further comments on comments on on an estimate of the decay rate for stable linear delay systems it is pointed out by a simple counterexample that the theorem derived in the above note is erroneous

w stability and local input output stability results a new type of input output stability is defined based on the use of a sobolev space w w is well suited like the lebesgue space l sub 2 to obtain stability characterizations in the time and frequency domains moreover if compared with l sub 2 w has additional properties which enable one to establish local stability results a local version of the small gain theorem is established in this framework as well as some consequences of this result in particular local versions of the passivity theorem and of the circle criterion the relationship between w stability and asymptotic stability is studied

further facts about input to state stabilization previously published results about input to state stabilizability are shown to hold even for systems which are not linear in controls provided that a more general type of feedback is allowed applications to certain stabilization problems and coprime factorizations as well as comparisons to other results on input to state stability are briefly discussed

poisson commutative subalgebras and complete integrability on non regular coadjoint orbits and flag varieties the purpose of this paper is to bring together various loose ends in the theory of integrable systems for a semisimple lie algebra mathfrak g we obtain several results on the completeness of homogeneous poisson commutative subalgebras of mathscr s mathfrak g on coadjoint orbits this concerns in particular gelfand tsetlin and mishchenko fomenko subalgebras our results reveal the crucial role of nilpotent orbits and sheets in mathfrak g simeq mathfrak g

on an estimate of the decay rate for stable linear delay systems in this paper it is shown that for a certain class of stable linear delay systems we can obtain an estimate of the decay rate of the solution by a simple computation

local l sub p stability and local small gain theorem for discrete time systems the notion of local l sub 2 stability is defined the relationship between this notion and lyapunov stability is clarified a local version of the small gain theorem is then established in the case of discrete time systems these results are applied to stability analysis of a nonlinear discrete time delay system

α stability of systems governed by a functional differential equation extension of results concerning linear delay systems abstract theorem 1 stated by mori et al 1982 and discussed by hmamed 1985 and mori 1986 is generalized in this note this theorem is extended to the case of a system governed by a more general functional differential equation theorem 3 claimed by hmamed 1986 is erroneous the correct result is established

on the geometry and quantization of symplectic howe pairs we study the orbit structure and the geometric quantization of a pair of mutually commuting hamiltonian actions on a symplectic manifold if the pair of actions fulfils a symplectic howe condition we show that there is a canonical correspondence between the orbit spaces of the respective moment images furthermore we show that reduced spaces with respect to the action of one group are symplectomorphic to coadjoint orbits of the other group in the kahler case we show that the linear representation of a pair of compact connected lie groups on the geometric quantization of the manifold is then equipped with a representation theoretic howe duality

coisotropic actions on compact homogeneous kahler manifolds abstract the main result of the paper is that a compact homogeneous kahler manifold admitting an isometric and coisotropic action with a fixed point is isometric to a hermitian symmetric space

coisotropic and polar actions on complex grassmannians the main result of the paper is the complete classification of the compact connected lie groups acting coisotropically on complex grassmannians this is used to determine the polar actions on the same manifolds

ρ stability and robustness discrete time case we say that a discrete time system is stable if roughly speaking k x k 0 where x k is the system state general stability theorems are established in this paper they concern systems governed by functional difference equations systems of this type are encountered in the robustness studies these stability theorems are a generalization of the well known lyapunov criterion these results are applied to the robustness quantification problem in the second part of the paper the case of discrete time lq regulators is deeply investigated robustness properties of continuous time lq regulators are found as the limit when the sampling period t tends to zero robustness deteriorates as t increases an upper bound is given for t under which the robustness remains satisfactory the practical interest of these theoretical results is illustrated on the basis of an industrial example

complete families of commuting functions for coisotropic hamiltonian actions abstract let g be an algebraic group defined over a field f of characteristic zero with g lie g the dual space g equipped with the lie poisson bracket is a poisson variety and each irreducible g invariant subvariety x g carries the induced poisson structure we prove that there is a set f 1 f l f x of algebraically independent polynomial functions which pairwise commute with respect to the poisson bracket such that l dim x tr deg f x g 2 we also discuss several applications of this result to complete integrability of hamiltonian systems on symplectic hamiltonian g varieties of corank zero and 2

spherical nilpotent orbits and the kostant sekiguchi correspondence let g be a connected linear semisimple lie group with lie algebra g and let k c aut p c be the complexified isotropy representation at the identity coset of the corresponding symmetric space the kostant sekiguchi correspondence is a bijection between the nilpotent k c orbits in p c and the nilpotent g orbits in g we show that this correspondence associates each spherical nilpotent k c orbit to a nilpotent g orbit that is multiplicity free as a hamiltonian k space the converse also holds

self similar measures and intersections of cantor sets it is natural to expect that the arithmetic sum of two cantor sets should have positive lebesgue measure if the sum of their dimensions exceeds 1 but there are many known counterexamples e g when both sets are the middle ca cantor set and ca e 1 1 we show that for any compact set k and for a e ag e 0 1 the arithmetic sum of k and the middle ae cantor set does indeed have positive lebesgue measure when the sum of their hausdorff dimensions exceeds 1 in this case we also determine the essential su premum as the translation parameter t varies of the dimension of the intersection of k t with the middle ca cantor set we also establish a new property of the infinite bernoutlli convolutions lj the distributions of random series e 0 a where the signs are chosen independently with probabilities p 1 p let 1 ql q2 2 for p 2 near 2 and for a e a in some nonempty interval iv is absolutely continuous 2 1 and its density is in lil but not in lq2 we also answer a question of kahane concerning the fourier transform of vl 2

comment regarding on delay independant stability of large scale systems with time delays this paper comments the result of a recent paper by xu ibid vol 40 p 930 3 1995 the commenter points out that these results have already been published in a more general framework by him int j contr vol 45 no 6 1987 and the following points are also clarified the state which has to be considered and a connection with the passivity theorem

homogeneous kahler and hamiltonian manifolds we consider actions of reductive complex lie groups g k mathbb c on kahler manifolds x such that the k action is hamiltonian and prove then that the closures of the g orbits are complex analytic in x this is used to characterize reductive homogeneous kahler manifolds in terms of their isotropy subgroups moreover we show that such manifolds admit k moment maps if and only if their isotropy groups are algebraic

coisotropic and polar actions on compact irreducible hermitian symmetric spaces we obtain the full classification of coisotropic and polar isometric actions of compact lie groups on irreducible hermitian symmetric spaces

simple stability criteria for nonlinear time varying discrete systems abstract we present two sufficient conditions for asymptotic stability of nonlinear time varying discrete systems our main results generalize mori s result for linear discrete time invariant systems to nonlinear time varying systems

bounded input bounded output stabilization of nonlinear systems using state detectors abstract this paper is devoted to the study of relations between lyapunov stabilization and bounded input bounded output bibo stabilization of nonlinear systems when the state is not available for measurement and various state detectors are employed for implementing feedback control it is found that with some constraints imposed on the detectors lyapunov stabilization implies bibo stabilization a feedback control scheme for achieving bibo stability is presented

polar and coisotropic actions on kahler manifolds the main result of the paper is that a polar action on a compact irreducible homogeneous kahler manifold is coisotropic this is then used to give new examples of polar actions and to classify coisotropic and polar actions on quadrics

h sub spl infin memoryless control with an spl alpha stability constraint for time delay systems an lmi approach focuses on the design of h sub spl infin memoryless state feedback controllers satisfying some spl alpha stability constraints on the closed loop poles for a class of linear systems with delayed state subject to disturbance inputs a sufficient condition for feasibility is derived in terms of linear matrix inequalities furthermore we also consider a particular optimization problem the maximal bound allowed on time delay such that the prescribed level on disturbance attenuation and the spl alpha stability constraints are still preserved this problem is converted into a linear matrix inequality lmi optimization problem and we give a suboptimal bound on the delay

iterated function systems with non distinct fixed points abstract the dimension theory of self similar sets is quite well understood in the cases when some separation conditions open set condition or weak separation condition or the so called transversality condition hold otherwise the study of the hausdorff dimension is far from well understood we investigate the properties of the hausdorff dimension of self similar sets such that some functions in the corresponding iterated function system share the same fixed point then it is not possible to apply directly known techniques in this paper we are going to calculate the hausdorff dimension for almost all contracting parameters and calculate the proper dimensional hausdorff measure of the attractor

fading memory feedback systems and robust stability abstract this paper considers fading memory for nonlinear time varying systems and associated problems of robust stability we define two notions of fading memory for stable dynamical systems uniform and pointwise we then provide conditions under which stable linear or nonlinear systems exhibit uniform or pointwise fading memory in particular we show that 1 all stable discrete time linear time varying ltv systems have uniform fading memory 2 all stable continuous time ltv systems have pointwise fading memory and 3 stable finite dimensional continuous time ltv systems have uniform fading memory we then show that a version of the small gain theorem which employs the asymptotic gain of a fading memory system is necessary for the stable invertibility of certain feedback operators these results are presented for both continuous time and discrete time systems using general lp or l p notions of input output stability and generalize existing results for l2 stability we further investigate fading memory in a closed loop context for linear plants we parametrize all nonlinear controllers which lead to closed loop pointwise fading memory

α stability and robustness of large scale interconnected systems abstract the a stability or the stability with degree of large scale interconnected systems is studied a general stability theorem is established that applies even when the subsystems are governed by a functional differential equation rather than by an o d e this theorem is then applied to robustness the result obtained is a generalization of the well known properties of lq regulators an algorithm enabling the design of a robust controller for a large scale interconnected system is indicated

when is a pure state of three qubits determined by its single particle reduced density matrices using techniques from symplectic geometry we prove that a pure state of three qubits is up to local unitaries uniquely determined by its one particle reduced density matrices exactly when their ordered spectra belong to the boundary of the so called kirwan polytope otherwise the states with given reduced density matrices are parameterized up to local unitary equivalence by two real variables given inevitable experimental imprecision this means that already for three qubits a pure quantum state can never be reconstructed from single particle tomography we moreover show that the knowledge of the reduced density matrices is always sufficient if one is given the additional promise that the quantum state is not convertible to the greenberger horne zeilinger state by stochastic local operations and classical communication and discuss generalizations of our results to an arbitrary number of qubits

comments on on an estimate of the delay rate for stable linear delay systems it is shown that an estimate of the decay rate of a class of stable linear delay systems can be obtained without solving the transcendental equation and is in addition less restrictive than that given by mori et al 1982