reduced order h filtering for linear systems with markovian jump parameters this paper addresses the reduced order h filtering problem for continuous time makovian jump linear systems where the jump parameters are modelled by a discrete time markov process sufficient conditions for the existence of the reduced order h filter are proposed in terms of linear matrix inequalities lmis and a coupling non convex matrix rank constraint in particular the sufficient conditions for the existence of the zero order h filter can be expressed in terms of a set of strict lmis the explicit parameterization of the desired filter is also given finally a numerical example is given to illustrate the proposed approach

robust linear filtering for discrete time hybrid markov linear systems in this paper we consider the robust linear filtering of hybrid discrete time markovian jump linear systems we assume that only an output of the system is available and therefore the values of the jump parameter are not known it is desired to design a dynamic linear filter such that the closed loop system is mean square stable and minimizes the stationary expected value of the square error we consider uncertainties on the parameters of the possible modes of operation of the system a linear matrix inequalities lmi formulation is proposed to solve the problem for the case in which there are no uncertainties on the modes of operation of the system we show that the lmi formulation provides a filter with the same stationary mean square error as the one obtained from the riccati equation approach

unbiased h filtering for neutral markov jump systems abstract the unbiased h filtering problem is studied for stochastic markov jump system with constant and neutral time delays by re constructing the system the dynamic filtering error characteristics of unknown inputs and time delays are obtained a sufficient condition is initially established on the existence of mode dependent unbiased h filter of constant time delay system using stochastic lyapunov krasovskii function then the unbiased h filter is also designed for the jump system with constant and neutral time delays the design criterions are presented in the form of linear matrix inequality finally the unbiased h filtering problems are described as optimization algorithms numerical examples illustrate the effectiveness of the developed techniques

tropical varieties for non archimedean analytic spaces generalizing the construction from tropical algebraic geometry we associate to every irreducible d dimensional closed analytic subvariety of mathbb g m n a tropical variety in n with respect to a complete non archimedean place by methods of analytic and formal geometry we prove that the tropical variety is a totally concave locally finite union of d dimensional polytopes for an algebraic morphism f x a to a totally degenerate abelian variety a we give a bound for the dimension of f x in terms of the singularities of a strictly semistable model of x a closed d dimensional subvariety x of a induces a periodic tropical variety a generalization of mumford s construction yields models of x and a which can be handled with the theory of toric varieties for a canonically metrized line bundle l on a the measures c1 l x d are piecewise haar measures on x using methods of convex geometry we give an explicit description of these measures in terms of tropical geometry in a subsequent paper this is a key step in the proof of bogomolov s conjecture for totally degenerate abelian varieties over function fields

optimal h filtering for singular markovian jump systems abstract this paper considers h filtering for continuous time singular markovian jump systems smjss while the existing researches in the literature suggested only sufficient conditions in terms of strict or non strict linear matrix inequalities lmis for sub optimal h filtering this paper successfully derives a necessary and sufficient condition in terms of strict lmis for optimal h filtering first the necessary and sufficient condition that guarantees the stochastic admissibility of the filtering error system is obtained in terms of matrix inequalities to reformulate it into strict lmis the congruence transformation by specially designed matrices is used two numerical examples show the validity of proposed h filtering

chern character for twisted k theory of orbifolds for an orbifold x and h 3 x z we introduce the twisted cohomology h c x and prove that the non commutative chern character of connes karoubi establishes an isomorphism between the twisted k groups k x c and the twisted cohomology h

paper low order control design for lmi problems using alternating projection methods computational techniques based on alternating projections are proposed to solve control design problems described by linear matrix inequalities lmis in particular we concentrate on the stabilization and the suboptimal h output feedback control design problems these problems can be described by a pair of lmis and an additional coupling condition this coupling condition is convex for the full order control design problem but convexity is lost for the control problem of order strictly less than the plant order we formulate these problems as feasibility problems with matrix constraint sets of simple geometry and we utilize this geometry to obtain analytical expressions for the orthogonal projection operators onto these sets full order and low order controllers are designed using alternating projection methods for the full order controller case global convergence of the alternating projection methods to a feasible solution is guaranteed however for the low order control case only local convergence is guaranteed an example is provided to illustrate the use of these methods for the full order and the low order controller design

fixed order robust h sub spl infin filter design for markovian jump systems with uncertain switching probabilities this paper discusses the fixed order robust h sub spl infin filtering problem for a class of markovian jump linear systems with uncertain switching probabilities the uncertainties under consideration are assumed to be norm bounded in the system matrices and to be elementwise bounded in the mode transition rate matrix respectively first a criterion based on linear matrix inequalities is provided for testing the h sub spl infin filtering level of a filter over all the admissible uncertainties then a sufficient condition for the existence of the fixed order robust h sub spl infin filters is established in terms of the solvability of a set of linear matrix inequalities with equality constraints to determine the filter a globally convergent algorithm involving convex optimization is suggested finally a numerical example is used to illustrate that the developed theory is more effective than the existing results

index theory gerbes and hamiltonian quantization we give an atiyah patodi singer index theory construction of the bundle of fermionic fock spaces parametrized by vector potentials in odd space dimensions and prove that this leads in a simple manner to the known schwinger terms faddeev mickelsson cocycle for the gauge group action we relate the aps construction to the bundle gerbe approach discussed recently by carey and murray including an explicit computation of the dixmier douady class an advantage of our method is that it can be applied whenever one has a form of the aps theorem at hand as in the case of fermions in an external gravitational field

h infintity control of large scale jump linear systems via averaging and aggregation this paper studies under state feedback policies the h infinity control design for large scale jump linear systems where the form process admits strong and weak interactions through an analysis that covers both finite and infinite horizon cases and using averaging and aggregation techniques an aggregate jump linear system of considerably smaller order has been obtained along with a corresponding compatible cost function this reduced order aggregate problem is another piecewise deterministic h infinity control problem and on the basis of the solution of this problem we obtain the asymptotic limit of the optimal performance level for the full order system as well as an approximate controller that can asymptotically achieve any desired performance level for the full order system a by product of this analysis is a similar decomposition for the piecewise deterministic linear regulator problem

reduced order filtering for networks with markovian jumping parameters and missing measurements abstractthe problem of reduced order h filters design for markovian jumping complex networks with polytopic time varying transition probability matrices is first addressed in this paper where th

a linear matrix inequality approach to robust h sub spl infin filtering we consider the robust h sub spl infin filtering problem for a general class of uncertain linear systems described by the so called integral quadratic constraints iqcs this problem is important in many signal processing applications where noise nonlinearity quantization errors time delays and unmodeled dynamics can be naturally described by iqcs the main contribution of this paper is to show that the robust h spl infin filtering problem can be solved using linear matrix inequality lmi techniques which are numerically efficient owing to recent advances in convex optimization the paper deals with both continuous and discrete time uncertain linear systems

robust energy to peak filter design for stochastic time delay systems abstract this paper considers the robust energy to peak filtering problem for uncertain stochastic time delay systems the stochastic uncertainties appear in both the dynamic and the measurement equations and the state delay is assumed to be time varying attention is focused on the design of full order and reduced order filters guaranteeing a prescribed energy to peak performance for the filtering error system sufficient conditions are formulated in terms of linear matrix inequalities lmis and the corresponding filter design is cast into a convex optimization problem which can be efficiently handled by using standard numerical algorithms in addition the results obtained are further extended to more general cases where the system matrices also contain uncertain parameters the most frequently used ways of dealing with parameter uncertainties including polytopic and norm bounded characterizations have been taken into consideration with convex optimization problems obtained for the design of desired robust energy to peak filters

skeletons and tropicalizations abstract let k be a complete algebraically closed non archimedean field with ring of integers k and let x be a k variety we associate to the data of a strictly semistable k model x of x plus a suitable horizontal divisor h a skeleton s x h in the analytification of x this generalizes berkovich s original construction by admitting unbounded faces in the directions of the components of h it also generalizes constructions by tyomkin and baker payne rabinoff from curves to higher dimensions every such skeleton has an integral polyhedral structure we show that the valuation of a non zero rational function is piecewise linear on s x h for such functions we define slopes along codimension one faces and prove a slope formula expressing a balancing condition on the skeleton moreover we obtain a multiplicity formula for skeletons and tropicalizations in the spirit of a well known result by sturmfels tevelev we show a faithful tropicalization result saying roughly that every skeleton can be seen in a suitable tropicalization we also prove a general result about existence and uniqueness of a continuous section to the tropicalization map on the locus of tropical multiplicity one

all controllers for the general h control problem lmi existence conditions and state space formulas this paper presents all controllers for the general h control problem with no assumptions on the plant matrices necessary and sufficient conditions for the existence of an h controller of any order are given in terms of three linear matrix inequalities lmis our existence conditions are equivalent to scherer s results but with a more elementary derivation furthermore we provide the set of all h controllers explicitly parametrized in the state space using the positive definite solutions to the lmis even under standard assumptions full rank etc our controller parametrization has an advantage over the q parametrization the freedom q a real rational stable transfer matrix with the h norm bounded above by a specified number is replaced by a constant matrix l of fixed dimension with a norm bound and the solutions x y to the lmis the inequality formulation converts the existence conditions to a convex feasibility problem and also the free matrix l and the pair x y define a finite dimensional design space as opposed to the infinite dimensional space associated with the q parametrization

deformation quantization of gerbes this is the first in a series of articles devoted to deformation quantization of gerbes we introduce basic definitions interpret deformations of a given stack as maurer cartan elements of a differential graded lie algebra dgla and classify deformations of a given gerbe in terms of maurer cartan elements of the dgla of hochschild cochains twisted by the cohomology class of the gerbe we also classify all deformations of a given gerbe on a symplectic manifold as well as provide a deformation theoretic interpretation of the first rozansky witten class

delay dependent robust h sub spl infin and l sub 2 l sub spl infin filtering for a class of uncertain nonlinear time delay systems this note presents delay dependent robust h sub spl infin and l sub 2 l sub spl infin filter designs for a class of nonlinear systems with multiple time varying delays in the state and parameter uncertainties residing in a polytope the nonlinearities are assumed to satisfy global lipschitz conditions attention is focused on the design of robust full order and reduced order filters guaranteeing a prescribed noise attenuation level in an h sub spl infin or l sub 2 l sub spl infin sense the admissible filters can be obtained from the solution of convex optimization problems in terms of linear matrix inequalities which can be solved via efficient interior point algorithms

h filtering for networked systems with partly known distribution transmission delays this paper studies the h filtering problem for a class of discrete time networked systems with partly known distribution transmission delays it is assumed that the random sensor filter delay satisfies markovian characteristics but the transition probabilities of the delay transferring from one value to others are partly known a novel measurement model is proposed to reflect the random delay of the transmission modes and the resulting filtering error system is modeled as a markovian jump system mjs with multiple modes and state delay sufficient conditions are derived for the filtering error system to be stochastically stable and ensure a prescribed h disturbance attenuation level bound by using mode dependent lyapunov functional approach based on the derived conditions a design procedure for the h filter is also presented a numerical example is provided to show the design process of the filter and the effectiveness of the proposed method

uniformization of deligne mumford curves we compute the fundamental groups of non singular analytic delignemumford curves classify the simply connected ones and classify analytic deligne mumford curves by their uniformization type as a result we find an explicit presentation of an arbitrary deligne mumford curve as a quotient stack along the way we compute the automorphism 2 groups of weighted projective stacks p n1 n2 nr we also discuss connections with the theory of f groups 2 groups and bass serre theory of graphs of groups

reduced order h sub spl infin filtering for stochastic systems this paper deals with the reduced order h sub spl infin filtering problem for stochastic systems necessary and sufficient conditions are obtained for the existence of solutions to the continuous time and discrete time problems in terms of certain linear matrix inequalities lmis and a coupling nonconvex rank constraint condition furthermore when these conditions are feasible an explicit parametrization of all desired reduced order filters corresponding to a feasible solution is given in particular when the reduced order filter is restricted to be a static one then simple conditions expressed by lmis only without any rank constraints are derived and a parametrization of all solutions is also given finally an illustrative example is provided to show the effectiveness of the proposed approach

filtering and smoothing in an h sup infinity setting the problems of filtering and smoothing are considered for linear systems in an h sup infinity setting i e the plant and measurement noises have bounded energies are in l sub 2 but are otherwise arbitrary two distinct situations for the initial condition of the system are considered the initial condition is assumed known in one case while in the other the initial condition is not known but the initial condition the plant and measurement noise are in some weighted ball of r sup n xl sub 2 finite horizon and infinite horizon cases are considered necessary and sufficient conditions are presented for the existence of estimators both filters and smoothers that achieve a prescribed performance bound and algorithms that result in performance within the bounds are developed in case of smoothers the optimal smoother is also presented the approach uses basic quadratic optimization theory in a time domain setting as a consequence of which both linear time varying and time invariant systems can be considered with equal ease in the smoothing problem for linear time varying systems one considers only the finite horizon case

design of optimal reduced order h2 filters abstract this paper shows that the design of a reduced order optimal h 2 filter is equivalent to a frequency weighted l 2 norm model reduction problem

optimal unbiased filtering via linear matrix inequalities abstract solutions to the optimal h and l2 l unbiased reduced order filtering problems are obtained in terms of linear matrix inequalities lmis the order of the optimal filter is equal to the number of measurements both continuous and discrete time results are presented an explicit parametrization of all optimal unbiased filters is provided in terms of a free contractive matrix

a delay dependent approach to robust h sub spl infin filtering for uncertain discrete time state delayed systems a delay dependent approach to robust h sub spl infin filtering is proposed for linear discrete time uncertain systems with multiple delays in the state the uncertain parameters are supposed to reside in a polytope and the attention is focused on the design of robust filters guaranteeing a prescribed h sub spl infin noise attenuation level the proposed filter design methodology incorporates some recently appeared results such as moon s new version of the upper bound for the inner product of two vectors and de oliveira s idea of parameter dependent stability which greatly reduce the overdesign introduced in the derivation process in addition to the full order filtering problem the challenging reduced order case is also addressed by using different linearization procedures both full and reduced order filters can be obtained from the solution of convex optimization problems in terms of linear matrix inequalities which can be solved via efficient interior point algorithms numerical examples have been presented to illustrate the feasibility and advantages of the proposed methodologies

kalman filtering for linear systems with coefficients driven by a hidden markov jump process abstract we present an explicit algorithm for the solution of the nonlinear filtering problem concerning a linear partially observed diffusion type model where the coefficients are driven by a hidden markov jump process of which one can observe the occurrence of a jump the recursive filter is of a branching type with its finite dimension growing for each jump of the hidden markov process

non abelian differentiable gerbes abstract we study non abelian differentiable gerbes over stacks using the theory of lie groupoids more precisely we develop the theory of connections on lie groupoid g extensions which we call connections on gerbes and study the induced connections on various associated bundles we also prove analogues of the bianchi identities in particular we develop a cohomology theory which measures the existence of connections and curvings for g gerbes over stacks we also introduce g central extensions of groupoids generalizing the standard groupoid s 1 central extensions as an example we apply our theory to study the differential geometry of g gerbes over a manifold

on the relative dual of an s1 gerbe over an orbifold abstract we construct a new effective orbifold y with an s 1 gerbe c to study an s 1 gerbe t on a g gerbe y over an orbifold b we view the former as the relative dual relative to b of the latter we show that the two pairs y t and y c have isomorphic categories of sheaves and also the associated twisted groupoid algebras are morita equivalent as a corollary the k theory and cohomology groups of y t and y c are isomorphic

partially mode dependent design of h filter for stochastic markovian jump systems with mode dependent time delays abstract this paper is concerned with the h filtering problem for stochastic delay systems with markovian jump parameters where both the state dynamics and measurements of systems are corrupted by wiener process in contrast with traditional mode dependent and mode independent filtering methods a new partially mode dependent filter is established via using a mode dependent lyapunov function where the system mode available to filter implementation is transmitted through an unreliable network and the stochastic property of mode available to a filter is considered sufficient conditions for the existence of h filters are obtained as linear matrix inequalities finally an example is used to show the effectiveness of the given theoretical results

robust h sub spl infin control of uncertain markovian jump systems with time delay this paper is concerned with the robust stochastic stabilizability and robust h sub spl infin disturbance attenuation for a class of uncertain linear systems with time delay and randomly jumping parameters the transition of the jumping parameters is governed by a finite state markov process sufficient conditions on the existence of a robust stochastic stabilizing and spl gamma suboptimal h sub spl infin state feedback controller are presented using the lyapunov functional approach it is shown that a robust stochastically stabilizing h sub spl infin state feedback controller can be constructed through the numerical solution of a set of coupled linear matrix inequalities

output feedback control of markov jump linear systems in continuous time this paper addresses the dynamic output feedback control problem of continuous time markovian jump linear systems the fundamental point in the analysis is an lmi characterization comprising all dynamical compensators that stabilize the closed loop system in the mean square sense the h sub 2 and h sub spl infin norm control problems are studied and the h sub 2 and h sub spl infin filtering problems are solved as a by product