covariance matrix

a note on some ft 2 concepts abstract in this note we study in particular the fuzzy hausdorffness concepts introduced by adnadjevic 1 ganguly and saha 4 and sarkar 17

a comparison of some ft 2 concepts abstract recently ghanim kerre and mashhour 2 have introduced and examined a fuzzy hausdorffness concept in this paper we compare it with some of the other existing concepts of fuzzy hausdorffness and note thereby that though it is a good extension of hausdorffness it is independent of several other fuzzy hausdorffness concepts currently in use

zero dimensional and strongly zero dimensional fuzzy topological spaces abstract concepts of zero dimensionality strong zero dimensionality and total disconnectedness are extended to fuzzy topological spaces their basic properties and interrelationships among them are studied a sum theorem for strongly zero dimensional fuzzy topological spaces is also obtained

technical communique unbiased minimum variance input and state estimation for linear discrete time systems with direct feedthrough this paper extends previous work on joint input and state estimation to systems with direct feedthrough of the unknown input to the output using linear minimum variance unbiased estimation a recursive filter is derived where the estimation of the state and the input are interconnected the derivation is based on the assumption that no prior knowledge about the dynamical evolution of the unknown input is available the resulting filter has the structure of the kalman filter except that the true value of the input is replaced by an optimal estimate

on lower separation axioms abstract in 3 mashhour et al introduced the concept of fuzzy disjointness two fuzzy sets a b in x are said to be fuzzy disjoint if a co b where co b is the complement of b using this concept they introduced fti separation axioms as a generalization for the basic separation axioms ti i 1 4 in 5 singal and rajvanshi used the concepts of regular open fuzzy sets 1 and fuzzy disjointness to introduce some fuzzy almost separation axioms which are stronger than those of mashhour unfortunately some results in 5 are incorrect in this paper we use the concept of the quasi coincident relation 4 to restate lower fuzzy separation axioms and give a corrected version for some definitions and results in 5

quasi locality and property a abstract let x be a metric space with bounded geometry p 0 1 and let e be a banach space the main result of this paper is that either if x has yu s property a and p 1 or without any condition on x when p 0 1 then quasi local operators on l p x e belong to the appropriate variant of the roe algebra of x this generalises the existing results of this type by lange and rabinovich engel tikuisis and the first author and li wang and the second author as consequences we obtain that uniform l p roe algebras of spaces with property a are closed under taking inverses and another condition characterising property a akin to the operator norm localisation for quasi local operators

regularity axioms in fuzzy topological spaces and fr i proximities abstract the purpose of this paper is to study the regularity axioms for the proximity notion in fuzzy topology we redefine the notion of cech proximity on i x which has been extended to fuzzy sets in 11 and we study the families m x c and m 1 x also we show that every fr i space can be derived from an r i proximity on i x and vice versa

connectedness and local connectedness in fuzzy topological spaces and heyting algebra valued sets abstract in this paper we introduce four notions of local connectedness in fuzzy topological spaces the question of these notions to be good extensions is discussed and their preservation under fuzzy quotients fuzzy sums and fuzzy products is investigated moreover we introduce the notion of quasi local connectedness which is a peculiarity of the fuzzy setting

brief paper on the global optimality of unbiased minimum variance state estimation for systems with unknown inputs in this paper a globally optimal filtering framework is developed for unbiased minimum variance state estimation for systems with unknown inputs that affect both the system state and the output the resulting optimal filters are globally optimal within the unbiased minimum variance filtering over all linear unbiased estimators globally optimal state estimators with or without output and or input transformations are derived through the global optimality evaluation of this research the performance degradation of the filter proposed by darouach zasadzinski and boutayeb darouach m zasadzinski m boutayeb m 2003 extension of minimum variance estimation for systems with unknown inputs automatica 39 867 876 is clearly illustrated and the global optimality of the filter proposed by gillijns and de moor gillijns s de moor b 2007b unbiased minimum variance input and state estimation for linear discrete time systems with direct feedthrough automatica 43 934 937 is further verified the relationship with the existing literature results is addressed a unified approach to design a specific globally optimal state estimator that is based on the desired form of the distribution matrix from the unknown input to the output is also presented a simulation example is given to illustrate the proposed results