an observer for infinite dimensional dissipative bilinear systems we consider bilinear systems of the form t a t u t b t y t t c on an infinite dimensional hilbert space h where a is the generator of a semigroup of contraction b is a bounded dissipative operator and c h the input signal u l r such that u t 0 for almost every t r we present a simple observer for this class of systems with the estimation error converging weakly to zero in h for every sufficiently rich input inputs that we call regularly persistent our result is a generalization of the previous results in 1 2

cohomogeneity one manifolds with positive ricci curvature one of the central problems in riemannian geometry is to determine how large the classes of manifolds with positive nonnegative sectional ricci or scalar curvature are see gr for scalar curvature the situation is fairly well understood by comparison special surgery constructions as in sy wr and bundle constructions as in na have resulted in a large number of interesting manifolds with positive ricci curvature so far the only known obstructions to have positive ricci curvature come from obstructions to have positive scalar curvature see li and rs and from the classical bonnet myers theorem which implies that a closed manifold with positive ricci curvature must have finite fundamental group it is well known that among homogeneous manifolds g h this is also a sufficient condition see e g the proof of corollary 3 5 or br in this paper we prove that this is true as well when the manifold admits an action by a compact lie group g with orbits of codimension one

necessary and sufficient consensus conditions for the eventwise aggregation of lower probabilities the paper gives sufficient and necessary conditions of consensus requirement for eventwise aggregation of various families of lower probabilities in particular of coherent lower probabilities and properties of the corresponding aggregation functions

smooth output feedback stabilization of planar systems without controllable observable linearization this note considers the problem of global stabilization by output feedback for a family of planar systems whose jacobian linearization is neither controllable nor observable the problem cannot be dealt with by existing output feedback design methods most of them are based on the separation principle under appropriate growth conditions we propose an output feedback control scheme that does not rely on the separation principle and achieves global asymptotic stabilization the novelty of our control scheme lies in the explicit design of a dynamic output compensator which combines a nonlinear gain observer design and the technique of adding a power integrator as a consequence an interesting global stabilization result by output feedback can be obtained for feedback linearizable systems in a triangular form which turns out to be new even in the two dimensional case

homogeneous einstein randers metrics on symplectic groups abstract in this paper we prove that lie group sp n n 3 admits at least one family of invariant einstein randers metrics which are not naturally reductive we also give the classification of these metrics under isometries and determine their group of isometries moreover we prove that if homogeneous randers space m f with navigation data h w is berwald then m f is naturally reductive if and only if the riemannian metric m h is naturally reductive

on fuzzy measure and fuzzy integral on fuzzy set abstract on a fuzzy algebra of fuzzy sets we discuss some structural characteristics of a fuzzy measure the pseudo autocontinuity and some other concepts for a fuzzy measure are introduced and the relations between these cre discussed for the case of fuzzy sets riesz s theorems and lebesgue s theorems for a sequence of measurable functions are proved the concept of the fuzzy integral on a fuzzy set is given and some properties of fuzzy integrals on fuzzy sets are studied finally we prove some convergence theorems of a sequence of fuzzy integrals on fuzzy sets

a separation principle for bilinear systems with dissipative drift input output stabilization of a class of bilinear systems using a nonlinear stabilizing feedback control law together with an observer is studied in some cases it can be proved that the result is a globally asymptotically stable system

kyp lemma state feedback and dynamic output feedback in discrete time bilinear systems abstract this paper shows how a generalization of the kalman yacubovitch popov kyp lemma can be built for discrete time bilinear passive systems and how the concepts of passivity and feedback equivalence can be applied to solve the problem of global stabilization via smooth state feedback bounded state feedback and dynamic output feedback for a class of discrete time bilinear systems the results generalize some recent advances due to gauthier and kupka 1992 in continuous time bilinear systems to their discrete time counterparts

lifting group actions and nonnegative curvature we examine the question when a group acting by cohomogeneity one on the base of a principal g bundle can be lifted to the total space and commutes with the action by g we answer this question completely when the base of the principle bundle is 4 dimensional

output feedback stabilization of a one dimensional schrodinger equation by boundary observation with time delay in this article we are concerned with the stabilization of a 1 d schrodinger equation with boundary control and observation the boundary observation is suffered from an arbitrary given time delay we first show that the proportional output feedback control that stabilizes exponentially the time delay free system can not stabilize the corresponding time delay system anymore we then use the observer and predictor to solve the stabilization problem of time delay system the state is estimated in the time span where the observation is available and the state is predicted in the time interval when the observation is not available it is shown that the estimated state feedback stabilizes exponentially the time delay system the numerical simulation is presented to illustrate the effect of the stabilizing controller

marginalization and linear opinion pools abstract suppose a decision maker has asked a group of experts to assess subjective probability distributions over some space and he wishes to find a consensus probability distribution as a function of these the assumption that finding the consensus distribution commutes with marginalization of the distributions implies that the consensus must be found using a linear opinion pool weighted average provided the space being considered contains three or more points some of the consequences of this result are discussed

a separation principle for distributed dissipative bilinear systems the problem of input output stabilization is generalized from finite dimensional bilinear systems to a class of distributed bilinear systems the solution is based on the nonlinear feedback stabilization results given previously by the authors 1999 with the observers presented by the same authors 1997 in another work

observers for a special class of bilinear systems design and application this note presents full and reduced order observation strategies for a subclass of systems that are bilinear in the immeasurable states lyapunov analysis is carried out to derive the conditions for convergence of the observed states for all strategies the full order observer is then utilized in the problem of bus voltage regulation effected by a static compensator statcom acting as a controlled reactive current source

design of state observers from a drift observability property in this paper the problem of state observation with exponential error decay for nonlinear systems affine in the input is considered and an observer is proposed for such an observer the drift observability property of the system i e observability for zero input together with an assumption on the input amplitude or on the observation relative degree are sufficient conditions for exponential convergence of the observation error the existence of an exponential observer is correlated to the existence of a solution for an h sub spl infin riccati like inequality global and semiglobal convergence results are presented

curvature and symmetry of milnor spheres since milnor s discovery of exotic spheres mi one of the most intriguing problems in riemannian geometry has been whether there are exotic spheres with positive curvature it is well known that there are exotic spheres that do not even admit metrics with positive scalar curvature hi on the other hand there are many examples of exotic spheres with positive ricci curvature cf ch1 he po and na and this work recently culminated in wr where it is shown that every exotic sphere that bounds a parallelizable manifold has a metric of positive ricci curvature this includes all exotic spheres in dimension 7 so far however no example of an exotic sphere with positive sectional curvature has been found in fact until now only one example of an exotic sphere with nonnegative sectional curvature was known the so called gromoll meyer sphere gm in dimension 7 as one of our main results we prove

exotic spheres and curvature since their discovery by milnor in 1956 exotic spheres have provided a fascinating object of study for geometers in this article we survey what is known about the curvature of exotic spheres

on the closure of families of fuzzy measures under eventwise aggregations the paper contains some results on eventwise aggregation of fuzzy measures from the various families of lower probabilities this investigation includes coherent lower probabilities k monotone measures belief measures etc we study sufficient and necessary conditions on aggregation operators satisfying the closure property it is necessary to guarantee that the aggregation belongs to the same family as generating measures we also propose an efficient way for constructing aggregation operators using the found unique properties of multilinear extension this representation method for fuzzy measures generalizes to the n dimensional case the well known one giving distorted probabilities

metrics of positive ricci curvature on quotient spaces one of the classical problems in differential geometry is the investigation of closed manifolds which admit riemannian metrics with given lower bounds for the sectional or the ricci curvature and the study of relations between the existence of such metrics and the topology and geometry of the underlying manifold despite many efforts during the past decades this problem is still far from being understood for example so far the only obstructions to the existence of a metric with positive ricci curvature come from the obstructions to the existence of metrics with positive scalar curvature li hi ro schy ta and the bonnet myers theorem which implies that the fundamental group of a closed manifold with positive ricci curvature must be finite fruitful constructions of metrics with positive ricci curvature on closed manifolds have so far been established by techniques that include deformation of metrics au eh we kahler geometry yau1 yau2 bundles and warping po na bb gpt special kinds of surgery sy wr metrical glueing gz2 and sasakian geometry bgn particularly large classes of examples of manifolds with positive ricci curvature are given by all compact homogeneous spaces with finite fundamental group na and all closed cohomogeneity one manifolds with finite fundamental group gz2 in this article we present several new classes of manifolds which admit metrics of positive or nonnegative ricci curvature the idea is to consider quotients of manifolds m g of positive or nonnegative ricci curvature by a free isometric action while taking such a quotient non decreases the sectional curvature it may well happen in general that the ricci curvature of the quotient is inferior to the one of m our first results however state that the quotient of m does admit metrics of positive ricci curvature if m belongs to one of the aforementioned classes of homogeneous spaces or spaces with a cohomogeneity one action more precisely we prove

guaranteed cost control for bilinear systems by static output feedback this paper proposes a static output feedback controller design technique for bilinear systems based on lyapunov s direct method a nonlinear control law is derived to stabilize the system in the presence of external disturbances sufficient condition is derived in terms of a state dependent nonlinear matrix inequality and then it is converted into a sum of squares sos optimization problem semidefinite programming and sos decomposition techniques are employed to solve the optimization problem the obtained output feedback controller guarantees an upper bound of the performance index the effectiveness of the proposed method is demonstrated through simulation results

existence and differential geometric properties of continuous families of periodic three body motions with non uniform mass distributions abstract using the method of analytic continuation in an equivariant differential geometric setting we exhibit two interesting families of vanishing angular momentum periodic orbits for the newtonian three body problem with non uniform mass distributions having two equal masses which connect at the celebrated figure 8 orbit exhibited by a chenciner and r montgomery 2000 in the case of equal masses and yield a continuous family of periodic three body motions in the plane at one end of the family when the two equal masses are infinitesimal and the third one reaches the value of 1 we arrive at a solution of a double kepler problem at the other end of the family when the third mass is infinitesimal we have a special case of periodic solution of a restricted three body problem