h control of uncertain fuzzy continuous time systems a new kind of dynamical fuzzy model is proposed to represent the continuous time complex system which includes both linguistic information and system uncertainties a new stability analysis and control system design approach is developed for this kind of dynamical fuzzy model since the fuzzy model considers the norm bounded disturbance the controller design problem becomes a h control problem a constructive algorithm is developed to obtain the h feedback control law finally an example is given to illustrate the application of the method

geometrical implications of certain infinite dimensional decompositions we investigate the connections between the global structure of a banach space i e the existence of certain finite and infinite dimensional de compositions and the geometrical properties of the closed convex bounded sub sets of such a space i e the existence of extremal and other topologically distin guished points the global structures of various supposedly pathological examples of banach spaces constructed by r c james turn out to be more universal than expected for instance james tree type resp james matrix type decompositions characterize banach spaces with the point of continuity property resp the radon nikodym property moreover the convex point of continuity property is stable under the formation of james infinitely branching tree type sums of infinite dimensional factors we also give several counterex amples to various questions relating some topological and geometrical concepts in banach spaces

on the complete separation of asymptotic structures in banach spaces abstract let e i i denote the unit vector basis of l p 1 p or c 0 we construct a reflexive banach space with an unconditional basis that admits e i i as a uniformly unique spreading model while it has no subspace with a unique asymptotic model and hence it has no asymptotic l p or c 0 subspace this solves a problem of e odell we also construct a space with a unique l 1 spreading model and no subspace with a uniformly unique l 1 spreading model these results are achieved with the utilization of a new version of the method of saturation under constraints that uses sequences of functionals with increasing weights

biorthogonal systems and quotient spaces via baire category methods we show that every banach space x of density smaller that the baire category number open image in new window admits a quotient with a long schauder basis that can be taken of length 1 if x is not separable so assuming that the baire category number open image in new window does not take its minimal possible value a banach space x is separable if and only if all biorthogonal systems of x are countable

fuzzy interval finite element statistical energy analysis for mid frequency analysis of built up systems with mixed fuzzy and interval parameters abstract this paper introduces mixed fuzzy and interval parametric uncertainties into the fe components of the hybrid finite element statistical energy analysis fe sea model for mid frequency analysis of built up systems thus an uncertain ensemble combining non parametric with mixed fuzzy and interval parametric uncertainties comes into being a fuzzy interval finite element statistical energy analysis fife sea framework is proposed to obtain the uncertain responses of built up systems which are described as intervals with fuzzy bounds termed as fuzzy bounded intervals fbis in this paper based on the level cut technique a first order fuzzy interval perturbation fe sea ffipfe sea and a second order fuzzy interval perturbation fe sea method sfipfe sea are developed to handle the mixed parametric uncertainties efficiently ffipfe sea approximates the response functions by the first order taylor series while sfipfe sea improves the accuracy by considering the second order items of taylor series in which all the mixed second order items are neglected to further improve the accuracy a chebyshev fuzzy interval method cfim is proposed in which the chebyshev polynomials is used to approximate the response functions the fbis are eventually reconstructed by assembling the extrema solutions at all cut levels numerical results on two built up systems verify the effectiveness of the proposed methods

normalization and stabilization for rectangular singular fractional order t s fuzzy systems abstract this paper considers the normalization and stabilization of rectangular singular fractional order takagi sugeno t s fuzzy systems with order 0 1 by using the proportional and derivative type dynamic compensator the rectangular singular fractional order t s fuzzy systems are transformed into an augmented square singular fractional order t s fuzzy systems and the admissibility of the augmented square singular fractional order t s fuzzy systems can guarantee the normalization and stabilization of the rectangular singular fractional order t s fuzzy systems two sufficient conditions are expressed in terms of a set of bilinear matrix inequalities which can be efficiently solved by an iterative lmi algorithm a numerical example is given to verify the effectiveness of the results proposed

symmetrically separated sequences in the unit sphere of a banach space abstract we prove the symmetric version of kottman s theorem that is to say we demonstrate that the unit sphere of an infinite dimensional banach space contains an infinite subset a with the property that x y 1 for distinct elements x y a thereby answering a question of j m f castillo in the case where x contains an infinite dimensional separable dual space or an unconditional basic sequence the set a may be chosen in a way that x y 1 e for some e 0 and distinct x y a under additional structural properties of x such as non trivial cotype we obtain quantitative estimates for the said e certain renorming results are also presented

an approximation for the point mobility at the intersection of two perpendicular plates abstract the problem of point excitation at a t intersection of two perpendicular plates is studied in order to establish expressions for the point mobility it is found that the theory for point excitation of the free surface of a semi infinite elastic solid is applicable in the frequency range associated with structure borne sound transmission from this theory the mobility for an infinite system is derived based on this model and on an experimental investigation an estimation procedure for the point mobility in the finite dimension case is developed the agreement with measurements performed in situ is quite acceptable both the theoretical and the experimental investigations reveal that the real part of this mobility is small although it is larger in the experimental results this indicates that other components of excitation are difficult to eliminate and may contribute to the power input in practice because of the small real part of the mobility it is advantageous with respect to the reduction of structure borne sound power transmission to locate the contact points between a source and the receiver at such intersections corrections are deduced for the measured magnitude of the mobility for the case when separate force and motion transducers are used

robust stability of uncertain discrete time singular fuzzy systems this paper considers the problem of robust stability analysis of uncertain discrete time singular fuzzy systems described by a class of extended takagi sugeno fuzzy dynamic models with time varying norm bounded parameter uncertainties a sufficient condition ensuring a discrete singular fuzzy system to be regular causal and stable is proposed in terms of a set of linear matrix inequalities based on this a robust stability condition is obtained both of these conditions can be checked by using recently developed algorithms in solving lmis examples are provided to demonstrate the reduced conservatism and effectiveness of the proposed conditions

the wave transmission coefficients and coupling loss factors of point connected structures this analysis is concerned with the calculation of the elastic wave transmission coefficients and coupling loss factors between an arbitrary number of structural components that are coupled at a point a general approach to the problem is presented and it is demonstrated that the resulting coupling loss factors satisfy reciprocity a key aspect of the method is the consideration of cylindrical waves in two dimensional components and this builds upon recent results regarding the energetics of diffuse wavefields when expressed in cylindrical coordinates specific details of the method are given for beam and thin plate components and a number of examples are presented

an infinite ramsey theorem and some banach space dichotomies a problem of banach asks whether every infinite dimensional banach space which is isomorphic to all its infinite dimensional subspaces must be isomorphic to a separable hilbert space in this paper we prove a result of a ramsey theoretic nature which implies an interesting dichotomy for subspaces of banach spaces combined with a result of komorowski and tomczakjaegermann this gives a positive answer to banachxs problem we then generalize the ramsey theoretic result and deduce a further dichotomy for banach spaces with an unconditional basis

robust h sub spl infin control for uncertain discrete time delay fuzzy systems via output feedback controllers this work investigates the problem of robust output feedback h sub spl infin control for a class of uncertain discrete time fuzzy systems with time delays the state space takagi sugeno fuzzy model with time delays and norm bounded parameter uncertainties is adopted the purpose is the design of a full order fuzzy dynamic output feedback controller which ensures the robust asymptotic stability of the closed loop system and guarantees an h sub spl infin norm bound constraint on disturbance attenuation for all admissible uncertainties in terms of linear matrix inequalities lmis a sufficient condition for the solvability of this problem is presented explicit expressions of a desired output feedback controller are proposed when the given lmis are feasible the effectiveness and the applicability of the proposed design approach are demonstrated by applying this to the problem of robust h sub spl infin control for a class of uncertain nonlinear discrete delay systems

the analytic complete continuity property abstract we introduce the notion of the analytic complete continuity property of banach spaces we give different characterizations of this property we show that this property is different from known related properties such as the complete continuity property and the analytic radon nikod m property

paper low order control design for lmi problems using alternating projection methods computational techniques based on alternating projections are proposed to solve control design problems described by linear matrix inequalities lmis in particular we concentrate on the stabilization and the suboptimal h output feedback control design problems these problems can be described by a pair of lmis and an additional coupling condition this coupling condition is convex for the full order control design problem but convexity is lost for the control problem of order strictly less than the plant order we formulate these problems as feasibility problems with matrix constraint sets of simple geometry and we utilize this geometry to obtain analytical expressions for the orthogonal projection operators onto these sets full order and low order controllers are designed using alternating projection methods for the full order controller case global convergence of the alternating projection methods to a feasible solution is guaranteed however for the low order control case only local convergence is guaranteed an example is provided to illustrate the use of these methods for the full order and the low order controller design

star finite coverings of banach spaces abstract we study star finite coverings of infinite dimensional normed spaces a family of sets is called star finite if each of its members intersects only finitely many other members of the family it follows from our results that an lur or a uniformly frechet smooth infinite dimensional banach space does not admit star finite coverings by closed balls on the other hand we present a quite involved construction of a star finite covering of c 0 by frechet smooth centrally symmetric bounded convex bodies a similar but simpler construction shows that every normed space of countable dimension and hence incomplete has a star finite covering by closed balls

the convex point of continuity property in banach spaces not containing l1 abstract we obtain a local characterization of the convex point of continuity property for every closed bounded and convex subset not containing sequences equivalent to the standard unit basis of l 1 as a consequence we prove in the setting of banach spaces without l 1 copies that the convex point of continuity property is determined on subspaces with a schauder basis which is a partial answer to a well known problem

a study of conditional spreading sequences abstract it is shown that every conditional spreading sequence can be decomposed into two well behaved parts one being unconditional and the other being convex block homogeneous i e equivalent to its convex block sequences this decomposition is then used to prove several results concerning the structure of spaces with conditional spreading bases as well as results in the theory of conditional spreading models among other things it is shown that the space c is universal for all spreading models i e it admits all spreading sequences both conditional and unconditional as spreading models moreover every conditional spreading sequence is generated as a spreading model by a sequence in a space that is quasi reflexive of order one

on the hereditary proximity to l1 in the first part of the paper we present and discuss concepts of local and asymptotic hereditary proximity to l1 the second part is devoted to a complete separation of the hereditary local proximity to l1 from the asymptotic one more precisely for every countable ordinal we construct a separable reflexive space x such that every infinite dimensional subspace of it has bourgain l1 index greater than and the space itself has no l1 spreading model we also present a reflexive hi space admitting no lp as a spreading model

applications of the theory of semi embeddings to banach space theory let x and y be banach spaces and t x y an injective bounded linear operator t is called a semi embedding if t maps the closed unit ball of x to a closed subset of y this concept was introduced by lotz peck and porta proc edinburgh math soc 22 1979 233 240 it is proved that if x semi embeds in y and x is separable then x has the radon nikodym property provided y does it is shown that if l1 semi embeds in y then y fails the schur property and contains a subspace isomorphic to l1 as a consequence of the proof it is shown that if x is a subspace of l1 either l1 embeds in x or l1 embeds in l1x the simpler result that l1 does not semi embed in c0 is treated separately this result is used to deduce the classic result of menchoff that there exists a singular probability measure on the circle with fourier coefficients vanishing at infinity some generalizations of the notion of semi embedding are given and several complements and open questions are discussed

borel properties of linear operators abstract given an injective bounded linear operator t x y between banach spaces we study the borel measurability of the inverse map t 1 tx x a remarkable result of saint raymond ann inst fourier grenoble 26 1976 211 256 states that if x is separable then the borel class of t 1 is if and only if x is the th iterated sequential weak closure of t y for some countable ordinal we show that saint raymond s result holds with minor changes for arbitrary banach spaces if we assume that t has certain property named co discreteness after hansell proc london math soc 28 1974 683 699 as an application we show that the borel class of the inverse of a co discrete operator t can be estimated by the image of the unit ball or the restrictions of t to separable subspaces of x our results apply naturally when x is a wcd banach space since in this case any injective bounded linear operator defined on x is automatically co discrete

on densely isomorphic normed spaces abstract in the first part of our note we prove that every weakly lindelof determined wld in particular every reflexive non separable banach x space contains two dense linear subspaces y and z that are not densely isomorphic this means that there are no further dense linear subspaces y 0 and z 0 of y and z which are linearly isomorphic our main result theorem b concerns the existence of biorthogonal systems in normed spaces in particular we prove under the continuum hypothesis ch that there exists a dense linear subspace of l 2 1 or more generally every wld space of density 1 which contains no uncountable biorthogonal system this result lies between two fundamental results concerning biorthogonal systems namely the construction of kunen under ch of a non separable banach space which contains no uncountable biorthogonal system and the construction of todorcevic under martin maximum of an uncountable biorthogonal system in every non separable banach space

point inertance of an infinite plate with respect to a force acting in its plane a corrected expression is given for the point inertance of an infinite plate with respect to a force acting in its plane as presented by nikiforov 1 it is noted that the small argument approximation is no longer valid however the large argument approximation remains the same

an approach to fuzzy control of nonlinear systems stability and design issues presents a design methodology for stabilization of a class of nonlinear systems first the authors represent a nonlinear plant with a takagi sugeno fuzzy model then a model based fuzzy controller design utilizing the concept of the so called parallel distributed compensation is employed the main idea of the controller design is to derive each control rule so as to compensate each rule of a fuzzy system the design procedure is conceptually simple and natural moreover the stability analysis and control design problems can be reduced to linear matrix inequality lmi problems therefore they can be solved efficiently in practice by convex programming techniques for lmis the design methodology is illustrated by application to the problem of balancing and swing up of an inverted pendulum on a cart

a characterization of banach spaces containing it is proved that a banach space contains a subspace isomorphic to 11 if and only if it has a bounded sequence with no weak cauchy subsequence the proof yields that a sequence of subsets of a given set has a subsequence that is either convergent or boolean independent a bounded sequence of elements fn in a banach space b is said to be equivalent to the usual 11 basis provided there is a a 0 so that for all n and choices of scalars c cn

diffuse wavefields in cylindrical coordinates a diffuse wavefield is normally defined in terms of plane waves to quote one textbook definition plane waves are incident from all directions with equal probability and random phase in some vibro acoustic problems the response of a two dimensional component such as a plate is more conveniently expressed in terms of cylindrical waves and it is not immediately obvious what properties should be assigned to the cylindrical waves to constitute a diffuse field it is shown here that a diffuse wavefield can be modeled as a summation of statistically independent cylindrical waves apart from the fact that each outgoing wave of a particular order is fully correlated to an incoming wave of the same order a simple relationship is derived between the energy flow p in each wave component and the energy density e of the wavefield p ec g k where c g is the group velocity and k is the wavenumber this result is shown to hold true for both bending waves and in plane waves longitudinal and shear in a plate the work has application to the calculation of coupling loss factors in statistical energy analysis

nonfragile control with guaranteed cost of t s fuzzy singular systems based on parallel distributed compensation this paper investigates the nonfragile guaranteed cost control problem for a class of uncertain nonlinear singular state delayed systems that is described by takagi sugeno models the upper bound of state delay is assumed to be available a linear quadratic cost function is specified as the performance index of the closed loop system attention is focused on the fuzzy state feedback controller design via parallel distributed compensation scheme which not only guarantees the regular impulse free and asymptotically stable of the closed loop fuzzy singular delay system but also provides an optimized upper bound of the guaranteed cost function for the possibility of feedback gain variation and all admissible uncertainties all derived sufficient conditions are given in terms of linear matrix inequalities some numerical examples are provided to illustrate the effectiveness of the proposed design scheme

weak polish banach spaces abstract a banach space x which is a subspace of the dual of a banach space y is said to be weak polish proviced x is separable and the closed unit ball of x is polish in the weak topology x is said to be polish provided it is weak polish when regarded as a subspace of x a variety of structural results are obtained for banach spaces with the point of continuity property pcp using the unifying concept of weak polish banach spaces it is proved that every weak polish banach space contains an infinite dimensional weak closed subspace this yields the result of edgar wheeler that every polish banach space has a reflexive subspace it also yields the result of ghoussoub maurey that every banach space with the pcp has a subspace isomorphic to a separable dual in virtue of the following known result linking the pcp and weak polish banach spaces a separable banach space has the pcp if edgar wheeler and only if ghoussoub maurey it is isometric to a weak polish subspace of the dual of some separable banach space for completeness a proof of this result is also given it is proved that if x and y are banach spaces with x y then x is weak polish if and only if x has a weak continuous boundedly complete skipped blocking decomposition combined with the above mentioned linkage this characterization of weak polish banach spaces gives the known result that a separable banach space has the pcp if bourgain rosenthal and only if ghoussoub maurey it has the boundedly complete skipped blocking property the proof of the characterization is a variation of the original arguments for this result the characterization also yields that a banach space is polish if and only if it has the reflexive skipped blocking property it is moreover demonstrated that a banach space has the pcp provided it has the pc skipped blocking property in particular this yields an exposition of the result of bourgain that a space has the pcp provided each of its subspaces with an fdd has the pcp it is proved that the pcp is a three space property thus completing the solution to a problem posed by edgar wheeler that is if y and x are banach spaces with y x then x has the pcp provided both y and x y have the pcp it is also shown that a banach space x has a separable dual provided it has the dual separable skipped blocking property the proof yields the dividend that x is separable provided x j is separable for every basic sequence x j in x

minimum norm regularization of descriptor systems by mixed output feedback we study the regularization problem for linear constant coefficient descriptor systems ex ax bu y1 cx y2 x by proportional and derivative mixed output feedback necessary and sufficient conditions are given which guarantee that there exist output feedbacks such that the closed loop system is regular has index at most one and e bg has a desired rank i e there is a desired number of differential and algebraic equations to resolve the freedom in the choice of the feedback matrices we then discuss how to obtain the desired regularizing feedback of minimum norm and show that this approach leads to useful results in the sense of robustness only if the rank of e is decreased numerical procedures are derived to construct the desired feedback gains these numerical procedures are based on orthogonal matrix transformations which can be implemented in a numerically stable way

robust stabilization for generalized state space systems with uncertainty this paper is concerned with the problem of robust stabilization for generalized state space systems with parameter uncertainty the parameter uncertainty under consideration is time invariant and unknown but is norm bounded the problem we address is to design a state feedback controller such that the resulting closed loop system is regular impulsefree and stable for all admissible uncertainties via the notion of stabilizability and impulse eliminatibility the robust stabilization problem is solved necessary and sufficient conditions for stabilizability and impulse eliminatibility are derived when these conditions are satisfied the desired stabilization state feedback controller can be constructed through finding parameters satisfying a certain matrix equation finally an illustrative example is given to show the feasibility of the proposed technique

comments on robust stabilization of a class of uncertain nonlinear systems via fuzzy control quadratic stabilizability h sup spl infin control theory and linear matrix inequalities this paper presents stability analysis for a class of uncertain nonlinear systems and a method for designing robust fuzzy controllers to stabilize the uncertain nonlinear systems first a stability condition for takagi and sugeno s fuzzy model is given in terms of lyapunov stability theory next new stability conditions for a generalized class of uncertain systems are derived from robust control techniques such as quadratic stabilization h sup spl infin control theory and linear matrix inequalities the derived stability conditions are used to analyze the stability of takagi and sugeno s fuzzy control systems with uncertainty which can be regarded as a generalized class of uncertain nonlinear systems the design method employs the so called parallel distributed compensation important issues for the stability analysis and design are remarked finally three design examples of fuzzy controllers for stabilizing nonlinear systems and uncertain nonlinear systems are presented

hybrid finite element statistical energy method for mid frequency analysis of structure acoustic systems with interval parameters abstract the hybrid finite element statistical energy analysis fe sea model for mid frequency analysis consists of two parts the fe components and the sea components which are called as the master system and the subsystem respectively the hybrid finite element statistical energy analysis approach is established on the assumption that the fe components have fully deterministic properties while the sea subsystems have a high degree of randomness this method has been recently extended to allow the properties of the fe components of built up structures to be uncertain like interval or probabilistic and the hybrid model with parametric and non parametric uncertainties is obtained by dealing with the non parametric uncertainty analytically and the parametric uncertainty with monte carlo simulations the distribution of the responses of the hybrid model can be obtained in this paper the interval parametric uncertainty is introduced into the hybrid fe sea framework for structure acoustic systems and the interval dynamic equilibrium equations are established thus a hybrid model with non parametric and interval parametric uncertainties for structure acoustic systems is obtained to improve the computational efficiency the second order interval perturbation finite element method is introduced into the hybrid fe sea framework and the second order interval perturbation finite element statistical energy analysis sipfem sea method is proposed for the structure acoustic system with interval parameters modeled by fe sea the parameters of fe components are considered as interval parameters instead of deterministic ones thus the expectations of the second order quantities such as the vibrational energy and the response cross spectrum in the fe sea framework become interval variables too in the sipfem sea the expectations of the second order response quantities of a structure acoustic system are expanded with the second order taylor series at the nominal values of interval parameters and for the sake of simplicity and efficiency the non diagonal elements of the hessian matrices are neglected then by searching the target positions of interval parameters that maximize or minimize the objective functions the bounds of the vibrational energy and the response cross spectrum can be obtained because of the neglect of the higher order terms of taylor series sipfem sea is limited to the interval analysis with narrow parameter intervals for larger parameter intervals the sub interval perturbation method based on the sipfem sea is introduced the proposed methods are illustrated by applications to two example structure acoustic systems in which the acoustic cavities are modeled by using the interval fe method and the structures are modeled by using the sea reference comparisons are made with the monte carlo simulations of the hybrid fe sea model the numerical results verify the accuracy and efficiency of the proposed methods

new approaches to h controller designs based on fuzzy observers for t s fuzzy systems via lmi the problems of relaxed quadratic stability conditions fuzzy observer designs and h controller designs for t s fuzzy systems have been studied first new stability conditions are obtained by relaxing the stability conditions derived in previous papers secondly new fuzzy observers based on the relaxed stability conditions for the t s fuzzy systems have been proposed thirdly two sufficient lmi conditions which guarantee the existence of the h controllers based on fuzzy observers for the t s fuzzy systems have been proposed the conditions are not only simple but also consider the interactions among the fuzzy subsystems finally by some examples using the lmi technique we show that the regulators the fuzzy observers and the h controller designs based on new observers for the t s fuzzy systems are very practical and efficient

interpolating hereditarily indecomposable banach spaces a banach space x is said to be hereditarily indecomposable h i if for any pair of closed subspaces y z of x with y z 0 y z is not a closed subspace throughout this section by the term subspace we mean a closed infinite dimensional subspace of x the h i spaces form a new and as we believe fundamental class of banach spaces the celebrated example of a banach space with no unconditional basic sequence due to w gowers and b maurey gm is the first construction of a h i space it is easily seen that every h i space does not contain any unconditional basic sequence actually the concept of h i spaces came after w johnson s observation that this was a property of the gowers maurey example to describe even further the peculiar structure of a h i space we recall an alternative definition of such a space a banach space x is a h i space if and only if for every pair of subspaces y z and e 0 there exist y y z z with y z 1 and y z e thus h i spaces are structurally irrelevant to classical banach spaces in particular to hilbert spaces other constructions of h i spaces already exist we mention argyros and deliyanni s construction of h i spaces which are asymptotic spaces ad2 v ferenczi s example of a uniformly convex h i space f2 and h i modified asymptotic spaces contained in adkm other examples of banach spaces which are h i or which have a h i subspace are given in g1 h os1 the construction of such a space requires several steps and it uses two fundamental ideas the first is tsirelson s recursive definition of saturated norms ts and the second is maurey rosenthal s construction of weakly null sequences without unconditional basic subsequences mr an important ingredient in the gowersmaurey construction is the schlumprecht space this is a tsirelson type banach space which is arbitrarily distortable and has been used in the solution of important problems thus beyond its use in the constructions of h i spaces it plays a central role in the solution of the distortion problem for hilbert spaces os the essential difference between schlumprecht and tsirelson spaces became more transparent in ad2 where the mixed tsirelson spaces were introduced it is natural to expect that h i spaces share special and interesting properties not found in the previously known banach spaces indeed the following theorem is proven in

the unconditional basic sequence problem we construct a banach space that does not contain any infinite un conditional basic sequence and investigate further properties of this space for example it has no subspace that can be written as a topological direct sum of two infinite dimensional spaces this property implies that every operator on the space is a strictly singular perturbation of a multiple of the identity in par ticular it is either strictly singular or fredholm with index zero this implies that the space is not isomorphic to any proper subspace trinity college cambridge cb2 1tq england current address department of mathematics university college london gower street lon don wc1e 6bt england e mail address wtg l o phx cam ac uk universit paris vii u f r de mathtmatiques 2 place jussieu 75251 paris cedex 05 france current address equipe d analyse et mathematiques appliquees universite de mamne la vallee 93160 noisy le grand france e mail address maurey logiquejussieu fr this content downloaded from 157 55 39 105 on fri 07 oct 2016 04 30 48 utc all use subject to http about jstor org terms

embedding uniformly convex spaces into spaces with very few operators we prove that every separable uniformly convex banach space x embeds into a banach space z which has the property that all bounded linear operators on z are compact perturbations of scalar multiples of the identity more generally the result holds for all separable reflexive banach spaces of szlenk index 0

stability analysis and design of fuzzy control systems abstract the stability analysis and the design technique of fuzzy control systems using fuzzy block diagrams are discussed first we show the concept of fuzzy blocks and consider the connection problems of fuzzy blocks diagrams we derive some theorems and corollaries with respect to two basic types of connections of fuzzy blocks in order to preserve some properties in a connection of fuzzy blocks continuous piecewise polynomial membership functions are defined secondly a sufficient condition which guarantees the stability of fuzzy systems is obtained in terms of lyapunov s direct method we give an important fact based on this condition thirdly we propose a new design technique of a fuzzy controller the fuzzy block diagrams and the stability analysis are applied to the design problems of a model based fuzzy controller

robust stabilization for delayed discrete time fuzzy systems via basis dependent lyapunov krasovskii function abstract this paper deals with the robust control problem for a class of uncertain discrete time fuzzy systems with time delay the uncertainty is assumed to be of structured linear fractional form which includes the norm bounded uncertainty as a special case and can describe a class of rational nonlinearities by using basis dependent lyapunov krasovskii function a robust control design approach is developed the control design approach is facilitated by introducing some additional instrumental matrix variables these additional matrix variables decouple the lyapunov krasovskii and the system matrices which make the control design feasible the proposed approach leads to some sufficient results in the form of strict linear matrix inequalities lmis the development represents an important step towards reducing the conservatism of previous design methods and the results also generalize earlier works for a more general parametric uncertainty structure numerical examples are also given to demonstrate the applicability of the proposed approach

robust fuzzy control for uncertain discrete time nonlinear markovian jump systems without mode observations this paper studies the robust fuzzy control problem of uncertain discrete time nonlinear markovian jump systems without mode observations the takagi and sugeno t s fuzzy model is employed to represent a discrete time nonlinear system with norm bounded parameter uncertainties and markovian jump parameters as a result an uncertain markovian jump fuzzy system mjfs is obtained a stochastic fuzzy lyapunov function flf is employed to analyze the robust stability of the uncertain mjfs which not only is dependent on the operation modes of the system but also directly includes the membership functions then based on this stochastic flf and a non parallel distributed compensation non pdc scheme a mode independent state feedback control design is developed to guarantee that the closed loop mjfs is stochastically stable for all admissible parameter uncertainties the proposed sufficient conditions for the robust stability and mode independent robust stabilization are formulated as a set of coupled linear matrix inequalities lmis which can be solved efficiently by using existing lmi optimization techniques finally it is also demonstrated via a simulation example that the proposed design method is effective

an extension of a structure theorem of bourgain abstract bourgain has shown that if x is a banach space which does not have the radon nikodym property respectively the point of continuity property then x has a subspace y which also fails to have the respective property but which has a finite dimensional schauder decomposition we extend this result to spaces x failing the convex point of continuity property

admissibility analysis and control synthesis for t s fuzzy descriptor systems the problem of admissibility analysis and control synthesis for takagi sugeno fuzzy descriptor systems is investigated first based on nonquadratic fuzzy lyapunov function and fully using the information of fuzzy membership functions a new relaxed sufficient condition ensuring a fuzzy descriptor system to be admissible regular impulse free and stable is proposed in which it is not necessary to require every fuzzy subsystem to be stable second the other sufficient condition for the admissibility is obtained without the information of time derivatives of fuzzy membership functions following the analysis both parallel and nonparallel distributed compensation controllers are designed linear matrix inequalities conditions are given to construct the controllers finally some examples are provided to illustrate the main results in this paper less conservative than some earlier related results

feedback control of nonlinear systems by extended linearization for single input multiple output nonlinear systems we consider a design method based on the family of linearizations of the system parameterized by constant operating points nonlinear state feedback control laws and observer state feedback control laws are designed such that the eigenvalues of the family of linearized closed loop systems are placed at specified values that are locally invariant with respect to the closed loop operating point the method is illustrated by application to the problem of automatically balancing an inverted pendulum

a problem on spreading models it is proved that if a banach spacexhas a basis en satisfying every spreading model of a normalized block basis of en is 1 equivalent to the unit vector basis of l1 respectively c0 thenxcontains l1 respectively c0 furthermore tsirelson s spacetis shown to have the property that every infinite dimensional subspace contains a sequence having spreading model 1 equivalent to the unit vector basis of l1 an equivalent norm is constructed ontso that s1 s2 2 whenever sn is a spreading model of a normalized basic sequence int

gδ embeddings in hilbert space ii in this paper which is a continuation of 10 we exhibit some topological conditions on a banach space which ensure that it contains isometric copies of infinite dimensional conjugate spaces this result is used to identify a large class of banach spaces that are hereditarily separable duals a method of defining a jamestree sum of a countable number of banach spaces is given it is used to construct various counterexamples for instance there exists for each integer n a banach space that can be mapped into hilbert space via the composition of n but not n 1 g embeddings we also continue the investigation of the global structure of some geometrically defined banach spaces for example it is shown that a separable banach space x with the radon nikodym property r n p has a subspace y with a boundedly complete finite dimensional decomposition f d d such that xy has an f d d and the r n p

passivity analysis and passive control of fuzzy systems with time varying delays this paper is concerned with the passive controller design problem for a class of continuous time takagi sugeno t s fuzzy systems with both state and input delays the delays are assumed to be time varying and differentiable a notion of very strict passivity is adopted the purpose is to design a state feedback fuzzy controller such that the resulting closed loop system is very strictly passive vsp delay dependent conditions for the solvability of the addressed problem are obtained by applying recently developed techniques for time delay systems and fuzzy systems these conditions are expressed by means of strict linear matrix inequalities lmis that can be easily solved a numerical example and simulation results are provided to demonstrate the effectiveness of the proposed method

the universality of l1 as a dual space let x be a banach space with a separable dual we prove that x embeds isomorphically into a mathcal l infty space z whose dual is isomorphic to l1 if moreover u is a space with separable dual so that u and x are totally incomparable then we construct such a z so that z and u are totally incomparable if x is separable and reflexive we show that z can be made to be somewhat reflexive

gδ embeddings in hilbert space abstract it is shown that a separable banach space x has the point of weak to norm continuity property resp the radon nikodym property if and only if there exists a compact g embedding resp an h embedding from x into l2 this solves several questions of j bourgain and h p rosenthal j funct anal 52 1983 it is also shown that every non relatively compact sequence in a banach space with property pc has a difference subsequence which is a boundedly complete basic sequence this solves a question of pelczynski and extends some results of w b johnson and h p rosenthal studia math 43 1972 77 92 various related questions asked in the above bourgain rosenthal reference and by g a edgar and r f wheeler pac j math 115 1984 and n ghoussoub and h p rosenthal math ann 264 1983 321 332 are also settled

robust fuzzy h control for uncertain nonlinear systems via state feedback an lmi approach this paper presents a method for designing robust fuzzy h controllers which stabilize nonlinear systems and guarantee an induced l2 norm bound constraint on disturbance attenuation for all admissible uncertainties takagi and sugeno fuzzy models with uncertainties are used as the model for the uncertain nonlinear systems fuzzy control systems utilize the concept of the so called parallel distributed compensation pdc using a single quadratic lyapunov function the stability with decay rate and disturbance attenuation for takagi and sugeno fuzzy model with parameter uncertainties are discussed a sufficient condition for the presence of the robust fuzzy h controllers is then presented in terms of linear matrix inequalities lmis finally design examples of robust fuzzy h controllers for uncertain nonlinear systems are presented

calculation of point mobilities at generic multi plate beam junctions a new method is presented for the calculation of point mobilities at generic multi plate beam junctions such a junction is considered to consist of an arbitrary number of semi infinite plates coupled together through a beam which may also be omitted plates and beams are assumed to obey mindlin and timoshenko theories respectively the calculation is based on a numerical wavenumber integration technique a specially adapted numerical integration technique is used to reduce the amount of numerical calculations to be done the method is applied to a number of example structures to test its results and to illustrate its application

brief paper stability and stabilization of continuous time singular hybrid systems in this paper the problems of stability and state feedback stabilization for a class of continuous time singular hybrid systems are investigated a new sufficient and necessary condition for a continuous time singular hybrid system to be regular impulse free and stochastically stable is proposed in terms of a set of coupled strict linear matrix inequalities lmis moreover a new sufficient and necessary condition is presented for the existence of the state feedback controller in terms of a set of coupled strict matrix inequalities finally a numerical example is given to illustrate the effectiveness of the obtained theoretical results

image restoration by the method of convex projections part 1ߞtheory a projection operator onto a closed convex set in hilbert space is one of the few examples of a nonlinear map that can be defined in simple abstract terms moreover it minimizes distance and is nonexpansive and therefore shares two of the more important properties of ordinary linear orthogonal projections onto closed linear manifolds in this paper we exploit the properties of these operators to develop several iterative algorithms for image restoration from partial data which permit any number of nonlinear constraints of a certain type to be subsumed automatically their common conceptual basis is as follows every known property of an original image f is envisaged as restricting it to lie in a well defined closed convex set thus m such properties place f in the intersection e0 ei of the corresponding closed convex sets e1 e2 em given only the projection operators pi onto the individual ei s i 1 m we restore f by recursive means clearly in this approach the realization of the pi s in a hilbert space setting is one of the major synthesis problems section i describes the geometrical significance of the three main theorems in considerable detail and most of the underlying ideas are illustrated with the aid of simple diagrams section ii presents rules for the numerical implementation of 11 specific projection operators which are found to occur frequently in many signal processing applications and the appendix contains proofs of all the major results

filtering and lqg problems for discrete time stochastic singular systems discrete time stochastic singular systems are discussed filtering and linear quadratic gaussian lqg problems are considered the problems are first transformed into the normal form via state augmentation and then solved by utilizing standard results for nonsingular systems the linear unbiased least squares state estimation algorithm and the optimal control law for the lqg problem are given the order of the filtering algorithm obtained in this way is not much increased moreover this algorithm allows the presence of some kinds of control inputs

on isometry groups and maximal symmetry we study problems of maximal symmetry in banach spaces this is done by providing an analysis of the structure of small subgroups of the general linear group gl x where x is a separable reflexive banach space in particular we provide the first known example of a banach space x without any equivalent maximal norm or equivalently such that gl x contains no maximal bounded subgroup moreover this space x may be chosen to be super reflexive in memory of greg hjorth 1963 2011 and nigel kalton 1946 2010

response variance prediction for uncertain vibro acoustic systems using a hybrid deterministic statistical method imperfections during the manufacturing process can cause significant variations in the noise and vibration levels exhibited by nominally identical structures any response calculations employed during the design process should ideally take account of these uncertainties and predict the expected range in performance recently a hybrid method has been developed to predict the ensemble average response of a built up system by combining a deterministic model of parts of the system with a statistical model of other components shorter p j and langley r s 2005 j sound vib 288 669 700 in this paper the method is extended to predict the ensemble variance of the response expressions are derived for the variance of the vibrational energies in the statistical components and for the variance of the cross spectrum of the response of the deterministic components which augment the mean values of these quantities predicted by the original theory the method employs a nonparametric model of uncertainty in the sense that the statistical components are taken to carry diffuse wave fields and this obviates the requirement for a detailed description of the system uncertainties the method is validated by application to a range of coupled plate structures and good agreement with detailed monte carlo simulations is found

technical communique stabilization of discrete time singular systems a matrix inequalities approach this paper is concerned with the state feedback stabilization problem of discrete time singular systems the singular system under consideration is not assumed to be regular the problem we address is to design state feedback controllers such that the resulting closed loop system is regular causal and stable conditions for the existence of solutions to this problem are obtained expressed in terms of certain matrix inequalities when these conditions are satisfied the explicit formula of desired state feedback controllers is also given without resorting to decomposing the system matrices

robust control for a class of uncertain nonlinear systems adaptive fuzzy approach based on backstepping a robust adaptive fuzzy control design approach is developed for a class of multivariable nonlinear systems with modeling uncertainties and external disturbances the controller design for the overall systems has been carried out through a number of simpler controller designs for a series of the relevant auxiliary systems based on the backstepping design technique for each auxiliary system an adaptive fuzzy logic system is introduced to learn the behavior of unknown dynamics and then a robust control algorithm is employed to efficiently compensate the approximation error and the external disturbances as well it is shown that the resulting closed loop systems guarantee a satisfactory transient and asymptotic performance a simulation example is also presented to illustrate the design procedure and controller performance

on the reciprocity relationship between direct field radiation and diffuse reverberant loading this analysis is concerned with the derivation of a diffuse field reciprocity relationship between the diffuse field excitation of a connection to a structural or acoustic subsystem and the radiation impedance of the connection such a relationship has been derived previously for connections described by a single degree of freedom in the present work it is shown that the diffuse field reciprocity relationship also arises when describing the ensemble average response of connections to structural or acoustic subsystems with uncertain boundaries furthermore it is shown that the existing diffuse field reciprocity relationship can be extended to encompass connections that possess an arbitrary number of degrees of freedom the present work has application to i the calculation of the diffuse field response of structural acoustic systems modeled by finite elements boundary elements and infinite elements ii the general calculation of the coupling loss factors employed in statistical energy analysis sea and iii the derivation of an alternative analysis method for describing the dynamic interactions of coupled subsystems with uncertain boundaries a generalized boundary approach to sea

delay dependent stability and h control for a class of fuzzy descriptor systems with time delay this paper addresses issues of stability analysis and h control for a class of fuzzy time delay descriptor systems described by an extended takagi sugeno t s fuzzy model a delay dependent stability criterion is first presented and a h control synthesis approach is then developed both the stability criterion and the h controller synthesis are based on the solutions of linear matrix inequalities lmis finally two examples are given to illustrate the effectiveness of the approaches proposed in this paper

szlenk indices and uniform homeomorphisms we prove some rather precise renorming theorems for banach spaces with szlenk index wo we use these theorems to show the invariance of certain quantitative szlenk type indices under uniform homeomorphisms

boundedly complete weak cauchy basic sequences in banach spaces with the pcp abstract it is proved that every non trivial weak cauchy sequence in a banach space with the pcp the point of continuity property has a boundedly complete basic subsequence the following result due independently to s bellenot and c finet is then deduced as a corollary if a banach space x has separable dual and the pcp then every non trivial weak cauchy sequence in x has a subsequence spanning an order one quasi reflexive space

a hereditarily indecomposable mathcal l _ infty space that solves the scalar plus compact problem we construct a hereditarily indecomposable banach space with dual space isomorphic to l1 every bounded linear operator on this space is expressible as i k with a scalar and k compact

conjugate operators that preserve the nonconvergence of bounded martingales we show that the conjugate t of an operator t x y with x and y banach spaces satisfies the following dichotomy either t preserves the nonconvergence of bounded martingales in y or there exists a compact operator k x y such that the kernel n t k fails the radon nikod m property

stability analysis of discrete singular fuzzy systems abstract this work mainly develops a discrete singular fuzzy model and discusses its stability the standard discrete t s model is generalized into the so called discrete singular takagi sugeno dst s model which can represent a larger class of nonlinear systems and the stability criteria of this system are then investigated these criteria are described by non strict linear matrix inequalities and we thus involve the projection method for ensuring stability based on some derived projection operators a projection algorithm is proposed for solving a feasible solution an illustrating example demonstrates the validity and effectiveness of the proposed method

banach spaces with projectional skeletons a projectional skeleton in a banach space is a directed family of projections onto separable subspaces covering the entire space the class of banach spaces with projectional skeletons is strictly larger than the class of plichko spaces i e banach spaces with a countably norming markushevich basis we show that every space with a projectional skeleton has a projectional resolution of the identity and has a norming space with similar properties to spaces we characterize the existence of a projectional skeleton in terms of elementary substructures providing simple proofs of known results concerning weakly compactly generated spaces and plichko spaces we prove a preservation result for plichko banach spaces involving transfinite sequences of projections as a corollary we show that a banach space is plichko if and only if it has a commutative projectional skeleton

tukey classification of some ideals on ω and the lattices of weakly compact sets in banach spaces abstract we study the lattice structure of the family of weakly compact subsets of the unit ball b x of a separable banach space x equipped with the inclusion relation this structure is denoted by k b x and also with the parametrized family of almost inclusion relations k l e b x where e 0 this structure is denoted by ak b x tukey equivalence between partially ordered sets and a suitable extension to deal with ak b x are used assuming the axiom of analytic determinacy we prove that separable banach spaces fall into four categories namely k b x is equivalent either to a singleton or to or to the family k q of compact subsets of the rational numbers or to the family c of all finite subsets of the continuum also under the axiom of analytic determinacy a similar classification of ak b x is obtained for separable banach spaces not containing l 1 we prove in zfc that k b x ak b x are equivalent to either 0 k q or c the lattice structure of the family of all weakly null subsequences of an unconditional basis is also studied

banach spaces with many boundedly complete basic sequences failing pcp we prove that there exist banach spaces not containing l1 failing the point of continuity property and satisfying that every semi normalized basic sequence has a boundedly complete basic subsequence this answers in the negative the problem of remark 2 in rosenthal 2007 12

fuzzy descriptor systems and nonlinear model following control this paper defines a fuzzy descriptor system by extending the ordinary takagi sugeno t s fuzzy model several kinds of stability conditions for the fuzzy descriptor system are derived and represented in terms of linear matrix inequalities lmis we illustrate an example of defining the fuzzy descriptor system instead of the ordinary t s fuzzy model an lmi design approach is employed to find stable feedback gains and a common lyapunov function in addition this paper presents a nonlinear model following control for the fuzzy descriptor system a new parallel distributed compensation the so called twin parallel distributed compensations tpdc to realize the nonlinear model following control is proposed we present a design technique based on the tpdc the proposed method is a unified approach to nonlinear model following control it contains the regulation and servo control problems as special cases

stability analysis and systematic design of fuzzy control systems abstract a method of the stability analysis and systematic design of fuzzy control systems is presented in this paper the fuzzy control system is formulated by a set of local takagi sugeno fuzzy models t s fuzzy model with aggregation the controller is designed by state feedback for each local model separately it is shown that under some conditions the controller designed can guarantee the global stability of the closed loop fuzzy system the stability of the whole closed loop fuzzy system is also proved via the piecewise lyapunov function the simulation results for the fuzzy control of a nonlinear system the ball and beam system bb system show that this method is effective