stability analysis of markovian jump stochastic bam neural networks with impulse control and mixed time delays this paper discusses the issue of stability analysis for a class of impulsive stochastic bidirectional associative memory neural networks with both markovian jump parameters and mixed time delays the jumping parameters are modeled as a continuous time discrete state markov chain based on a novel lyapunov krasovskii functional the generalized ito s formula mathematical induction and stochastic analysis theory a linear matrix inequality approach is developed to derive some novel sufficient conditions that guarantee the exponential stability in the mean square of the equilibrium point at the same time we also investigate the robustly exponential stability in the mean square of the corresponding system with unknown parameters it should be mentioned that our stability results are delay dependent which depend on not only the upper bounds of time delays but also their lower bounds moreover the derivatives of time delays are not necessarily zero or smaller than one since several free matrices are introduced in our results consequently the results obtained in this paper are not only less conservative but also generalize and improve many earlier results finally two numerical examples and their simulations are provided to show the effectiveness of the theoretical results

hilbert schmidtness of some finitely generated submodules in h2 d2 abstract a closed subspace m of the hardy space h 2 d 2 over the bidisk is called a submodule if it is invariant under multiplication by coordinate functions z 1 and z 2 whether every finitely generated submodule is hilbert schmidt is an unsolved problem this paper proves that every finitely generated submodule m containing z 1 z 2 is hilbert schmidt where is any finite blaschke product some other related topics such as fringe operator and fredholm index are also discussed

invariant subspaces dilation theory and the structure of the predual of a dual algebra i on etudie la structure des preduaux d algebres d operateurs on obtient un nouveau theoreme de sous espace invariant on trouve des proprietes concernant le treillis sous espace invariant de l operateur decalage de bergman

asymptotical boundedness for stochastic coupled systems on networks driven by g brownian motion abstract this paper investigates a class of stochastic coupled systems on networks driven by g brownian motion g scsn in short by means of inequality techniques kth vertex g lyapunov functions and graph theory we obtain the asymptotical boundedness for g scsn moreover pth exponential stability is derived as an application a class of stochastic coupled cohen grossberg neural networks driven by g brownian motion are discussed moreover an example is given to illustrate the theory obtained

stabilization of hybrid stochastic differential equations by feedback control based on discrete time state observations recently mao 2013 discusses the mean square exponential stabilization of continuous time hybrid stochastic differential equations by feedback controls based on discrete time state observations mao 2013 also obtains an upper bound on the duration between two consecutive state observations however it is due to the general technique used there that the bound on is not very sharp in this paper we will consider a couple of important classes of hybrid sdes making full use of their special features we will be able to establish a better bound on our new theory enables us to observe the system state less frequently so costs less but still to be able to design the feedback control based on the discrete time state observations to stabilize the given hybrid sdes in the sense of mean square exponential stability

the spectral picture of reinhardt measures using a combination of techniques from the theory of groupoids the theory of several complex variables and single and multivariable operator theory we describe in detail the spectral picture of the commuting pair mz1 mz2 of multiplication operators by the coordinate functions z1 and z2 acting on the hilbert space p2 c z1 z2 l2 for an arbitrary reinhardt measure on c2

subalgebras of c algebras iii multivariable operator theory a d contraction is a d tuple t1 td of mutually commuting operators acting on a common hilbert space h such that t1 1 t2 2 td d 1 2 d for all 1 2 d h these are the higher dimensional counterparts of contractions we show that many of the operator theoretic aspects of function theory in the unit disk generalize to the unit ball bd in complex d space including von neumann s inequality and the model theory of contractions these results depend on properties of the d shift a distinguished d contraction which acts on a new h2 space associated with bd and which is the higher dimensional counterpart of the unilateral shift h 2 and the d shift are highly unique indeed by exploiting the noncommutative choquet boundary of the d shift relative to its generated c algebra we find that there is more uniqueness in dimension d 2 than there is in dimension one

operator theory in the hardy space over the bidisk iii this paper is a continuation of a project of developing a systematic operator theory inh2 d2 a large part of it is devoted to a study ofevaluation operator which is a very useful tool in the theory a number of elementary properties of the evaluation operator are exhibited and these properties are used to derive results in other topics such as interpretation of characteristic opertor function inh2 d2 spectral equivalence compactness compressions of shift operators etc even though some results reflect the two variable nature ofh2 d2 the goal of this paper is to manifest a close tie between the operator theory inh2 d2 and classical single operator theory the unilateral shift of a finite multiplicity and the bergman shift will be used as examples to illustrate some of the results

free resolutions in multivariable operator theory let ad be the complex polynomial ring in d variables a contractive ad module is hilbert space h equipped with an ad action such that for any 1 2 d h z1 1 z2 zd d 2 1 2 2 2 d 2 such objects have been shown to be useful for modeling d tuples of mutually commuting operators acting on a hilbert space there is a subclass of the category of contractive ad modules whose members play the role of free objects given a contractive ad module one can construct a free resolution i e an exact sequence of partial isometries of the following form 2f1 1f0 0h 0 where fi is a free module for each i 0 the notion of a localization of a free resolution will be defined in which for each bd there is a vector space complex of linear maps derived from 3 c2 2 c1 1 c0 we shall show that the homology of this complex is isomorphic to the homology of the koszul complex of the d tuple 1 2 d of where i is the ith coordinate function of a mobius transform on bd such that 0

stability analysis for neural networks with time varying delay based on quadratic convex combination in this paper a novel method is developed for the stability problem of a class of neural networks with time varying delay new delay dependent stability criteria in terms of linear matrix inequalities for recurrent neural networks with time varying delay are derived by the newly proposed augmented simple lyapunov krasovski functional different from previous results by using the first order convex combination property our derivation applies the idea of second order convex combination and the property of quadratic convex function which is given in the form of a lemma without resorting to jensen s inequality a numerical example is provided to verify the effectiveness and superiority of the presented results

technical communique stabilization of continuous time hybrid stochastic differential equations by discrete time feedback control in this paper we are concerned with the mean square exponential stabilization of continuous time hybrid stochastic differential equations also known as stochastic differential equations with the markovian switching by discrete time feedback controls although the stabilization by continuous time feedback controls for such equations has been discussed by several authors see e g ji and chizeck 1990 mao lam and huang 2008 mao yin and yuan 2007 wu shi and gao 2010 wu su and shi 2012 there is so far no result on the stabilization by discrete time feedback controls our aim here is to initiate the study in this area by establishing some new results

dilations wandering subspaces and inner functions the objective of this paper is to study wandering subspaces for commuting tuples of bounded operators on hilbert spaces it is shown that for a large class of analytic functional hilbert spaces h k on the unit ball in c n wandering subspaces for restrictions of the multiplication tuple m z m z1 m zn can be described in terms of suitable h k inner functions we prove that h k inner functions are contractive multipliers and deduce a result on the multiplier norm of quasi homogeneous polynomials as an application along the way we prove a refinement of a result of arveson on the uniqueness of minimal dilations of pure row contractions c 2017 elsevier inc all rights reserved

stabilization of multi group models with multiple dispersal and stochastic perturbation via feedback control based on discrete time state observations abstract this paper focuses on the multi group models with multiple dispersal and stochastic perturbation mgmds the effect of both multiple dispersal among groups and stochastic perturbation are taken into consideration the stabilization of mgmds is investigated via feedback control based on the discrete time state observations in addition a systematic method is given to construct a global lyapunov function for mgmds by means of graph theory and lyapunov method some sufficient conditions are obtained to ensure the stabilization in the sense of mean square asymptotical stability an upper bound of the duration between two consecutive state observations is estimated moreover to show the applicability of our results the main theory is employed to a stochastic coupled oscillators finally a numerical example is given to illustrate the effectiveness and feasibility of the theoretical results

the dirac operator of a commuting d tuple abstract given a commuting d tuple t t1 td of otherwise arbitrary operators on a hilbert space there is an associated dirac operator dt significant attributes of the d tuple are best expressed in terms of dt including the taylor spectrum and the notion of fredholmness in fact all properties of t derive from its dirac operator we introduce a general notion of dirac operator in dimension d 1 2 that is appropriate for multivariable operator theory we show that every abstract dirac operator is associated with a commuting d tuple and that two dirac operators are isomorphic iff their associated operator d tuples are unitarily equivalent by relating the curvature invariant introduced in a previous paper to the index of a dirac operator we establish a stability result for the curvature invariant for pure d contractions of finite rank it is shown that for the subcategory of all such t that are a fredholm and and b graded the curvature invariant k t is stable under compact perturbations we do not know if this stability persists when t is fredholm but ungraded although there is concrete evidence that it does

robust stability and stabilization of fractional order linear systems with polytopic uncertainties robust stability and stabilization of fractional order uncertain linear systems with order 0 1 and 1 2 are considered in the paper a new polytopic type uncertain state space model for fractional order linear systems is addressed which allows second order uncertain parameters the uncertainty in the fractional order model appears in terms of a polytope of matrices some sufficient criteria for the robust asymptotical stable and stabilization for such fractional order uncertain linear systems are derived all the results are obtained in terms of linear matrix inequalities lmis numerical examples are presented to demonstrate the validity and feasibility of the obtained results

stochastic approach for the solution of multi pantograph differential equation arising in cell growth model in this paper a computational technique is introduced for the solution of the first order multi pantograph differential equation mpde through some well known optimization algorithms like sequential quadratic programming sqp and active set technique ast furthermore artificial neural network ann is used for networking of the first order multi pantograph differential equation in used to provide mathematical model based on unsupervised error for equation moreover mathematical modeling has been performed perfectly through multi runs for simulation to justify the better convergence of the solutions also two examples are presented to exhibit the aptitude of the method sqp and ast the comparative study will be made with reported techniques such as variational iteration technique vit 6 and collocation based on bernstein polynomial method bcm 6

robust h_ infty fuzzy output feedback control with multiple probabilistic delays and multiple missing measurements in this paper the robust h control problem is investigated for a class of uncertain discrete time fuzzy systems with both multiple probabilistic delays and multiple missing measurements a sequence of random variables all of which are mutually independent but obey the bernoulli distribution is introduced to account for the probabilistic communication delays the measurement missing phenomenon occurs in a random way the missing probability for each sensor satisfies a certain probabilistic distribution in the interval here the attention is focused on the analysis and design of h fuzzy output feedback controllers such that the closed loop takagi sugeno t s fuzzy control system is exponentially stable in the mean square the disturbance rejection attenuation is constrained to a given level by means of the h performance index intensive analysis is carried out to obtain sufficient conditions for the existence of admissible output feedback controllers which ensures the exponential stability as well as the prescribed h performance the cone complementarity linearization procedure is employed to cast the controller design problem into a sequential minimization one that is solved by the semi definite program method simulation results are utilized to demonstrate the effectiveness of the proposed design technique in this paper

the curvature of a hilbert module over ℂ z1 zd a notion of curvature is introduced in multivariable operator theory the curvature invariant of a hilbert module over z1 zd is a nonnegative real number which has significant extremal properties which tends to be an integer and which is hard to compute directly it is shown that for graded hilbert modules the curvature agrees with the euler characteristic of a certain finitely generated algebraic module over the appropriate polynomial ring this result is a higher dimensional operator theoretic counterpart of the gauss bonnet formula which expresses the average gaussian curvature of a compact oriented riemann surface as the alternating sum of the betti numbers of the surface and it solves the problem of calculating the curvature of graded hilbert modules the proof of that result is based on an asymptotic formula which expresses the curvature of a hilbert module in terms that allow its comparison to a corresponding asymptotic expression for the euler characteristic

spherical contractions and interpolation problems on the unit ball in this note fractional representations of multipliers on vector valued functional hilbert spaces are used to give a proof of arveson s version of von neumann s inequality for n contractions on the unit ball we prove a commutant lifting theorem for operators on the classical hardy space over the unit ball in mathbb c n as applications we obtain interpolation results for functions in the schur class we deduce a toeplitz corona theorem on the unit ball and we give a simplified definition of arveson s curvature invariant for n contractions with finite dimensional defect space in the final part we describe a solution of the operator valued nevanlinna pick problem with uniform bounds on uniqueness sets in the unit ball

stabilisation of hybrid stochastic differential equations by delay feedback control this paper is concerned with the exponential mean square stabilisation of hybrid stochastic differential equations also known as stochastic differential equations with markovian switching by delay feedback controls although the stabilisation by non delay feedback controls for such equations has been discussed by several authors there is so far little on the stabilisation by delay feedback controls and our aim here is mainly to close the gap to make our theory more understandable as well as to avoid complicated notations we will restrict our underlying hybrid stochastic differential equations to a relatively simple form however our theory can certainly be developed to cope with much more general equations without any difficulty

an invariant subspace of the bergman space having the codimension two property nutzungsbedingungen digizeitschriften e v gewahrt ein nicht exklusives nicht ubertragbares personliches und beschranktes recht auf nutzung dieses dokuments dieses dokument ist ausschlieslich fur den personlichen nicht kommerziellen gebrauch bestimmt das copyright bleibt bei den herausgebern oder sonstigen rechteinhabern als nutzer sind sie sind nicht dazu berechtigt eine lizenz zu ubertragen zu transferieren oder an dritte weiter zu geben die nutzung stellt keine ubertragung des eigentumsrechts an diesem dokument dar und gilt vorbehaltlich der folgenden einschrankungen sie mussen auf samtlichen kopien dieses dokuments alle urheberrechtshinweise und sonstigen hinweise auf gesetzlichen schutz beibehalten und sie durfen dieses dokument nicht in irgend einer weise abandern noch durfen sie dieses dokument fur offentliche oder kommerzielle zwecke vervielfaltigen offentlich ausstellen auffuhren vertreiben oder anderweitig nutzen es sei denn es liegt ihnen eine schriftliche genehmigung von digizeitschriften e v und vom herausgeber oder sonstigen rechteinhaber vor mit dem gebrauch von digizeitschriften e v und der verwendung dieses dokuments erkennen sie die nutzungsbedingungen an

stochastic dissipativity and passivity analysis for discrete time neural networks with probabilistic time varying delays in the leakage term this paper deals with the dissipativity and passivity analysis for discrete time stochastic neural networks with probabilistic time varying delays the main contribution of this paper is to reduce the conservatism of the dissipativity conditions for the considered neural networks by utilizing the reciprocally convex combination approach this approach is proposed to bound the forward differences of the double and triple summable terms taken in the lyapunov functional by introducing a stochastic variable with a bernoulli distribution the information of probability distribution of the time varying delays are considered and transformed into one with deterministic time varying delays by employing lyapunov functional approach sufficient conditions are derived in terms of linear matrix inequalities to guarantee that the considered neural networks to be strictly q s r dissipative and passive finally numerical examples are given to demonstrate the effectiveness of the obtained results

global stability problem for coupled systems of differential equations on networks the global stability problem of equilibria is investigated for coupled systems of differential equations on networks using results from graph theory we develop a systematic approach that allows one to construct global lyapunov functions for large scale coupled systems from building blocks of individual vertex systems the approach is applied to several classes of coupled systems in engineering ecology and epidemiology and is shown to improve existing results

rhythm synchronization and chaotic modulation of coupled van der pol oscillators in a model for the heartbeat we investigate a phenomenological model for the heartbeat consisting of two coupled van der pol oscillators the coupling between these nodes can be both unidirectional or bidirectional and an external driving produced by a pacemaker is also included in this model in order to warrant a robust operation it is desirable that both units oscillate in a synchronized way even though in the presence of external in0uences or parameter mismatches which are unavoidable in a physiological setting we study the synchronization properties of such an association with respect to the nature andintensity of coupling we analyze in particular the generalized synchronization of rhythms characterizedby a chaotic mod ulation of the oscillator frequencies we also investigate the shadowing breakdown of numerically generated chaotic trajectories of the coupled oscillator system via unstable dimension variability in its chaotic invariant set c

the stability of stochastic coupled systems with time varying coupling and general topology structure we introduce a class of novel stochastic coupled systems in which the coupling structure is time varying and the topology structure is not strongly connected and first establish the system on a digraph with a time varying weight matrix motivated by du and li 2014 we give a hierarchical method to deal with digraphs without strong connectivity and establish the corresponding hierarchical algorithm to realize this approach also an example is given to illustrate our hierarchical algorithm and its feasibility in the sequel based on the theory of asymptotically autonomous systems kirchhoff s matrix tree theorem and lyapunov method several moment exponential stability criteria are presented including a lyapunov type theorem and a coefficient type criterion furthermore theoretical results are applied to stochastic coupled oscillators with time varying coupling structure sctcs and the stability criterion of sctcs is obtained finally the effectiveness of theoretical results is illustrated by two numerical examples

fredholm and invertible tuples of operators the deformation problem using j l taylor s definition of joint spectrum we study fredholm and invertible tuples of operators on a hilbert space we give the foundations for a several variables theory including a natural generalization of atkinson s theorem and an index which well behaves we obtain a characterization of joint invertibility in terms of a single operator and study the main examples at length we then consider the deformation problem and solve it for the class of almost doubly commuting fredholm pairs with a semi fredholm coordinate 1 introduction 1 let t be a bounded linear operator on a banach space t is said to be invertible if there exists an operator s on such that ts st 1 the identity operator on 9c by the open mapping theorem this is equivalent to ker t 0 and r t range of t the last formulation does not rely upon the existence of an inverse for t but rather on the action of the operator t when t is replaced by an tuple of commuting operators several definitions of nonsingular ity exist j l taylor 19 has obtained one which reflects the actions of the operators by considering the koszul complex associated with the tuple 2 in this paper we develop a general several variables theory on the basis of taylor s work and study commuting and almost commuting commuting mod ulo the compacts tuples of operators on a hilbert space we obtain a characterization of joint invertibility in terms of the invertibility of a single operator which is essential for our approach from that we get a number of corollaries which generalize nicely the known elementary results in one variable at the same time the referred characterization allows us to define a continuous invariant under compact perturbations integer valued index on the class of fred holm tuples those almost commuting tuples which are invertible in the calkin algebra this index extends the classical one for fredholm operators we prove that an almost commuting tuple of essentially normal operators with all commu tators in trace class has index zero 2 and that a natural generalization of atkinson s theorem holds for tuples

the structure of inner multipliers on spaces with complete nevanlinna pick kernels let k be the reproducing kernel for a hilbert space h k of analytic functions on bd the open unit ball in cd d 1 k is called a complete np kernel if k0 1 and if 1 1 k z is positive definite on bd bd let d be a separable hilbert space and consider h k d h k d and think of it as a space of d valued h k functions a theorem of mccullough and trent j funct anal 178 2000 226 249 partially extends the beurling lax halmos theorem for the invariant subspaces of the hardy space h2 d they show that if k is a complete np kernel and if d is a separable hilbert space then for any scalar multiplier invariant subspace m of h k d there exists an auxiliary hilbert space e and a multiplication operator h k e h k d such that is a partial isometry and m h k e such multiplication operators are called inner multiplication operators and they satisfy the orthogonal projection onto m in this paper we shall show that for many interesting complete np kernels the analogy with the beurling lax halmos theorem can be strengthened we show that for almost every z bd the nontangential limit z of the multiplier bd b e d associated with an inner multiplication operator is a partial isometry and that rank z is equal to a constant almost everywhere the result applies to certain weighted dirichlet spaces and to the space h2d which is determined by the kernel k z 11 z d z bd in particular our result implies that the curvature invariant of arveson proc natl acad sci usa96 1999 11 096 11 099 of a pure contractive hilbert module of finite rank is an integer this answers a question of w arveson proc natl acad sci usa96 1999 11096 11099

invariant subspaces in banach spaces of analytic functions we study the invariant subspace structure of the operator of multiplication by z mz on a class of banach spaces of analytic functions for operators on hilbert spaces our class coincides with the adjoints of the operators in the cowendouglas class 1 q we say that an invariant subspace x satisfies cod x 1 if zx has codimension one in x we give various conditions on invariant subspaces which imply that codx 1 in particular we give a necessary and sufficient condition on two invariant subspaces x x with cod x cod x 1 so that their span again satisfies cod x v x 1 this result will be used to show that any invariant subspace of the bergman space l p 1 which is generated by functions in l2p must satisfy cod x 1 for an invariant subspace x we then consider the operator s m 1xl under some extra assumption on the domain of holomorphy we show that the spectrum of s coincides with the approximate point spectrum iff cod x 1 finally in the last section we obtain a structure theorem for invariant subspaces with cod x 1 this theorem applies to dirichlet type spaces

linear graph transformations on spaces of analytic functions let h be a hilbert space of analytic functions with multiplier algebra m h and let m f t 1 f t n 1 f f is an element of d be an invariant graph subspace for m h n here n 2 d subset of h is a vector subspace t i d h are linear transformations that commute with each multiplication operator m phi is an element of m h and m is closed in h n in this paper we investigate the existence of non trivial common invariant subspaces of operator algebras of the type a m a is an element of b h ad subset of d at i f t i af for all f is an element of d in particular for the bergman space l 0 2 we exhibit examples of invariant graph subspaces of fiber dimension 2 such that a m does not have any nontrivial invariant subspaces that are defined by linear relations of the graph transformations for m c 2015 elsevier inc all rights reserved less

a novel approach to output feedback control of fuzzy stochastic systems this paper investigates the problem of hankel norm output feedback controller design for a class of t s fuzzy stochastic systems the full order output feedback controller design technique with the hankel norm performance is proposed by the fuzzy basis dependent lyapunov function approach and the conversion on the hankel norm controller parameters sufficient conditions are established to design the controllers such that the resulting closed loop system is stochastically stable and satisfies a prescribed performance the desired output feedback controller can be obtained by solving a convex optimization problem which can be efficiently solved by standard numerical algorithms finally a henon map system is used to illustrate the effectiveness of the proposed techniques

schlesinger transformations for the second members of pii and piv hierarchies in this paper we give a method to obtain the schlesinger transformations for the second members of second and fourth painlev e hierarchies the procedure involves formulating a riemann hilbert problem for a transformation matrix which transforms the solution of the linear problem but leaves the associated monodromy data the same

curvature invariant on noncommutative polyballs abstract in this paper we develop a theory of curvature resp multiplicity invariant for tensor products of full fock spaces f 2 h n 1 f 2 h n k and also for tensor products of symmetric fock spaces f s 2 h n 1 f s 2 h n k this is an attempt to find a more general framework for these invariants and extend some of the results obtained by arveson for the symmetric fock space by the author and kribs for the full fock space and by fang for the hardy space h 2 d k over the polydisc to prove the existence of the curvature and its basic properties in these settings requires a new approach based on noncommutative berezin transforms and multivariable operator theory on polyballs and varieties as well as summability results for completely positive maps the results are presented in the more general setting of regular polyballs

cyclic row contractions and rigidity of invariant subspaces abstract it is known that pure row contractions with one dimensional defect spaces can be classified up to unitary equivalence by compressions of the standard d shift acting on the full fock space upon settling for a softer relation than unitary equivalence we relax the defect condition and simply require the row contraction to admit a cyclic vector we show that cyclic pure row contractions can be transformed in a precise technical sense into compressions of the standard d shift cyclic decompositions of the underlying hilbert spaces are the natural tool to extend this fact to higher multiplicities we show that such decompositions face multivariate obstacles of an algebraic nature nevertheless decompositions are obtained for nilpotent commuting row contractions by analyzing function theoretic rigidity properties of their invariant subspaces

a comprehensive review of stability analysis of continuous time recurrent neural networks stability problems of continuous time recurrent neural networks have been extensively studied and many papers have been published in the literature the purpose of this paper is to provide a comprehensive review of the research on stability of continuous time recurrent neural networks including hopfield neural networks cohen grossberg neural networks and related models since time delay is inevitable in practice stability results of recurrent neural networks with different classes of time delays are reviewed in detail for the case of delay dependent stability the results on how to deal with the constant variable delay in recurrent neural networks are summarized the relationship among stability results in different forms such as algebraic inequality forms m matrix forms linear matrix inequality forms and lyapunov diagonal stability forms is discussed and compared some necessary and sufficient stability conditions for recurrent neural networks without time delays are also discussed concluding remarks and future directions of stability analysis of recurrent neural networks are given

global stability of multi group epidemic models with distributed delays abstract we investigate a class of multi group epidemic models with distributed delays we establish that the global dynamics are completely determined by the basic reproduction number r 0 more specifically we prove that if r 0 1 then the disease free equilibrium is globally asymptotically stable if r 0 1 then there exists a unique endemic equilibrium and it is globally asymptotically stable our proof of global stability of the endemic equilibrium utilizes a graph theoretical approach to the method of lyapunov functionals

invariant subspaces and nevanlinna pick kernels abstract a theorem of beurling lax halmos represents a subspace m of h2 c d the hardy space of analytic functions with values in the hilbert space e and square summable power series invariant for multiplication by z as h2 f where f is a subspace of e and is an inner function with values in l f e when the hardy space is replaced by the hilbert space h k determined by a nevanlinna pick kernel k such as the dirichlet kernel or the row contraction kernel on the ball in c d the blh theorem survives with f an auxiliary hilbert space and a l f e valued function which is inner in the sense that the operator m of multiplication by is a partial isometry under mild additional hypotheses when e c mz the operator of multiplication by z is cellularly indecomposable and has the codimension one property however if m is invariant for mz m mz m need not be a cyclic subspace for mz restricted to m

global stability of the endemic equilibrium of multigroup sir models with nonlinear incidence in this paper we introduce a basic reproduction number for a multigroup epidemic model with nonlinear incidence then we establish that global dynamics are completely determined by the basic reproduction number r 0 it shows that the basic reproduction number r 0 is a global threshold parameter in the sense that if it is less than or equal to one the disease free equilibrium is globally stable and the disease dies out whereas if it is larger than one there is a unique endemic equilibrium which is globally stable and thus the disease persists in the population finally a numerical example is also included to illustrate the effectiveness of the proposed result

stabilization of hybrid systems by feedback control based on discrete time state observations recently mao automatica j ifac 49 2013 pp 3677 3681 initiated the study the mean square exponential stabilization of continuous time hybrid stochastic differential equations by feedback controls based on discrete time state observations in the same paper mao also obtains an upper bound on the duration tau between two consecutive state observations however it is due to the general technique used there that the bound on tau is not very sharp in this paper we will be able to establish a better bound on tau making use of lyapunov functionals we will discuss the stabilization not only in the sense of exponential stability as mao does in automatica j ifac 49 2013 pp 3677 3681 but also in other sense that of h infty stability or asymptotic stability we will consider not only the mean square stability but also the almost sure stability

stabilization of stochastic delay systems via a disordered controller abstract in this paper the stabilization for stochastic delay systems is achieved by a disordered controller different from the traditionally stabilizing controllers the controller designed here experiences a disorder between control gains and system states by exploiting the robust method the above disorder is described as a controller having special uncertainties moreover the probability distribution of such uncertainties is embodied by a bernoulli variable a sufficient condition for the existence of such a disordered controller is given with lmis where the probability is considered in its design procedure based on this description a more general but complicated case where the corresponding probability is not exact but has a uncertainty is further studied whose lmi conditions are presented too finally a numerical example is exploited to demonstrate the effectiveness and superiority of the proposed methods