on the observer design for descriptor systems for the descriptor system ex ax bu y cx du an observer of the order p rank e p sub 1 0

almost invariant subspaces an approach to high gain feedback design part ii almost conditionally invariant subspaces in part i of this paper almost controlled invariant subspaces were studied in this part we will consider their duals the almost conditionally invariant subspaces these concepts give immediately by dualization of the almost disturbance decoupling control by state feedback the solution of the almost disturbance decoupled estimation problem finally we consider the problem of approximate disturbance decoupling by measurement feedback and it is shown that this problem is solvable to any arbitrary degree of accuracy if and only if 1 almost disturbance decoupling by state feedback and 2 almost disturbance decoupled estimation of the to be controlled output are both possible

the henstock stieltjes integral for fuzzy number valued functions in this paper we firstly define and discuss the henstock stieltjes integral for fuzzy number valued functions which is an extension of the usual fuzzy riemann stieltjes integral in addition several necessary and sufficient conditions of the integrability for fuzzy number valued functions are given by means of the henstock stieltjes integral of real valued functions and henstock integral of fuzzy number valued functions secondly the continuity and the differentiability of the primitive for the fuzzy henstock stieltjes integral are discussed we find that there exists a fuzzy number valued function which is fuzzy henstock stieltjes integrable but whose primitive is not a differentiable almost everywhere thirdly we introduce some quadrature rules for the fuzzy henstock stieltjes integral by giving error bounds for the mappings of bounded variation and of lipschitz type we also consider the generalization of classical quadrature rules such as midpoint type trapezoidal and simpson s quadrature finally we propose the concept of weak equi integrability for sequences of fuzzy henstock stieltjes integrable functions under this concept we prove two convergence theorems for sequences of the fuzzy henstock stieltjes integrable functions at the same time the formula of integration by parts is also studied

development of fuzzy and control charts using α cuts statistical process control spc is an approach that uses statistical techniques to monitor the process shewhart introduced the control charts that are one of the most important techniques of quality control to detect if assignable causes exist the widely used control charts are and these are called traditional variable control charts in the traditional variable control charts center line upper control limit and lower control limit are represented by numeric values a process is either in control or out of control depending on numeric observation values for many problems control limits could not be so precise uncertainty comes from the measurement system including operators and gauges and environmental conditions in this context fuzzy set theory is a useful tool to handle this uncertainty numeric control limits can be transformed to fuzzy control limits by using membership functions if a sample mean is too close to the control limits and the used measurement system is not so sensitive the decision may be faulty fuzzy control limits provide a more accurate and flexible evaluation this study constructs the fuzzy and control charts with a cuts an application is presented for fuzzy control charts by using fuzzy and control charts the flexibility of traditional control limits is increased

the theoretical foundations of statistical learning theory based on fuzzy number samples statistical learning theory based on real valued random samples has been regarded as a better theory on statistical learning with small sample the key theorem of learning theory and bounds on the rate of convergence of learning processes are important theoretical foundations of statistical learning theory in this paper the theoretical foundations of the statistical learning theory based on fuzzy number samples are discussed the concepts of fuzzy expected risk functional fuzzy empirical risk functional and fuzzy empirical risk minimization principle are redefined the key theorem of learning theory based on fuzzy number samples is proved furthermore the bounds on the rate of convergence of learning processes based on fuzzy number samples are discussed

controllability observability and duality in singular systems the concepts of controllability and observability for systems of the form e dot x ax bu y cx e singular are considered a theory is presented which unifies the three main approaches to this topic already existing in the literature the development includes a generalization of the duality theorem from state space theory

λ statistical limit points of the sequences of fuzzy numbers aytar has introduced the concepts of statistical limit and cluster points of a sequence of fuzzy numbers based on the definitions given in fridy s study for sequences of real numbers in this paper we define l statistical limit and l statistical cluster points of sequences of fuzzy numbers and discuss the relations among the sets of ordinary limit points l statistical limit points and l statistical cluster points of sequences of fuzzy numbers

design of a class of luenberger observers for descriptor systems a new approach to the design of a class of luenberger observers for descriptor systems is presented the design is performed in a straightforward manner the conditions required in the design are given in terms of the original system matrices the relationship among these and other well known conditions is highlighted

some results related with statistical convergence and berezin symbols abstract the concept of discrete statistical abel convergence is introduced in terms of berezin symbols we present necessary and sufficient condition under which a series n 0 a n with bounded sequence a n n 0 of complex numbers is discrete statistically abel convergent by using concept of statistical convergence we also give slight strengthening of a result of gokhberg and krein on compact operators

on the ideal convergence of sequences of fuzzy numbers in this paper we introduce and study the concepts of i convergence i convergence and i cauchy sequence for sequences of fuzzy numbers where i denotes the ideal of subsets of n the set of positive integers

on matrix summability of spliced sequences and a density of points abstract for y r and a sequence x x n l we define the new notion of a density a y of indices of those x n s which are close to y where a is a non negative regular matrix we present connections between a densities a y of indices of x n and the a limit of x n our main result states that if the set of limit points of x n is countable and a y exists for any y r where a is a non negative regular matrix then lim n a x n y r a y y which presents a different view of osikiewicz theorem

geometric structure and feedback in singular systems the output nulling a e r b invariant subspaces are defined for singular systems rigorously justifying the name and demonstrating that special cases of these geometric objects are the familiar subspace of admissible conditions and the supremal a e r b invariant subspace a novel singular system structure algorithm is used to compute them by numerically efficient means their importance for describing the possible closed loop geometric structure in terms of the open loop geometric structure is shown an approach to spectrum assignment in singular systems that is based on a generalized lyapunov equation is introduced the equation is used to compute feedback gains to place poles and assign various closed loop invariant subspaces while guaranteeing closed loop regularity

statistical cluster and extreme limit points of sequences of fuzzy numbers in this paper we investigate the relations between statistical limit superior or statistical limit inferior and statistical cluster points of a statistically bounded sequence of fuzzy numbers and show that the set of statistical cluster points of a sequence of this type might be empty

observer design for descriptor systems two detectability notions are introduced for the most general class of linear descriptor systems necessary and sufficient conditions are derived for the detectabilities and for the existence of observers depending on existence conditions satisfied the observers can be either in the familiar luenberger form or in a generalized form i e in descriptor form as the original system itself is a unified procedure is provided for the design of observers in both forms

ideal convergence characterization of the completion of linear n normed spaces in this paper we give the completion of a linear n normed space in terms of ideal convergence by introducing the concept of a uniformly continuous n norm

the banach principle for ideal convergence in the classical and noncommutative context abstract versions of the banach principle for different types of convergence with respect to an ideal are established both in the commutative and noncommutative von neumann algebraic context

statistically monotonic and statistically bounded sequences of fuzzy numbers we introduce the statistical monotonicity and boundedness of a sequence of fuzzy numbers we also derive the analogue of monotone convergence theorem and prove the decomposition theorems for this type of sequences

a generalization of levy s concentration variance inequality sharp lower bounds are found for the concentration of a probability distribution as a function of the expectation of any given convex symmetric function in the case x x c 2 wherec is the expected value of the distribution these bounds yield the classical concentration variance inequality of levy an analogous sharp inequality is obtained in a similar linear search setting where a sharp lower bound for the concentration is found as a function of the maximum probability swept out from a fixed starting point by a path of given length

on the reduced order causal observer for generalized control systems abstract this paper considers the problem of a causal state observer for a square singular system necessary and sufficient conditions for solvability of the problem have been established the approach of this study leads to a new insight concerning synthesis of a causal observer and establishes new results with regard to the structure and the dimension of a reduced order observer for singular systems

addendum to statistically monotonic and statistically bounded sequences of fuzzy numbers informat sci 176 2006 734 744 abstract in this short note we state that one side of implication of the statistical monotone convergence theorem given in s aytar s pehlivan statistically monotonic and statistically bounded sequences of fuzzy numbers informat sci 176 2006 734 744 is incorrect and elaborate on this shortcoming

some properties of limit inferior and limit superior for sequences of fuzzy real numbers abstract the limit inferior and limit superior of a bounded sequence of fuzzy real numbers have been introduced by aytar et al 2008 1 in this paper we give a simplified expressions for limit inferior and limit superior the expressions is concise and convenient for use as a straightforward corollary of this expressions we can easily prove some properties of the limit inferior and limit superior

equi statistical σ convergence of positive linear operators in this paper we introduce the notion of equi statistical s convergence which is stronger than the uniform convergence in the ordinary sense statistical uniform convergence and statistical uniform s convergence then we also give its use in the korovkin type approximation theory we also compute the rate of equi statistical s convergence of a sequence of positive linear operators

differentials of fuzzy functions abstract in this paper the radstrom embedding theorem proc amer math soc 3 1952 165 is generalized and is used to define the concept of the differential of a fuzzy function

statistical limit points of sequences of fuzzy numbers in the current work we extend the concepts of statistical limit and cluster points of a sequence of fuzzy numbers corresponding to the definitions in proc am math soc 4 1993 1187 for the sequences of real numbers later we discuss the relations among sets of ordinary limit points statistical limit points and statistical cluster points of sequences of fuzzy numbers

the supremum and infimum of the set of fuzzy numbers and its application abstract in this paper we prove that the bounded set of fuzzy numbers must exist supremum and infimum and give the concrete representation of supremum and infimum as an application we obtain that the continuous fuzzy valued function on a closed interval exists supremum and infimum and give the precise representation we also show that the bounded fuzzy valued function on a closed interval can define the lower and upper sums and the lower and upper integrals of riemann and riemann stieltjes by the usual way

geometric design techniques for observers in singular systems abstract we present geometric design techniques for observer design in generalized state space or singular systems the unknown input conditioned invariant subspaces are defined for singular systems and are related to the solution of a generalized lyapunov equation the approach emphasizes solution procedures based on the lyapunov equation and a singular system structure algorithm this paper extends the singular system observer theory both by providing a geometric basis for it and showing the best that may be accomplished if the system is not observable

a tutorial on the geometric analysis of linear time invariant implicit systems abstract a background of recent work in nonregular and regular implicit systems of the form e x ax bu is provided then the output nulling unknown input and composite subspaces are defined for singular systems with recursions given for their computation inner subspaces that is those in the domain of e and a are distinguished from outer subspaces those in the codomain of e and a the notions of composite preimage and composite image are introduced the result is a framework that unifies some of the recent work in the geometric theory of implicit systems system properties are discussed for both regular and nonregular systems and duality is investigated

integral and ideals in riesz spaces a convergence in riesz spaces is given axiomatically a bochner type integral for riesz space valued functions is introduced and some vitali and lebesgue dominated convergence theorems are proved some properties and examples are investigated

l metric on the space of l fuzzy numbers abstract in this article a natural l topology is constructed on the set of l fuzzy numbers which is called the standard l topology it is proved that the standard l topology can be induced by an l metric the space of trapezoidal fuzzy numbers can be regarded as a subspace of the space of l fuzzy numbers an l metric on the set of trapezoidal fuzzy numbers is presented

a note on the sendograph metric of fuzzy numbers in this paper by studying the attainable properties of sendograph metric in fuzzy number space we generalize monotone convergence theorem and nested theorem of intervals from the space of real numbers to the space of fuzzy numbers

statistical cluster points and turnpike theorem in nonconvex problems in this paper we develop the method suggested by s pehlivan and m a mamedov statistical cluster points and turnpike submitted where it was proved that under some conditions optimal paths have the same unique stationary limit point stationary cluster point this notion was introduced by j a fridy 1993 proc amer math soc 118 1187 1192 and it turns out to be a very useful and interesting tool in turnpike theory the purpose of this paper is to avoid the convexity conditions here the turnpike theorem is proved under conditions that are quite different from those of pehlivan and mamedov and may be satisfied for the mappings with nonconvex images and for nonconcave functions in the definition of functionals

on λ statistical convergence of difference sequences of fuzzy numbers in this paper the concept of strongly d l p 2 cesaro summability of a sequence of fuzzy numbers is introduced also some inclusion relations between the set of strongly d l p 2 cesaro convergent and d l 2 statistically convergent sequences of fuzzy numbers are given

kalman filtering for general discrete time linear systems recursive state estimation problems for explicit and implicit time invariant linear systems both for systems with and without unknown inputs can be formulated as a single problem usually referred to as descriptor kalman filtering solutions to this problem have been proposed in the literature however these solutions either neglect possible contributions of future dynamics to the current estimate or make unnecessary assumptions on the structure of the system in this paper the authors propose a solution to this problem which leads to a constructive method lifting these unnecessary assumptions this method uses a generalization of the shuffle algorithm

on statistically convergent sequences of fuzzy numbers abstract in this paper we study some equivalent alternative conditions for a sequence of fuzzy numbers to be statistically cauchy

l fuzzy numbers and their properties in this paper the notions of l fuzzy convex sets and l fuzzy numbers are introduced where l is a completely distributive lattice the notions of 0 1 fuzzy convex sets and 0 1 fuzzy numbers are generalized furthermore their properties and characterizations are presented in terms of cut sets of l fuzzy sets

on the level convergence of a sequence of fuzzy numbers abstract in this paper we first give a simplified proof of the existence theorem of supremum and infimum in fuzzy number space e 1 established by wu and wu j math anal appl 210 1997 499 and improve the expressions of the supremum and infimum as a straightforward corollary of this result we obtain a necessary and sufficient condition under which for a bounded sequence of fuzzy numbers u n the pair of functions sup n u n and sup n u n can determine a fuzzy number secondly we give a necessary and sufficient condition for a sequence of fuzzy numbers u n to be levelwise convergent in e 1 and generalize some important theorems in real number spaces to fuzzy number spaces finally we prove the existence of supremum and infimum for the level continuous fuzzy valued function on a closed interval and give a necessary and sufficient condition under which its supremum and infimum can be attained

tauberian theorems via statistical convergence the concept of statistical convergence which is related to the usual concept of convergence in probability provides a regular summability method for abstract metric spaces by using probabilistic tools we provide some tauberian theorems which have best possible order tauberian conditions furthermore these methods can be used to unify and improve the classical pointwise tauberian theorems of summability theory for the random walk type methods as proved by bingham and hausdorff methods as proved by lorentz

i selection principles for sequences of functions abstract we generalize three classical selection principles arzela ascoli theorem mazurkiewicz s theorem and helly s theorem on the ideal convergence in particular we show that for every analytic p ideal i with the bw property and every f ideal i the following selection theorems hold if f n n is a sequence of uniformly bounded equicontinuous functions on 0 1 then there exists a i such that f n n a is uniformly convergent if f n n is a sequence of uniformly bounded continuous functions then there exists a perfect set p and a set a i such that f n p n a is pointwise convergent if f n n is a sequence of uniformly bounded monotone functions then there exists a set a i such that f n n a is pointwise convergent

on the computation of the fundamental subspaces for descriptor systems abstractin this paper we investigate several theoretical and computational aspects of fundamental subspaces for linear time invariant descriptor systems which appear in the solution of many control and estimation problems different types of reachability and controllability for descriptor systems are described and discussed the rosenbrock system matrix pencil is employed for the computation of supremal output nulling subspaces and supremal output nulling reachability subspaces for descriptor systems

robust eigenvalue assignment for generalized systems abstract in this paper we examine the problem of robust pole placement using state feedback in generalized systems we develop a robustness theory for the finite generalized spectrum of the system as a partial problem and for the infinite pole placement problem as a second partial problem where perfect conditioning is always achievable we also give bounds between the complete closed loop robust eigenvalue problem and the two partial ones the basic tool that is exploited in the presented theory is the concept of chordal metric in this paper we take advantage of this notion and present a compact theory for the robust eigenvalue assignment problem in generalized systems the proposed theory is easy to implement retrieves the results for the state variable case as a special case and takes advantage of well known computational results

vitali type theorems for filter convergence related to vector lattice valued modulars and applications to stochastic processes a vitali type theorem for vector lattice valued modulars with respect to filter convergence is proved some applications are given to modular convergence theorems for moment operators in the vector lattice setting and also for the brownian motion and related stochastic processes

a reduced order observer for descriptor systems abstract in this paper a reducer order observer is analyzed for so called generalized state space or descriptor systems based on the staircase form for generalized state space models a recursive algorithm is presented to construct a reduced order observer for a given observable descriptor system in the algorithm only the eigenfrequencies of the observer have to be specified

fuzzifying ideal convergence in fuzzifying topological linear spaces in this study we propose a framework for fuzzifying ideal convergence in fuzzifying topological linear spaces after defining fuzzifying ideal convergence we discuss many properties of fuzzifying ideal convergence in fuzzifying topological linear spaces we also introduce a stronger convergence than fuzzifying ideal convergence and a sufficient condition called ap fuzzifying condition under which fuzzifying ideal convergence implies the stronger convergence above is proved

the equivalence of convergences of sequences of fuzzy numbers and its applications to the characterization of compact sets in this paper with the help of the convergence of sequences of fuzzy numbers with respect to the lebesgue measure we study the relationship between convergences of sequences of fuzzy numbers with respect to the endograph metric the sendograph metric and the l p metric we prove that these convergences are equivalent under proper conditions in addition by applying our result we give a new characterization of compact sets in fuzzy number space with the sendograph metric

a characterization of banach spaces with separable duals via weak statistical convergence abstract let b be a banach space a b valued sequence xk is weakly statistically null provided lim n 1 n k n f x k e 0 for all e 0 and every continuous linear functional f on b a banach space is finite dimensional if and only if every weakly statistically null b valued sequence has a bounded subsequence if b is separable b is separable if and only if every bounded weakly statistically null b valued sequence contains a large weakly null sequence a characterization of spaces containing an isomorphic copy of l1 is given and it is also shown that l2 has a statistical m basis which is not a schauder basis

ideal invariant injections abstract for an ideal i on we introduce the notions of i invariant and bi i invariant injections from to we study injections that are invariant with respect to selected classes of ideals we show some applications to ideal convergence

statistical convergence and ideal convergence for sequences of functions abstract let i p n stand for an ideal containing finite sets we discuss various kinds of statistical convergence and i convergence for sequences of functions with values in r or in a metric space for real valued measurable functions defined on a measure space x m we obtain a statistical version of the egorov theorem when x we show that in its assertion equi statistical convergence on a big set cannot be replaced by uniform statistical convergence also we consider statistical convergence in measure and i convergence in measure with some consequences of the riesz theorem we prove that outer and inner statistical convergences in measure for sequences of measurable functions are equivalent if the measure is finite

statistical limit inferior and limit superior for sequences of fuzzy numbers in this paper we extend the concepts of statistical limit superior and limit inferior as introduced by fridy and orhan statistical limit superior and limit inferior proc amer math soc 125 12 1997 3625 3631 12 to statistically bounded sequences of fuzzy numbers and give some fuzzy analogues of properties of statistical limit superior and limit inferior for sequences of real numbers

a measure theoretical subsequence characterization of statistical convergence the concept of statistical convergence of a sequence was first introduced by h fast statistical convergence was generalized by r c buck and studied by other authors using a regular nonnegative summability matrix a in place of c1 the main result in this paper is a theorem that gives meaning to the statement s s converges to l statistically t if and only if most of the subsequences of s converge in the ordinary sense to l here t is a regular nonnegative and triangular matrix corresponding results for lacunary statistical convergence recently defined and studied by j a fridy and c orhan are also presented introduction the concept of the statistical convergence of a sequence of reals s sn was first introduced by h fast 9 the sequence s sn is said to converge statistically to l and we write lim s l stat if for every e n oo rim n k e1 0 where jai denotes the cardinality of the set a properties of statistically convergent sequences were studied in 5 6 12 and 16 in 13 fridy and miller gave a characterization of statistical convergence for bounded sequences using a family of matrix summability methods statistical convergence can be generalized by using a regular nonnegative summability matrix a in place of c this idea was first mentioned by r c buck 3 in 1953 and has been further studied by sember and freedman 10 and 11 and connor 5 and 7 regular nonnegative summability matrices turn out to be too general for our purposes here instead we use the concept of a mean a matrix t amn will be called a mean if amn 0 when n m e iamn 1 for all m and limm 0oam 0 for each n if t amn is a mean following buck a sequence s sn is said to be statistically t summable to l and we write sn l stat t if for every e 0 received by the editors august 18 1993 and in revised form february 14 1994 originally communicated to the proceedings of the ams by andrew bruckner 1991 mathematics subject classification primary 40d25 secondary 40g99 28a12 1995 american mathematical society 0002 9947 95 1 00 s 25 per page

comments on on the robust popov criterion for interval lur e systems this paper supplements the remarks made in a paper by dahleh et al ieee trans automat contr vol 38 p 1400 5 1993 regarding the popov sector of lur e systems with interval plants a numerical example is provided to show that strict inequalities hold among three sectors those obtained by the theorem of the paper by applying popov theorem to each member system and by applying that to each of the systems with kharitonov plants this counterexample negates a tempting conjecture on strong robust popov criterion

generalized statistical convergence and convergence free spaces abstract many results about statistical convergence in a general setting can be derived by consideration of the convergence free space of null sequences and its related cofilter and filter we derive algebraic and order properties preservation under uniform convergence cauchy properties and properties of cluster points we also show that for certain types of statistical convergence stronger convergence properties also hold finally we discuss the relationship between generalized statistical convergence and subsets of the stone cech compactification of the integers