invertibility and inversion of linear periodic systems abstract in this paper the invertibility properties of periodic discrete time systems are studied necessary and sufficient conditions for the existence and a synthesis procedure for constructing left and right inverses are given

disturbance localization with dead beat control for linear periodic discrete time systems in this paper the classical notion of a controlled invariant subspace together with its main properties is extended to the case of linear periodic discrete time systems and used for deriving necessary and sufficient solvability conditions for the disturbance localization problem and a synthesis procedure for the solution moreover the notions of outer and inner controllable subspaces are introduced and studied for the same class of system thus allowing the derivation of necessary and sufficient solvability conditions for the disturbance localization problem with output or state dead beat control and to give synthesis procedures for the solutions

the algebra of bounded linear operators on lp lq has infinitely many closed ideals the first author s research was supported by nsf grant dms 1160633 the second author was supported by the 2014 workshop in analysis and probability at texas a m university

network tomography estimating source destination traffic intensities from link data abstract the problem of estimating the node to node traffic intensity from repeated measurements of traffic on the links of a network is formulated and discussed under poisson assumptions and two types of traffic routing regimens deterministic a fixed known path between each directed pair of nodes and markovian a random path between each directed pair of nodes determined according to a known markov chain fixed for that pair maximum likelihood estimation and related approximations are discussed and computational difficulties are pointed out a detailed methodology is presented for estimates based on the method of moments the estimates are derived algorithmically taking advantage of the fact that the first and second moment equations give rise to a linear inverse problem with positivity restrictions that can be approached by an em algorithm resulting in a particularly simple solution to a hard problem a small simulation study is carried out

control of linear discrete time periodic systems a decentralized control approach a decentralized control technique is applied to the problem of periodic output feedback stabilization or pole assignment for a periodically time varying discrete time system it is shown that the problem can be reduced to that of stabilizing or pole assigning a general proper multichannel system by static output feedback on the basis of the equivalence between periodic systems and a class of linear time invariant systems the notion of periodic fixed mode is introduced for a periodic system similar to the notion of uncontrollable or unobservable modes in terms of this notion both necessary conditions and sufficient conditions for the solvability of the problem are obtained

uniformly factoring weakly compact operators abstract let x and y be separable banach spaces suppose y either has a shrinking basis or y is isomorphic to c 2 n and a is a subset of weakly compact operators from x to y which is analytic in the strong operator topology we prove that there is a reflexive space with a basis z such that every t a factors through z likewise we prove that if a l x c 2 n is a set of operators whose adjoints have separable range and is analytic in the strong operator topology then there is a banach space z with separable dual such that every t a factors through z finally we prove a uniform version of this result in which we allow the domain and range spaces to vary

controllability stabilizability and matrix riccati equations for periodic systems in this note controllability stabilizahility and related concepts for periodically time varying systems are discussed especially it is proved that the definition of controllability employed in connection with the existence of periodic solutions of periodic matrix riccati equations is equivalent to kalman s original definition

adaptive robust output regulation of uncertain linear periodic systems this paper considers the robust output regulation problem for parameterized families of periodic systems to extend the solution of the output regulation problem to the periodic or time varying setup a classification of the immersion mappings based on various non equivalent observability properties is derived the connections between different canonical realizations of internal models that fully exploit such properties for robust and adaptive output regulation design in periodic systems are investigated it is shown how non minimal realizations of suitable periodic internal models are instrumental in achieving the possibility of performing adaptive redesign to deal with parameterized families of exosystem models an important feature of the proposed solution is the fact that a persistence of excitation condition for the exogenous signals is not required for asymptotic regulation

a stochastic kaczmarz algorithm for network tomography we develop a stochastic approximation version of the classical kaczmarz algorithm that is incremental in nature and takes as input noisy real time data our analysis shows that with probability one it mimics the behavior of the original scheme starting from the same initial point our algorithm and the corresponding deterministic kaczmarz algorithm converge to precisely the same point the motivation for this work comes from network tomography where network parameters are to be estimated based upon end to end measurements numerical examples via matlab based simulations demonstrate the efficacy of the algorithm

the bourgain l1 index of mixed tsirelson space abstract suppose that f n n 0 is a sequence of regular families of finite subsets of n such that f 0 contains all singletons and n n 1 is a nonincreasing null sequence in 0 1 the mixed tsirelson space t f 0 n f n n 1 is the completion of c00 with respect to the implicitly defined norm x max x f 0 sup n n sup n i 1 k e i x where x f 0 sup f f 0 fx l 1 and the last supremum is taken over all sequences ei i 1k in n such that max e i min e i 1 and min e i 1 i k f n in this paper we compute the bourgain l1 index of the space t f 0 n f n n 1 as a consequence it is shown that if is a countable ordinal not of the form for some limit ordinal then there is a banach space whose l1 index is

ideals in l l_1 the main result is that there are infinitely many in fact a continuum of closed two sided ideals in the banach algebra l l 1 of bounded linear operators on l 1 0 1 this answers a question from pietsch s 1978 book operator ideals the proof also shows that l c 0 1 contains a continuum of closed ideals finally a duality argument yields that l ell infty has a continuum of closed ideals

disturbance localization by measurement feedback for linear periodic discrete time systems abstract the recent notions of inner controllable outer controllable and outer reconstructible subspaces together with the extension of the notion of c a b pair of subspaces to the class of linear periodic discrete time systems are the main tools used in this paper in order to study the disturbance localization problem by measurement feedback for the same class of systems by means of these concepts the necessary and sufficient solvability conditions of such a problem and synthesis procedures of the solutions are found for three different cases i e with and without an additional requirement of output or state dead beat control

norm closed operator ideals in lorentz sequence spaces abstract in this paper we study the structure of closed algebraic ideals in the algebra of operators acting on a lorentz sequence space

analysis of the periodic lyapunov and riccati equations via canonical decomposition a new proof is given of the following result a periodic riccati equation admits a unique positive semidefinite periodic solution and the solution is stabilizing if and only if the underlying system is stabilizable and detectable the proof hinges on the decomposition of the riccati equation induced by the system canonical decomposition the solution structure is therefore naturally pointed out

dead beat control of linear periodic discrete time systems in this paper the dead beat control of linear periodic discrete time systems subject to periodic disturbances is studied necessary and sufficient conditions are given for the existence of a linear periodic controller such that both output dead beat control under periodic disturbances and state dead beat control under no disturbance are performed moreover synthesis procedures of the controller as well as of state dead beat observers are given which can be applied also to a class of bilinear systems

new examples of c 0 saturated banach spaces for every p 1 an isomorphically polyhedral banach space ep is constructed which has an unconditional basis and does not embed isomorphically into a c k space for any countable and compact metric space k moreover ep admits a quotient isomorphic to lp

discrete time linear periodic systems gramian and modal criteria for reachability and controllability this paper deals with the reachability and controllability of periodic discrete time systems first we supply two necessary and sufficient complete reachability conditions which apply to reversible and non reversible systems respectively then a necessary and sufficient complete controllability condition is provided this condition as well as the complete reachability criteria is given in terms of the reachability gramian matrix equivalent modal criteria for reachability and controllability are established in the second part of the paper

modified mixed tsirelson spaces we study the modified and boundedly modified mixed tsirelson spacestm fkn n n 1 andtm s fkn n n 1 respectively defined by a subsequence fkn of the sequence of schreier families fn these are reflexive asymptotic l1spaces with an unconditional basis ei ihaving the property that every sequence xi ni 1of normalized disjointly supported vectors contained in ei i nis equivalent to the basis of ln1 we show that if lim 1 nn 1 then the spacet fn n n 1 and its modified variationstm fn n n 1 ortm s fn n n 1 are totally incomparable by proving thatc0is finitely disjointly representable in every block subspace oft fn n n 1 next we present an example of a boundedly modified mixed tsirelson spacexm 1 u tm 1 fkn n n 1 which is arbitrarily distortable finally we construct a variation of the spacexm 1 uwhich is hereditarily indecomposable

spaceability and operator ideals abstract let i 1 and i 2 be arbitrary operator ideals in the sense of pietsch and e and f be banach spaces such that the set i 1 e f i 2 e f is non empty we give a quite general sufficient condition on the banach spaces in order to obtain the spaceability of i 1 e f i 2 e f some consequences are provided when considering the ideals of compact operators strictly singular operators finitely strictly singular operators and schatten operator classes

multivariable multirate sampled data systems state space description transfer characteristics and nyquist criterion first a discrete time state space description is derived for multivariable multirate sampled data systems then the multirate impulse modulation mim and the symmetric coordinate multirate impulse modulation smim of a transfer matrix are defined and their relation to the discrete time state space description is clarified based on the above results four stability criteria are derived the contents of the paper will be useful to extend the modern results about continuous time and single rate sampled data control systems to the multirate sampled data case especially extensions of the ina method and of the robust stability conditions will be straightforward

sequence singular operators abstract in this paper we study l p related collections of operators introduced by beanland and freeman in 6 on the subject of forming operator ideals we show that these collections are not always closed under addition and hence do not form operator ideals nevertheless they allow us to construct an uncountable chain of closed ideals in each of the operator algebras l l 1 l q 1 q and l l 1 c 0 this finishes answering a longstanding question of pietsch

factorization of asplund operators abstract we give necessary and sufficient conditions for an operator a x y on a banach space having a shrinking fdd to factor through a banach space z such that the szlenk index of z is equal to the szlenk index of a we also prove that for every ordinal 0 1 1 a limit ordinal there exists a banach space g having a shrinking basis and szlenk index such that for any separable banach space x and any operator a x y having szlenk index less than a factors through a subspace and through a quotient of g and if x has a shrinking fdd a factors through g

genericity and amalgamation of classes of banach spaces abstract we study universality problems in banach space theory we show that if a is an analytic class in the effros borel structure of subspaces of c 0 1 of non universal separable banach spaces then there exists a non universal separable banach space y with a schauder basis that contains isomorphs of each member of a with the bounded approximation property the proof is based on the amalgamation technique of a class c of separable banach spaces introduced in the paper we show among others that there exists a separable banach space r not containing l 1 0 1 such that the indices and r n d are unbounded on the set of baire 1 elements of the ball of the double dual r of r this answers two questions of h p rosenthal we also introduce the concept of a strongly bounded class of separable banach spaces a class c of separable banach spaces is strongly bounded if for every analytic subset a of c there exists y c that contains all members of a up to isomorphism we show that several natural classes of separable banach spaces are strongly bounded among them the class of non universal spaces with a schauder basis the class of reflexive spaces with a schauder basis the class of spaces with a shrinking schauder basis and the class of spaces with schauder basis not containing a minimal banach space x

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

operators on c 0 1 preserving copies of asymptotic l1 spaces given separable banach spaces x y z and a bounded linear operator t x y then t is said to preserve a copy of z provided that there exists a closed linear subspace e of x isomorphic to z and such that the restriction of t to e is an into isomorphism it is proved that every operator on c 0 1 which preserves a copy of an asymptotic l1 space also preserves a copy of c 0 1

disturbance localization for left invertible linear periodic discrete time systems the disturbance localization problem for left invertible linear periodic discrete time systems is solved using periodic state feedback controllers the proposed technique is of algebraic nature and has the following two main characteristics i it yields simple algebraic criteria for testing the solvability of the problem as compared to known geometric criteria which may not be so easy to check ii it derives analytically the general expressions of all periodic controllers admissible for disturbance localization as compared to known techniques which lead to nonanalytic parametrizations of the admissible controllers via constructive procedures moreover for the aforementioned class of periodic systems the state feedback simultaneous disturbance localization and stabilization or pole placement problem is treated and conditions for its solvability are established on the basis of a decentralized control approach that makes use of the equivalence between the above problem and the stabilization or pole placement problem of a general proper multichannel system by decentralized static output feedback

pole assignment for linear time invariant systems by periodic memoryless output feedback it is well known that the poles of a linear time invariant controllable and observable system can be assigned arbitrarily by state feedback when only the output is available pole assignment is still possible by means of dynamic output feedback in this paper the potential of time varying memoryless output feedback is considered it is shown that up to some technical conditions it is indeed possible to allocate the poles of a linear time invariant discrete time system by memoryless output feedback with periodic gains the period of the gains is n 1 with n the order of the system the power of the design technique is proved to be comparable to what can be achieved by the classical dynamic feedback approach

closed ideals of operators on the tsirelson and schreier spaces abstract let b x denote the banach algebra of bounded operators on x where x is either tsirelson s banach space or the schreier space of order n for some n n we show that the lattice of closed ideals of b x has a very rich structure in particular b x contains at least continuum many maximal ideals our approach is to study the closed ideals generated by the basis projections indeed the unit vector basis is an unconditional basis for each of the above spaces so there is a basis projection p n b x corresponding to each non empty subset n of n a closed ideal of b x is spatial if it is generated by p n for some n we can now state our main conclusions as follows the family of spatial ideals lying strictly between the ideal of compact operators and b x is non empty and has no minimal or maximal elements for each pair i j of spatial ideals there is a family l l where the index set has the cardinality of the continuum such that l is an uncountable chain of spatial ideals l is a closed ideal that is not spatial and i l j and l m j whenever l m are distinct and l l m m

operators on c k spaces preserving copies of schreier spaces it is proved that an operator t c k x k compact metrizable x a separable banach space for which the e szlenk index of t bx is greater than or equal to 1 is an isomorphism on a subspace of c k isomorphic to x the schreier space of order as a corollary one obtains that a complemented subspace of c k with szlenk index equal to 1 contains a subspace isomorphic to x

deadbeat error control of discrete multivariable systemsdagger abstract the main objective of this paper is to delineate conditions under which deadbeat error control can be achieved between a plant output and a discrete reference input signal all facets of this problem are considered in the linear multivariable case i e when the reference is any non diminishing signal whether the plant is truly discrete or a discretized continuous one and whether the initial conditions are zero or unknown the results presented can also be used to resolve the case of known non zero initial conditions on the state of the plant as well as the compensator

minimal time minimal order deadbeat regulator with internal stability this paper is concerned with the output deadbeat finite settling time regulation with internal stability for linear discrete time multivariable systems the two cases are treated separately the one is the regulation by state feedback and the other is the regulation through function observers for both cases the basic solvability conditions the minimal settling time and the characterizations of the minimal time regulators are derived throughout the paper the well posedness condition plays a fundamental role a deterministic version of the so called separation theorem in lqg problem is derived namely the minimal time state feedback regulator combined with the minimal time minimal order function observer yields the overall minimal time minimal order regulator by output feedback

disturbance localization and pole shifting by dynamic compensation this paper concerns the problem of disturbance localization and pole shifting by dynamic compensation in multivariable linear systems with inaccessible state vector a necessary and sufficient condition for the solvability of the problem is given two synthesis procedures of the compensator are presented one is based on an observer and the other is based on a dual observer the observer designed by the proposed procedure acts as as unknown input observer for a linear function an improved procedure of designing a reduced order unknown input observer is also given the result may be applicable to reducing the compensator order

the realization problem for linear periodic systems abstract the realization problem for discrete time linear periodic systems is considered deep insight on the various complicated aspects of minimal quasi minimal and uniform realization is provided based on the knowledge of the structural properties of discrete time periodic systems the results hinge on the lifting isomorphism between such systems and time invariant ones

geometric and algebraic structure at infinity of discrete time linear periodic systems a notion of structure at infinity for linear discrete time periodic system is proposed and investigated in particular two equivalent characterizations of such notion are given a geometric one and an algebraic one the first is based on an extension to the periodic case of the controlled invariant subspace algorithm and the second is based on a newly developed periodic version of the structure algorithm an application to a model matching problem is described

block decoupling of linear omega periodic discrete time systems the paper considers block decoupling control of a linear omega periodic discrete time system with state feedback the notion of the maximal reachability subspace and the method to calculate it are extended to the periodic case under the assumption that the input transformation is nonsingular a necessary and sufficient solvability condition for block decoupling is represented in terms of the maximal reachability subspace

output dead beat controllers and function dead beat observers for linear periodic discrete time systems in this paper two problems are considered that of finding a possibly dynamic linear periodic controller such that both the regulated output and the control input of a linear periodic discrete time system become and remain zero and that of designing a dead beat observer of a linear function of the state of the system for both these problems necessary and sufficient conditions for the existence of a solution are given and synthesis procedures of both the controller and the observer are provided by the sufficiency proofs such conditions are very simple and concise when expressed in terms of controllable and or unreconstructible states

classes of operators determined by ordinal indices abstract we introduce and study the bourgain index of an operator between two banach spaces in particular we study the bourgain l p and c 0 indices of an operator several estimates for finite and infinite direct sums are established we define classes determined by these indices and show that some of these classes form operator ideals we characterize the ordinals which occur as the index of an operator and establish exactly when the defined classes are closed we study associated indices for non preservation of l p and c 0 spreading models and indices characterizing weak compactness of operators between separable banach spaces we also show that some of these classes are operator ideals and discuss closedness and distinctness of these classes

the lattice of closed ideals in the banach algebra of operators on certain banach spaces very few banach spaces e are known for which the lattice of closed ideals in the banach algebra of all bounded linear operators on e is fully understood indeed up to now the only such banach spaces are up to isomorphism hilbert spaces and the sequence spaces c0 and lp for 1p we add a new member to this family by showing that there are exactly four closed ideals in for the banach space e l2n c0 that is e is the c0 direct sum of the finite dimensional hilbert spaces l21 l22 l2n

multicast topology inference from measured end to end loss the use of multicast inference on end to end measurement has been proposed as a means to infer network internal characteristics such as packet link loss rate and delay we propose three types of algorithm that use loss measurements to infer the underlying multicast topology i a grouping estimator that exploits the monotonicity of loss rates with increasing path length ii a maximum likelihood estimator mle and iii a bayesian estimator we establish their consistency compare their complexity and accuracy and analyze the modes of failure and their asymptotic probabilities

robust tracking and regulation of linear periodic discrete time systems in this paper the robust asymptotic tracking and disturbance rejection problem is studied for linear periodic discrete time systems and for general classes of disturbance functions and reference signals consisting in free responses of periodic processes the necessary and sufficient conditions for the existence of a solution which involve the periodic notion of invariant zero are found a constructive design procedure of the periodic compensator is given it is based on the internal model principle

isomorphisms and strictly singular operators in mixed tsirelson spaces abstract we study the family of isomorphisms and strictly singular operators in mixed tsirelson spaces and their modified versions setting we show sequential minimality of modified mixed tsirelson spaces t m s n n n satisfying some regularity conditions and present results on existence of strictly singular non compact operators on subspaces of mixed tsirelson spaces defined by the families a n n and s n n

simultaneous pole assignment in linear periodic systems by constrained structure feedback the authors present methods for pole assignment by feedback with constrained structure in linear periodic systems using generalized sampled data hold functions gshf constrained structure is taken to mean that the input of each channel is restricted to depend only on the measurements of some specific output channels the basic idea of gshf control is to use sample and hold but to consider the hold function as a design parameter four strategies are proposed for closing a control loop using gshf the key to the results obtained is that when gshf control with constrained structure is applied to a periodic system a discrete time time invariant decentralized system is obtained for which control design methods are available

zeros of discrete time linear periodic systems in this note the concept of zero for linear discrete time siso periodic systems is discussed the definition is based on a time invariant mimo equivalent representation an input output characterization of the zeros is provided which extends a well known property for time invariant systems

linear function dead beat observers with disturbance localization for linear periodic discrete time systems abstract in this paper the classical notion of a conditioned invariant subspace is extended to the case of linear periodic discrete time systems properly characterized and suitably specialized to the notion of an outer reconstructible subspace these ideas are used in order to find necessary and sufficient conditions for the existence of a linear function dead beat observer for such systems under unknown and unmeasurable disturbances and a synthesis procedure for such an observer

pole placement problem for discrete time linear periodic systems the pole placement problem for the monodromy matrix of a discrete time linear periodic system is considered given a partition of the complex plane into a good part and a bad part b the result obtained by wonham 1979 is extended to the periodic case this extension is based on the decomposition of a completely controllable periodic system into two subsystems such that the first subsystem is completely reachable and the eigenvalues of the monodromy matrix of the second one are equal to zero

on deadbeat controllers the possibility of achieving a deadbeat regulation and tracking in linear multivariable systems independently of their initial conditions is investigated necessary and sufficient conditions for the existence of various deadbeat controllers are established in a constructive way a detailed analysis of the control sequence generated by any deadbeat controller is then presented

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

on zippin s embedding theorem of banach spaces into banach spaces with bases abstract we present a new proof of zippin s embedding theorem that every separable reflexive banach space embeds into one with shrinking and boundedly complete basis and every banach space with a separable dual embeds into one with a shrinking basis this new proof leads to improved versions of other embedding results

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

proximity to l1and distortion in asymptotic l1spaces abstract for an asymptotic l 1 space x with a basis x i certain asymptotic l 1 constants x are defined for 1 x measures the equivalence between all normalized block bases y i k i 1 of x i which are s admissible with respect to x i s is the th schreier class of sets and the unit vector basis of l k 1 this leads to the concept of the delta spectrum of x x which reflects the behavior of stabilized limits of x the analogues of these constants under all renormings of x are also defined and studied we investigate x both in general and for spaces of bounded distortion we also prove several results on distorting the classical tsirelson s space t and its relatives

ripple free robust output regulation and tracking for multirate sampled data control the problem of the robust continuous time asymptotic tracking and disturbance rejection for a multivariable multirate sampled data system is studied the necessity of a continuous time internal model of the exogenous signals except for the constant ones if any for obtaining a ripple free zero error response is proven the conditions are given for the existence of a hybrid control system including possibly a continuous time subcompensator for which the exponential stability and a continuous time convergence to zero of the tracking error are guaranteed at least in a neighbourhood of the nominal parameters this in particular both for when the dead beat convergence of the state free response and the continuous time error response is required at the nominal parameters and for when an exponential convergence with a prescribed rate of decay is required including design procedures of the continuous time and the discrete time subcompensators both for when the available description of the plant has a

proximity to lp and c0 in banach spaces abstract we construct a class of minimal trees and use these trees to establish a number of coloring theorems on general trees among the applications of these trees and coloring theorems are quantification of the bourgain l p and c 0 indices dualization of the bourgain c 0 index establishing sharp positive and negative results for constant reduction and estimating the bourgain l p index of an arbitrary banach space x in terms of a subspace y and the quotient x y

ξ completely continuous operators and ξ schur banach spaces abstract for each ordinal 0 1 we introduce the notion of a completely continuous operator and prove that for each ordinal 0 1 the class v of completely continuous operators is a closed injective operator ideal which is not surjective symmetric or idempotent we prove that for distinct 0 1 the classes of completely continuous operators and completely continuous operators are distinct we also introduce an ordinal rank v for operators such that v a 1 if and only if a is completely continuous and otherwise v a is the minimum countable ordinal such that a fails to be completely continuous we show that there exists an operator a such that v a if and only if 1 1 and there exists a banach space x such that v i x if and only if there exists an ordinal 1 such that finally prove that for every 0 1 the class a l v a is 1 1 complete in l the coding of all operators between separable banach spaces this is in contrast to the class v l which is 2 1 complete in l

uniqueness of the maximal ideal of the banach algebra of bounded operators on c 0 ω1 let 1 be the smallest uncountable ordinal by a result of rudin bounded operators on the banach space c 0 1 have a natural representation as 0 1 0 1 matrices loy and willis observed that the set of operators whose final column is continuous when viewed as a scalar valued function on 0 1 defines a maximal ideal of codimension one in the banach algebra b c 0 1 of bounded operators on c 0 1 we give a coordinate free characterization of this ideal and deduce from it that b c 0 1 contains no other maximal ideals we then obtain a list of equivalent conditions describing the strictly smaller ideal of operators with separable range and finally we investigate the structure of the lattice of all closed ideals of b c 0 1

acceleration of stochastic approximation by averaging a new recursive algorithm of stochastic approximation type with the averaging of trajectories is investigated convergence with probability one is proved for a variety of classical optimization and identification problems it is also demonstrated for these problems that the proposed algorithm achieves the highest possible rate of convergence

brief performance limitations in the robust servomechanism problem for discrete time periodic systems fundamental limitations for error tracking regulation are obtained for the robust servomechanism problem rsp for discrete time periodic systems in studying this problem the rsp for a multi input multi output discrete time system is considered application of these results is then made to the periodic system robust servomechanism problem and explicit expressions for the limiting costs for error tracking regulation are obtained these limitations can be characterized completely by the number and location of the non minimum phase transmission zeros of the system s associated lifted system together with a term which depends on the order of the system the number of inputs the number of transmission zeros and the system s period

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

h controllability and observability of linear periodic systems with reference to linear periodic systems the classical notion of controllability introduced by kalman k controllability is shown to be equivalent to the characterization of controllability h controllability first proposed by hewer as a natural extension to the periodic case of an eigenvalue eigenvector controllability condition independently introduced by several authors for time invariant systems only the proof of such an equivalence also leads to the conclusion that if a t periodic system s is k controllable and k is the degree of the minimal polynomial of the monodromy matrix associated with s then at any time t s is controllable over t t kt since k is lower than or equal to the system order a well known result due to brunovsky is slightly strengthened by duality the corresponding observability results follow

model reference adaptive control system for discrete linear time varying systems with periodically varying parameters and time delay this paper presents a new method for designing a model reference adaptive control system for a class of discrete linear time varying systems with periodically varying parameters and time delay based on lyapunov s stability theorem adaptive control algorithms guarantee the asymptotic stability of the error between the plant output and the reference sequence using no anticipative value of the plant output the validity of the theoretical result is illustrated by numerical examples

non three space properties and szlenk index abstract we prove that for any non zero countable ordinal which is not additively indecomposable the property of having szlenk index not exceeding is not a three space property this complements a result of brooker and lancien which states that if is additively indecomposable then having szlenk index not exceeding is a three space property

a canonical decomposition of linear periodic discrete time systems in this paper a linear periodic discrete time system is studied on the basis of simple properties of the subspaces of controllable states and of unreconstructible ones a canonical structure theorem is derived this generalizes 1o such a system the classical kalman decomposition while preserving the constant dimensionality of the four subsystems which arise when a periodic continuous time system is decomposed the dynamic matrices of the non controllable and or non reconstructible subsystems are shown to be non singular at each time instant as those for a time invariant discrete time system are

rigidity of composition operators on the hardy space h p abstract let be an analytic map taking the unit disk d into itself we establish that the class of composition operators f c f f exhibits a rather strong rigidity of non compact behaviour on the hardy space h p for 1 p and p 2 our main result is the following trichotomy which states that exactly one of the following alternatives holds i c is a compact operator h p h p ii c fixes a linearly isomorphic copy of l p in h p but c does not fix any copies of l 2 in h p iii c fixes a copy of l 2 in h p moreover in case iii the operator c actually fixes a copy of l p 0 1 in h p provided p 1 we reinterpret these results in terms of norm closed ideals of the bounded linear operators on h p which contain the compact operators k h p in particular the class of composition operators on h p does not reflect the quite complicated lattice structure of such ideals

pole assignment for linear periodic systems by memoryless output feedback we consider linear periodic discrete time systems we are interested in the problem of placing the poles of the monodromy map by means of periodic output feedback of the same or multiple period it is well known that in general the poles of time invariant systems cannot be assigned by constant output feedback this is in contrast with what can be obtained in the context of time variant systems the main contribution of this paper is that periodic output feedback suffices for pole placement of periodic systems