the homogeneous shifts abstract a bounded linear operator t on a complex hilbert space is called homogeneous if the spectrum of t is contained in the closed unit disc and all bi holomorphic automorphisms of this disc lift to automorphisms of the operator modulo unitary equivalence we prove that all the irreducible homogeneous operators are block shifts therefore as a first step in classifying all of them it is natural to begin with the homogeneous scalar shifts in this paper we determine all the homogeneous scalar weighted shifts they consist of the unweighted bilateral shift two one parameter families of unilateral shifts adjoints of each other a one parameter family of bilateral shifts and a two parameter family of bilateral shifts this classification is obtained by a careful analysis of the possibilities for the projective representation of the mobius group associated with an irreducible homogeneous shift

residual finite dimensionality and representations of amenable operator algebras abstract we consider a version of a famous open problem formulated by kadison asking whether bounded representations of operator algebras are automatically completely bounded we investigate this question in the context of amenable operator algebras and we provide an affirmative answer for representations whose range is residually finite dimensional furthermore we show that weak closed amenable residually finite dimensional operator algebras are similar to c algebras and in particular have the property that all their bounded representations are completely bounded we prove our results for operator algebras having the so called total reduction property which is known to be weaker than amenability

every completely polynomially bounded operator is similar to a contraction it is proved that a bounded operator on a hilbert space is similar to a contraction if and only if it is completely polynomially bounded this gives a partial answer to problem 6 of halmos bull amer math soc 76 1970 877 933 the set of completely bounded maps between c algebras is studied to obtain some structure representation and extension theorems for this class of maps these allow a characterization of the completely bounded representations on a hilbert space of any subalgebra of a c algebra to be obtained the result in the title follows by applying this characterization to the disk algebra

on quotient modules the case of arbitrary multiplicity let m be a hilbert module of holomorphic functions defined on a bounded domain cm let m0 be the submodule of functions vanishing to order k on a hypersurface z in in this paper we describe the quotient module mq

design of inner coupling matrix for robustly self synchronizing networks abstract a self synchronizing network may undergo change of scale and topology during its functioning thus adjustment of parameters is necessary to enable the synchronization the adjustment cost and runtime break demand a method to maintain continuous operation of the network to address these issues this paper presents an analytical method for the design of the inner coupling matrix the proposed method renders the synchronization robust to change of network scale and topology it is usual in network models that scale and topology are represented by outer coupling matrix in this paper we only consider diffusively coupled networks for these networks the eigenvalues of the outer coupling matrix are all non positive by utilizing this property the designed inner coupling matrix can cover the entire left half of complex plane within the synchronized region to underlie robustness of synchronization after elaborating the applicability of several types of synchronization state for a robustly self synchronizing network the analytical design method is given for the stable equilibrium point case sometimes the jacobian matrix of the node dynamical equation may lead to an unrealizable complex inner coupling matrix in the method we then introduce a lemma of matrix transformation to prevent this possibility additionally we investigated the choice of inner coupling matrix to get a desirable self synchronization speed the corresponding condition in the design procedure is given to drive the network synchronization faster than convergence of each node finally the article includes examples that show effectiveness and soundness of the method

cat k spaces weak convergence and fixed points abstract in this paper we show that some of the recent results on fixed point for cat 0 spaces still hold true for cat 1 spaces and so for any cat k space under natural boundedness conditions we also introduce a new notion of convergence in geodesic spaces which is related to the convergence and applied to study some aspects on the geometry of cat 0 spaces at this point two recently posed questions in w a kirk b panyanak a concept of convergence in geodesic spaces nonlinear anal 68 12 2008 3689 3696 are answered in the negative the work finishes with the study of the lifsic characteristic and property p of lim xu to derive fixed point results for uniformly lipschitzian mappings in cat k spaces a conjecture raised in s dhompongsa w a kirk b sims fixed points of uniformly lipschitzian mappings nonlinear anal 65 2006 762 772 on the lifsic characteristic function of cat k spaces is solved in the positive

brief paper robust filtering with stochastic nonlinearities and multiple missing measurements this paper is concerned with the filtering problem for a class of discrete time uncertain stochastic nonlinear time delay systems with both the probabilistic missing measurements and external stochastic disturbances the measurement missing phenomenon is assumed to occur in a random way and the missing probability for each sensor is governed by an individual random variable satisfying a certain probabilistic distribution over the interval 01 such a probabilistic distribution could be any commonly used discrete distribution over the interval 01 the multiplicative stochastic disturbances are in the form of a scalar gaussian white noise with unit variance the purpose of the addressed filtering problem is to design a filter such that for the admissible random measurement missing stochastic disturbances norm bounded uncertainties as well as stochastic nonlinearities the error dynamics of the filtering process is exponentially mean square stable by using the linear matrix inequality lmi method sufficient conditions are established that ensure the exponential mean square stability of the filtering error and then the filter parameters are characterized by the solution to a set of lmis illustrative examples are exploited to show the effectiveness of the proposed design procedures

a classification of homogeneous operators in the cowen douglas class a complete list of homogeneous operators in the cowen douglas class b n mathbb d is given this classification is obtained from an explicit realization of all the homogeneous hermitian holomorphic vector bundles on the unit disc under the action of the universal covering group of the bi holomorphic automorphism group of the unit disc

homogeneous vector bundles and intertwining operators for symmetric domains the main features of homogeneous cowen douglas operators well known for the unit disk are generalised to the setting of hermitian bounded symmetric domains of arbitrary rank c 2016 elsevier inc all rights reserved

k group and similarity classification of operators abstract let h be a complex separable hilbert space and l h denote the collection of bounded linear operators on h an operator a in l h is said to be a cowen douglas operator if there exist a connected open subset of complex plane c and n a positive integer such that a a z c a z is not invertible b ran a z y a z x y x h h for z in c z ker a z h and d dim ker a z n for z in in the paper we give a similarity classification of cowen douglas operators by using the ordered k group of the commutant algebra as an invariant and characterize the maximal ideals of the commutant algebras of cowen douglas operators the theorem greatly generalizes the main result in canada j math 156 4 2004 742 by simply removing the restriction of strong irreducibility of the operators the research is also partially inspired by the recent classification theory of simple ah algebras of elliott gong in documenta math 7 2002 255 on the classification of simple inductive limit c algebras ii the isomorphism theorem preprint also see j funct anal 1998 1 ann math 144 1996 497 amer j math 1996 187

h_ infty state estimation for discrete time complex networks with randomly occurring sensor saturations and randomly varying sensor delays in this paper the state estimation problem is investigated for a class of discrete time delay nonlinear complex networks with randomly occurring phenomena from sensor measurements the randomly occurring phenomena include randomly occurring sensor saturations rosss and randomly varying sensor delays rvsds that result typically from networked environments a novel sensor model is proposed to describe the rosss and the rvsds within a unified framework via two sets of bernoulli distributed white sequences with known conditional probabilities rather than employing the commonly used lipschitz type function a more general sector like nonlinear function is used to describe the nonlinearities existing in the network the purpose of the addressed problem is to design a state estimator to estimate the network states through available output measurements such that for all probabilistic sensor saturations and sensor delays the dynamics of the estimation error is guaranteed to be exponentially mean square stable and the effect from the exogenous disturbances to the estimation accuracy is attenuated at a given level by means of an h norm in terms of a novel lyapunov krasovskii functional and the kronecker product sufficient conditions are established under which the addressed state estimation problem is recast as solving a convex optimization problem via the semidefinite programming method a simulation example is provided to show the usefulness of the proposed state estimation conditions

a concept of convergence in geodesic spaces abstract a cat 0 space is a geodesic space for which each geodesic triangle is at least as thin as its comparison triangle in the euclidean plane a notion of convergence introduced independently several years ago by lim and kuczumow is shown in cat 0 spaces to be very similar to the usual weak convergence in banach spaces in particular many banach space results involving weak convergence have precise analogues in this setting at the same time many questions remain open

classification of quasi homogeneous holomorphic curves and operators in the cowen douglas class abstract in this paper we study quasi homogeneous operators which include the homogeneous operators in the cowen douglas class we give two separate theorems describing canonical models with respect to equivalence under unitary and invertible operators respectively for these operators using techniques from complex geometry this considerably extends the similarity and unitary classification of homogeneous operators in the cowen douglas class obtained recently by the last author and a koranyi in a significant generalization of the properties of the homogeneous operators we show that quasi homogeneous operators are irreducible and determine which of them are strongly irreducible applications include the equality of the topological and algebraic k group of a quasi homogeneous operator and an affirmative answer to a well known question of halmos

state estimation for stochastic complex networks with switching topology this technical note studies the state estimation problem for stochastic complex networks with switching topology a set of bernoulli random variables are used to describe the switching behavior of the network by using the structure of the extended kalman filter ekf a recursive estimator is developed for each node to guarantee an optimized upper bound on the state estimation error covariance despite the switching coupling and linearization errors compared with the existing results on state estimation for stochastic complex networks a distinct feature for the proposed estimator is that the estimation errors for all nodes are not formulated in an augmented vector so that the gain matrix can be determined separately for each node by solving two riccati like difference equations based on the stochastic analysis theory it is shown that the estimation error is bounded in mean square under certain conditions simulation results are provided to verify the effectiveness of the proposed estimator

bounded h_ infty synchronization and state estimation for discrete time varying stochastic complex networks over a finite horizon in this paper new synchronization and state estimation problems are considered for an array of coupled discrete time varying stochastic complex networks over a finite horizon a novel concept of bounded h synchronization is proposed to handle the time varying nature of the complex networks such a concept captures the transient behavior of the time varying complex network over a finite horizon where the degree of bounded synchronization is quantified in terms of the h norm a general sector like nonlinear function is employed to describe the nonlinearities existing in the network by utilizing a timevarying real valued function and the kronecker product criteria are established that ensure the bounded h synchronization in terms of a set of recursive linear matrix inequalities rlmis where the rlmis can be computed recursively by employing available matlab toolboxes the bounded h state estimation problem is then studied for the same complex network where the purpose is to design a state estimator to estimate the network states through available output measurements such that over a finite horizon the dynamics of the estimation error is guaranteed to be bounded with a given disturbance attenuation level again an rlmi approach is developed for the state estimation problem finally two simulation examples are exploited to show the effectiveness of the results derived in this paper

synchronization in complex networks with stochastically switching coupling structures synchronization in complex networks with time dependent coupling and stochastically switching coupling structure is discussed a novel approach investigating synchronization based on the scramblingness property of the coupling matrix is proposed some sufficient condition for a network with general time varying coupling structure to reach complete synchronization is provided based on the general theorem networks with stochastically switching coupling structures is investigated in particular two kinds of stochastic switching coupling networks are addressed a independent and identically distributed switching processes and b markov jump processes in both cases some sufficient condition for almost sure synchronization of the networks is given also numerical simulations are provided to illustrate the theoretical results

synchronization of complex networks via aperiodically intermittent pinning control in this note synchronization for linearly coupled network is investigated by pinning a simple aperiodically intermittent controller nodes dynamical behaviors in the network are described by continuous time ordinary differential equations some sufficient conditions to guarantee global synchronization are presented furthermore an adaptive algorithm is designed for the pinning control gain and its validity is also proved rigorously finally numerical simulations are given to demonstrate the correctness of obtained results

robust kalman filtering for uncertain discrete time systems this paper is concerned with the problem of a kalman filter design for uncertain discrete time systems the system under consideration is subjected to time varying norm bounded parameter uncertainty in both the state and output matrices the problem addressed is the design of a linear filter such that the variance of the filtering error is guaranteed to be within a certain bound for all admissible uncertainties furthermore the guaranteed cost can be optimized by appropriately searching a scaling design parameter

robust discrete time minimum variance filtering the bounded variance filtered estimation of the state of an uncertain linear discrete time system with an unknown norm bounded parameter matrix is considered an upper bound on the variance of the estimation error is found for all admissible systems and estimators are derived that minimize the latter bound we treat the finite horizon time varying case and the infinite time case where the nominal system model is time invariant in the special stationary case where it is known that the uncertain system is time invariant we provide a robust filter for all uncertainties that still keep the system asymptotically stable

homogeneous operators on hilbert spaces of holomorphic functions i in this paper we construct a large class of multiplication operators on reproducing kernel hilbert spaces which are homogeneous with respect to the action of the m o bius group consisting of bi holomorphic automorphisms of the unit disc mathbb d for every m in n we have a family of operators depending on m 1 positive real parameters the kernel function is calculated explicitly it is proved that each of these operators is bounded lies in the cowen douglas class of mathbb d and is irreducible these operators are shown to be mutually pairwise unitarily inequivalent

a contraction theory based analysis of the stability of the deterministic extended kalman filter the contraction properties of the extended kalman filter viewed as a deterministic observer for nonlinear systems are analyzed the approach relies on the study of an auxiliary virtual dynamical system some conditions under which exponential convergence of the state error can be guaranteed are derived moreover contraction provides a simple formalism to study some robustness properties of the filter especially with respect to measurement errors as illustrated by a simplified inertial navigation example this technical note sheds another light on the theoretical properties of this popular observer

state estimation for coupled uncertain stochastic networks with missing measurements and time varying delays the discrete time case this paper is concerned with the problem of state estimation for a class of discrete time coupled uncertain stochastic complex networks with missing measurements and time varying delay the parameter uncertainties are assumed to be norm bounded and enter into both the network state and the network output the stochastic brownian motions affect not only the coupling term of the network but also the overall network dynamics the nonlinear terms that satisfy the usual lipschitz conditions exist in both the state and measurement equations through available output measurements described by a binary switching sequence that obeys a conditional probability distribution we aim to design a state estimator to estimate the network states such that for all admissible parameter uncertainties and time varying delays the dynamics of the estimation error is guaranteed to be globally exponentially stable in the mean square by employing the lyapunov functional method combined with the stochastic analysis approach several delay dependent criteria are established that ensure the existence of the desired estimator gains and then the explicit expression of such estimator gains is characterized in terms of the solution to certain linear matrix inequalities lmis two numerical examples are exploited to illustrate the effectiveness of the proposed estimator design schemes

rigidity of the flag structure for a class of cowen douglas operators the explicit description of irreducible homogeneous operators in the cowen douglas class and the localization of hilbert modules naturally leads to the definition of a smaller class possessing a flag structure these operators are shown to be irreducible it is also shown that the flag structure is rigid that is the unitary equivalence class of the operator and the flag structure determine each other a complete set of unitary invariants which are somewhat more tractable than those of an arbitrary operator in the cowen douglas class is obtained c 2017 elsevier inc all rights reserved

exponential synchronization of linearly coupled neural networks with impulsive disturbances this brief investigates globally exponential synchronization for linearly coupled neural networks nns with time varying delay and impulsive disturbances since the impulsive effects discussed in this brief are regarded as disturbances the impulses should not happen too frequently the concept of average impulsive interval is used to formalize this phenomenon by referring to an impulsive delay differential inequality we investigate the globally exponential synchronization of linearly coupled nns with impulsive disturbances the derived sufficient condition is closely related with the time delay impulse strengths average impulsive interval and coupling structure of the systems the obtained criterion is given in terms of an algebraic inequality which is easy to be verified and hence our result is valid for large scale systems the results extend and improve upon earlier work as a numerical example a small world network composing of impulsive coupled chaotic delayed nn nodes is given to illustrate our theoretical result

h_ infty state estimation for discrete time nonlinear singularly perturbed complex networks under the round robin protocol this paper investigates the h infty state estimation problem for a class of discrete time nonlinear singularly perturbed complex networks spcns under the round robin rr protocol a discrete time nonlinear spcn model is first devised on two time scales with their discrepancies reflected by a singular perturbation parameter spp the network measurement outputs are transmitted via a communication network where the data transmissions are scheduled by the rr protocol with hope to avoid the undesired data collision the error dynamics of the state estimation is governed by a switched system with a periodic switching parameter a novel lyapunov function is constructed that is dependent on both the transmission order and the spp by establishing a key lemma specifically tackling the spp sufficient conditions are obtained such that for any spp less than or equal to a predefined upper bound the error dynamics of the state estimation is asymptotically stable and satisfies a prescribed h infty performance requirement furthermore the explicit parameterization of the desired state estimator is given by means of the solution to a set of matrix inequalities and the upper bound of the spp is then evaluated in the feasibility of these matrix inequalities moreover the corresponding results for linear discrete time spcns are derived as corollaries a numerical example is given to illustrate the effectiveness of the proposed state estimator design scheme

tensor products of operator spaces abstract in this paper we lay the foundations for a systematic study of tensor products of subspaces of c algebras to accomplish this various notions of duality are introduced and employed elementary proofs of the complete injectivity of the haagerup norm and of the extension theorem for completely bounded maps are given pisier s gamma norms are examined and found to be special cases of the haagerup norm we identify the greatest operator space cross norm and show that the spatial tensor norm is the least operator space cross norm in an appropriate sense indeed most of the elementary theory of banach space tensor norms generalizes to the category of operator spaces

the curvature invariant for a class of homogeneous operators for an operator t in the class b n introduced by cowen and douglas the simultaneous unitary equivalence class of the curvature and the covariant derivatives up to a certain order of the corresponding bundle e t determine the unitary equivalence class of the operator t in a subsequent paper the authors ask if the simultaneous unitary equivalence class of the curvature and these covariant derivatives are necessary to determine the unitary equivalence class of the operator t is an element of b n here we show that some of the covariant derivatives are necessary our examples consist of homogeneous operators in b n for homogeneous operators the simultaneous unitary equivalence class of the curvature and all its covariant derivatives at any point w in the unit disc are determined from the simultaneous unitary equivalence class at 0 this shows that it is enough to calculate all the invariants and compare them at just one point say 0 these calculations are then carried out in number of examples one of our main results is that the curvature along with its covariant derivative of order 0 1 at 0 determines the equivalence class of generic homogeneous hermitian holomorphic vector bundles over the unit disc

equivalence of quotient hilbert modules ii for any open connected and bounded set c m let a be a natural function algebra consisting of functions holomorphic on let m be a hilbert module over the algebra a and m0 m be the submodule of functions vanishing to order k on a hypersurface z recently the authors have obtained an explicit complete set of unitary invariants for the quotient module q m m0 in the case of k 2 in this paper we relate these invariants to familiar notions from complex geometry we also find a complete set of unitary invariants for the general case we discuss many concrete examples in this setting as an application of our equivalence results we characterise certain homogeneous hilbert modules over the bi disc algebra one source of fascination in the study of operator theory is the wide variety of connections made with other branches of mathematics techniques from algebra topology geometry and analysis are used to understand bounded linear operators on hilbert space and in many instances the behavior and properties of the operators can be used to illustrate critical features and aspects of the other fields this is particularly true in the case of multivariate operator theory that is when several operators or an algebra of operators is studied here the setting and results from these other areas can be quite sophisticated and the techniques used to understand multivariate operator theory often require additional development such is the focus of this paper although the spectral theorem is a key tool in the study of self adjoint and normal opera tors there are large and important classes of naturally occurring operators to which this theory doesn t apply examples illustrating such phenomena can be obtained by considering multipli cation operators on spaces of holomorphic functions on some domain in c m for domains in c one is in the realm of single operator theory while it is multivariate operator theory for m 1 if one considers the unit ball b m in c m and the bergman space a 2 b m for it one obtains a

similarity classification of holomorphic curves abstract let h be a complex separable hilbert space for an open connected subset of c we shall say that a map f gr n h is a holomorphic curve if there exist n holomorphic h valued functions 1 2 n on such that f 1 n where gr n h denotes the grassmann manifold the set of all n dimensional subspaces of h in the paper we give a similarity classification of some holomorphic curves by using the k group of its commutant algebra as an invariant

a variance constrained approach to recursive state estimation for time varying complex networks with missing measurements in this paper the recursive state estimation problem is investigated for an array of discrete time varying coupled stochastic complex networks with missing measurements a set of random variables satisfying certain probabilistic distributions is introduced to characterize the phenomenon of the missing measurements where each sensor can have individual missing probability the taylor series expansion is employed to deal with the nonlinearities and the high order terms of the linearization errors are estimated the purpose of the addressed state estimation problem is to design a time varying state estimator such that in the presence of the missing measurements and the random disturbances an upper bound of the estimation error covariance can be guaranteed and the explicit expression of the estimator parameters is given by using the riccati like difference equations approach the estimator parameter is characterized by the solutions to two riccati like difference equations it is shown that the obtained upper bound is minimized by the designed estimator parameters and the proposed state estimation algorithm is of a recursive form suitable for online computation finally an illustrative example is provided to demonstrate the feasibility and effectiveness of the developed state estimation scheme

h_ infty state estimation for complex networks with uncertain inner coupling and incomplete measurements in this paper the h state estimation problem is investigated for a class of complex networks with uncertain coupling strength and incomplete measurements with the aid of the interval matrix approach we make the first attempt to characterize the uncertainties entering into the inner coupling matrix the incomplete measurements under consideration include sensor saturations quantization and missing measurements all of which are assumed to occur randomly by introducing a stochastic kronecker delta function these incomplete measurements are described in a unified way and a novel measurement model is proposed to account for these phenomena occurring with individual probability with the measurement model a set of h state estimators is designed such that for all admissible incomplete measurements as well as the uncertain coupling strength the estimation error dynamics is exponentially mean square stable and the h performance requirement is satisfied the characterization of the desired estimator gains is derived in terms of the solution to a convex optimization problem that can be easily solved using the semidefinite program method finally a numerical simulation example is provided to demonstrate the effectiveness and applicability of the proposed design approach

extended kalman filtering with stochastic nonlinearities and multiple missing measurements in this paper the extended kalman filtering problem is investigated for a class of nonlinear systems with multiple missing measurements over a finite horizon both deterministic and stochastic nonlinearities are included in the system model where the stochastic nonlinearities are described by statistical means that could reflect the multiplicative stochastic disturbances the phenomenon of measurement missing occurs in a random way and the missing probability for each sensor is governed by an individual random variable satisfying a certain probability distribution over the interval 0 1 such a probability distribution is allowed to be any commonly used distribution over the interval 0 1 with known conditional probability the aim of the addressed filtering problem is to design a filter such that in the presence of both the stochastic nonlinearities and multiple missing measurements there exists an upper bound for the filtering error covariance subsequently such an upper bound is minimized by properly designing the filter gain at each sampling instant it is shown that the desired filter can be obtained in terms of the solutions to two riccati like difference equations that are of a form suitable for recursive computation in online applications an illustrative example is given to demonstrate the effectiveness of the proposed filter design scheme

stochastic stability of the discrete time extended kalman filter the authors analyze the error behavior for the discrete time extended kalman filter for general nonlinear systems in a stochastic framework in particular it is shown that the estimation error remains bounded if the system satisfies the nonlinear observability rank condition and the initial estimation error as well as the disturbing noise terms are small enough this result is verified by numerical simulations for an example system

mode dependent stochastic synchronization for markovian coupled neural networks with time varying mode delays this paper investigates the stochastic synchronization problem for markovian hybrid coupled neural networks with interval time varying mode delays and random coupling strengths the coupling strengths are mutually independent random variables and the coupling configuration matrices are nonsymmetric a mode dependent augmented lyapunov krasovskii functional lkf is proposed where some terms involving triple or quadruple integrals are considered which makes the lkf matrices mode dependent as much as possible this gives significant improvement in the synchronization criteria i e less conservative results can be obtained in addition by applying an extended jensen s integral inequality and the properties of random variables new delay dependent synchronization criteria are derived the obtained criteria depend not only on upper and lower bounds of mode delays but also on mathematical expectations and variances of the random coupling strengths finally two numerical examples are provided to demonstrate the feasibility of the proposed results

synchronization of complex dynamical networks with switching topology a switched system point of view in this paper we study the synchronization problem for complex dynamical networks with switching topology from a switched system point of view the synchronization problem is transformed into the stability problem for time varying switched systems we address two basic problems synchronization under arbitrary switching topology and synchronization via design of switching within a pre given collection of topologies when synchronization cannot be achieved by using any topology alone in this collection for the both problems we first establish synchronization criteria for general connection topology then under the condition of simultaneous triangularization of the connection matrices a common lyapunov function for the first problem and a single lyapunov and multiple lyapunov functions for the second problem are systematically constructed respectively by those of several lower dimensional dynamic systems in order to achieve synchronization using multiple lyapunov functions a stability condition and switching law design method for time varying switched systems are also presented which avoid the usual non increasing condition

finite time state estimation for coupled markovian neural networks with sensor nonlinearities this paper investigates the issue of finite time state estimation for coupled markovian neural networks subject to sensor nonlinearities where the markov chain with partially unknown transition probabilities is considered a luenberger type state estimator is proposed based on incomplete measurements and the estimation error system is derived by using the kronecker product by using the lyapunov method sufficient conditions are established which guarantee that the estimation error system is stochastically finite time bounded and stochastically finite time stable respectively then the estimator gains are obtained via solving a set of coupled linear matrix inequalities finally a numerical example is given to illustrate the effectiveness of the proposed new design method

a polynomially bounded operator on hilbert space which is not similar to a contraction let e 0 we prove that there exists an operator te e2 2 such that for any polynomial p we have iip te ii not similar to a contraction i e there does not exist an invertible operator s f2 e f2 such that jis 1tesii tributed to halmos after his well known 1970 paper ten problems in hilbert space we also give some related finite dimensional estimates department of mathematics texas a m university college station texas 77843 universite paris vi equipe d7analyse case 186 75252 paris cedex 05 france e mail address gipqccr jussieu fr this content downloaded from 157 55 39 104 on sun 19 jun 2016 06 52 47 utc all use subject to http about jstor org terms

fixed point theory for almost convex functions traditionally metric fixed point theory has sought classes of spaces in which a given type of mapping nonexpansive assymptotically or generalized nonexpansive uniformly lipschitz etc from a nonempty weakly compact convex set into itself always has a fixed point in some situations the class of space is determined by the application while there is some degree of freedom in constructing the map to be used with this in mind we seek to relax the conditions on the space by considering more restrictive types of mappings

mixed h_2 h_ infty state estimation for discrete time switched complex networks with random coupling strengths through redundant channels this article investigates the mixed h 2 h infty state estimation problem for a class of discrete time switched complex networks with random coupling strengths through redundant communication channels a sequence of random variables satisfying certain probability distributions is employed to describe the stochasticity of the coupling strengths a redundant channel based data transmission mechanism is adopted to enhance the reliability of the transmission channel from the sensor to the estimator the purpose of the addressed problem is to design a state estimator for each node such that the error dynamics achieves both the stochastic stability with probability 1 and the prespecified mixed h 2 h infty performance requirement by using the switched system theory an extensive stochastic analysis is carried out to derive the sufficient conditions ensuring the stochastic stability as well as the mixed h 2 h infty performance index the desired state estimator is also parameterized by resorting to the solutions to certain convex optimization problems a numerical example is provided to illustrate the validity of the proposed estimation scheme