output feedback h_ infty control of continuous time infinite markovian jump linear systems via lmi methods the output feedback h infty control is addressed for a class of continuous time markov jump linear systems with the markov process taking values in an infinite countable set mathcal s we consider that only an output and the jump parameters are available to the controller via a certain bounded real lemma together with some extensions of schur complements and of the projection lemma a theorem which characterizes whether there exists a full order solution to the disturbance attenuation problem is devised in terms of two different linear matrix inequality lmi feasibility problems this result connects a certain projection approach to an lmi problem which is more amenable to computer solution and hence for design we conclude the paper with some design algorithms for the construction of such controllers and an illustrative example

grid structures and undecidable constraint theories abstract we prove three new undecidability results for computational mechanisms over finite trees there is a linear ultra shallow noetherian and strongly confluent rewrite system r such that the fragment of the first order theory of one step rewriting by r is undecidable the emptiness problem for tree automata with equality tests between cousins is undecidable and the fragment of the first order theory of set constraints with the union operator is undecidable the common feature of these three computational mechanisms is that they allow us to describe the set of first order terms that represent grids we extend our representation of grids by terms to a representation of linear two dimensional patterns by linear terms which allows us to transfer classical techniques on the grid to terms and thus to obtain our undecidability results

decidability of systems of set constraints with negative constraints set constraints are relations between sets of terms they have been used extensively in various applications in program analysis and type inference recently several algorithms for solving general systems of positive set constraints have appeared in this paper we consider systems of mixed positive and negative constraints which are considerably more expressive than positive constraints alone we show that it is decidable whether a given such system has a solution the proof involves a reduction to a number theoretic decision problem that may be of independent interest

standard monomial theory for g2 let g be a semi simple algebraic group and b a borel subgroup let x be a schubert variety in g b let l be an ample line bundle on g b as well as its restriction to x a standard monomial theory for schubert varieties in g b is developed in 9 11 8 10 as a generalization of the classical hodge young theory cf 3 4 this theory consists in the construction of a characteristic free basis for h0 x l this theory is extended to schubert varieties in the infinite dimensional flag variety ln b in 13 see also 12 in this paper we extend the theory to schubert varieties in the infinite dimensional flag variety p2n b

dissipativity analysis for singular systems with time varying delays this paper is concerned with the dissipativity analysis problem for singular systems with time varying delays a delay dependent criterion is established to guarantee the dissipativity of the underlying systems using the delay partitioning technique all the results given in this paper are not only dependent upon the time delay but also dependent upon the number of delay partitions the effectiveness and the reduced conservatism of the derived results are demonstrated by two illustrative examples

admissibility and dissipativity analysis for discrete time singular systems with mixed time varying delays abstract the problems of admissibility and dissipativity are studied for discrete time singular systems with mixed time varying delays the mixed time delays consist of both discrete and distributed delays by taking advantage of the delay partitioning technique a criterion that warrants the admissibility of the considered systems is established based on the criterion a dissipativity condition is also given all the results presented depend upon not only discrete delay and distributed delay but also depend upon the number of delay partitions some numerical examples are included to demonstrate the improvement and effectiveness of the proposed methods

observer synthesis method for lipschitz nonlinear discrete time systems with time delay an lmi approach abstract in this paper we address the problem of observer design for a class of lipschitz nonlinear discrete time systems with time delay the main contribution lies in the use of a new structure of the proposed observer with a novel lyapunov krasovskii functional thanks to these designs new nonrestrictive synthesis conditions expressed in terms of linear matrix inequalities lmis are obtained indeed the obtained lmis contain more degree of freedom than those established by the approaches available in the literature which consider a simple luenberger observer with a simple lyapunov function for the stability analysis an extension of the presented result to h performance analysis is given in order to take into account the noise if it exists affecting the considered system

synchronization in complex dynamical networks with nonsymmetric coupling based on the work of nishikawa and motter who have extended the well known master stability framework to include non diagonalizable cases we develop another extension of the master stability framework to obtain criteria for global synchronization several criteria for global synchronization are provided which generalize some previous results the jordan canonical transformation method is used in stead of the matrix diagonalization method especially we show clearly that the synchronizability of a dynamical network with nonsymmetric coupling is not always characterized by its second largest eigenvalue even though all the eigenvalues of the nonsymmetric coupling matrix are real furthermore the effects of the asymmetry of coupling on synchronizability of networks with different structures are analyzed numerical simulations are also done to illustrate and verify the theoretical results on networks in which each node is a dynamical limit cycle oscillator consisting of a two cell cellular neural network

finite time h filtering for a class of discrete time markovian jump systems with switching transition probabilities subject to average dwell time switching an extension of fixed transition probability markovian switching model to combine time varying transition probabilities has offered another set of useful regime switching models this paper investigated the problem of finite time h filtering for a class of discrete time markovian jump systems with switching transition probabilities subject to average dwell time switching based on the results of finite time boundness and average dwell time a novel sufficient condition for finite time bounded of h filtering is derived and the system trajectory stays within a prescribed bound finally an example is provided to illustrate the usefulness and effectiveness of the proposed method

bases for some reciprocity algebras i for a complex vector space v let p v be the algebra of polynomial functions on v in this paper we construct bases for the algebra of all gl n c x gl m1 c x gl m2 c x x gl mr c highest weight vectors in p c n c m where m m 1 m r and mj n for all 1 j r and the algebra of gl n c x gl k c x gl 1 c highest weight vectors in p c n c k c n c l

tensor operators iii some fundamental tensor operator identities let s 2 and let a1 a2 as where s ai z and a1 a2 as 1 let 1 t s the method of undetermined coefficients was used to investigate natural transformations a1 a2 as and t a1 at as at necessary and sufficient conditions were found on the coefficients defining and sufficient conditions on the coefficients defining t explicit formulas for 1 and s are given herein

iterative solution to linear matrix inequality arising from time delay descriptor systems linear matrix inequalities lmis are widely used to analyze the stability or performance of time delay descriptor systems tddss they are solved by the well known interior point method ipm via minimizing a strictly convex function by transforming the matrix variable into an expanded vector variable newton s method is used to get the unique minimizer of the strictly convex function by the iteration involving its gradient and hessian the obvious disadvantage of the ipm is the high storage requirement for the hessian hence this often renders that the ipm cannot solve large lmi problems due to finite memory limit to overcome this shortcoming for the first time an iterative algorithm based on the steepest descent method sdm is proposed to solve lmis by keeping matrix variable form instead of transforming it to an expanded vector and without using hessian matrix the gradient of the proposed objective function is explicitly given by a matrix function with the same dimension of the original matrix variable the efficiency of the proposed method is verified with numerical examples

stochastic stabilization of singular systems with markovian switchings this paper studies the stochastic stabilization problem for a class of singular markovian jump system the aim is to determine whether or not there is a stochastic feedback controller stabilizing a given singular markovian jump system smjs a new kind of stochastic controller only in the diffusion part is proposed such that the closed loop system has a unique solution and is almost surely exponentially admissible new sufficient condition for the existence of such a controller is given as linear matrix inequalities lmis based on this more extensions to transition probability matrix tpm with elements partially unknown and system states partially observable are developed a numerical example is used to demonstrate the effectiveness of the proposed methods

set constraints and automata we define a new class of automata which is an acceptor model for mappings from the set of terms t over a ranked alphabet into a set e of labels when e is a set of tuples of binary values an automaton can be viewed as an acceptor model for n tuples of tree languages we prove decidability of emptiness and closure properties for this class of automata as a consequence of these results we prove decidability of satisfiability of systems of positive and negative set constraints without projection symbols we prove the decidability of the satisfiability problem for systems of positive and negative set constraints without projection symbols moreover we prove that a non empty set of solutions always contain a regular solution i e a n tuple of regular tree languages we also deduce decidability results for properties of sets of solutions of systems of set constraints

on extended dissipativity of discrete time neural networks with time delay in this brief the problem of extended dissipativity analysis for discrete time neural networks with time varying delay is investigated the definition of extended dissipativity of discrete time neural networks is proposed which unifies several performance measures such as the h infty performance passivity l 2 l infty performance and dissipativity by introducing a triple summable term in lyapunov function the reciprocally convex approach is utilized to bound the forward difference of the triple summable term and then the extended dissipativity criterion for discrete time neural networks with time varying delay is established the derived condition guarantees not only the extended dissipativity but also the stability of the neural networks two numerical examples are given to demonstrate the reduced conservatism and effectiveness of the obtained results

stabilization of continuous time randomly switched systems via the lmi approach this paper is concerned on the stabilization problem of continuous time switched systems with random switching signal where the dwell time in each subsystem consists of a fixed part and random part new sufficient conditions for stabilizing controllers including mode independent case are provided in terms of lmis which could be solved directly moreover the obtained results are extended to a more general case that the corresponding operation mode of a controller experiences a disordering phenomenon without designing a controller depending on new operation modes noms a kind of controller only depending on the original operation modes ooms is proposed and satisfies a minimum variance approximation whose solvable conditions are also with lmi forms finally numerical examples are used to demonstrate the effectiveness of the proposed methods

observer based synchronization in complex dynamical networks with nonsymmetric coupling abstract based on a general complex dynamical network model with nonsymmetric coupling some criteria for synchronization are proposed based on the approach of state observer design unlike the nonobserver based dynamical networks where the coupling between two connected nodes is defined by an inner coupling matrix and full state coupling is typically needed in this paper smaller amount of coupling variables or even only a scalar output signal of each node is needed to synchronize the network unlike the commonly researched complex network model where the coupling between nodes is symmetric here in our network model the coupling configuration matrix is not assumed to be symmetric and may have complex eigenvalues the matrix jordan canonical formalization method is used instead of the matrix diagonalization method so in our synchronization criteria the coupling configuration matrix is not required to be diagonalizable especially the proposed step by step approach is simpler in computation than the existent ones which usually rely heavily on numerical toolbox and may be done by hand completely an example is given to illustrate the step by step approach in which each node is a two dimensional dynamical limit cycle oscillator system consisting of a two cell cellular neural network and numerical simulations are also done to verify the results of design

passivity analysis and passification of discrete time hybrid systems for discrete time hybrid systems in piecewise affine or piece wise polynomial pwp form this note proposes sufficient passivity analysis and synthesis criteria based on the computation of piecewise quadratic or pwp storage functions by exploiting linear matrix inequality techniques and sum of squares decomposition methods passivity analysis and synthesis of passifying controllers can be carried out through standard semidefinite programming packages providing a tool particularly important for stability of interconnected heterogeneous dynamical systems

a generalization of the littlewood richardson rule for the general linear group gz the littlewood richardson rule see 18 193 gives a method to calculate the decomposition of a tensor product of two irreducible g representations the aim of this article is to give a generalization of this rule for all simple simply connected algebraic groups of type a b c d g2 and e we obtain also partial results for g of type f4 e and es the restrictions in the last three cases come from the fact that for the formulation of the decomposition rules we need the notion of a standard young tableau such a notion has been developed by seshadri lakshmibai musili and rajeswari in a series of articles see ll 13 14 16 but not yet for all representations of the last three exceptional groups the advantage of the notion of a young tableau developed by seshadri et al is that it is independent of the type of the group for the convenience of the reader not used to this notion we give first a seperate proof for g sz using the classical notion of a standard young tableau of course for applications the classical notion is much more appropriate in the appendix we give a translation of the notion of a standard young tableau in the sense of seshadri et al into the classical notion of a young tableau for g sp2 and spin in 3 8 we give also such a translation for g g for the other exceptional groups such a translation is not known to the author let p be a dominant weight for g and denote by i the corresponding simple g module we assume that the character of vp is given by ct eycr where the sum has to be taken over all standard young tableaux f of shape p p and v 5 is the weight of the tableau y now by the

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

bibo stabilization of feedback control systems with time dependent delays abstract this paper investigates the bounded input bounded output bibo stability in a class of control system of nonlinear differential equations with time delay the proofs are based on our studies on the boundedness of the solutions of a general class of nonlinear volterra integral equations

robust finite time stability and stabilization of uncertain markovian jump systems with time varying delay this paper deals with the robust finite time stability and stabilization problems of uncertain stochastic delayed jump systems where the uncertainty is in the form of additive perturbations and exists in the drift and diffusion sections simultaneously though perturbation time varying delay and brownian motion existing at the same time two conditions checking its robust finite time stability are proposed by a mode dependent parameter approach which are different from some existing methods based on the proposed results sufficient conditions for the existence of the state feedback controller are provided with lmis which could be solved directly it is seen that all the features of the underlying system such as time varying delay perturbation diffusion mode dependent parameters and uncertain transition rate matrix play important roles in the system analysis and synthesis of finite time stability finally numerical examples are used to demonstrate the effectiveness and superiority of the proposed methods

further improvement of free weighting matrices technique for systems with time varying delay a novel method is proposed in this note for stability analysis of systems with a time varying delay appropriate lyapunov functional and augmented lyapunov functional are introduced to establish some improved delay dependent stability criteria less conservative results are obtained by considering the additional useful terms which are ignored in previous methods when estimating the upper bound of the derivative of lyapunov functionals and introducing the new free weighting matrices the resulting criteria are extended to the stability analysis for uncertain systems with time varying structured uncertainties and polytopic type uncertainties numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method

set constraints with projections set constraints form a constraint system where variables range over the domain of sets of trees they give a natural formalism for many problems in program analysis syntactically set constraints are conjunctions of inclusions between expressions built over variables constructors constants and function symbols from a given signature and a choice of set operators that defines the specific class of set constraints in this article we are interested in the class of set constraints with projections which is the class with all boolean operators union intersection and complement and projections that in program analysis directly correspond to type destructors we prove that the problem of existence of a solution of a system of set constraints with projections is in nexptime and thus that it is nexptime complete

on character generators for simple lie algebras we study character generating functions character generators of simple lie algebras the expression due to patera and sharp derived from the weyl character formula is first reviewed a new general formula is then found it makes clear the distinct roles of outside and inside elements of the integrity basis and helps determine their quadratic incompatibilities we review analyse and extend the results obtained by gaskell using the demazure character formulae we find that the fundamental generalized poset graphs underlying the character generators can be deduced from such calculations these graphs introduced by baclawski and towber can be simplified for the purposes of constructing the character generator the generating functions can be written easily using the simplified graphs and associated demazure expressions the rank two algebras are treated in detail but we believe our results are indicative of those for general simple lie algebras

polytopes associated to demazure modules of symmetrizable kac moody algebras of rank two let 1 2 be the two fundamental weights of a symmetrizable kac moody algebra g of rank two hence necessarily affine or finite and an element of the weyl group in this paper we construct polytopes p 1 p 2 rl and a linear map rl h such that for any dominant weight k1 1 k2 2 we have char e e e x where the sum is over all the integral points x of the polytope k1p 1 k2p 2 furthermore we show that there exists a flat deformation of the schubert variety s into the toric variety defined by p 1 p 2

dissipativity analysis and design for uncertain markovian jump systems with time varying delays this paper deals with the problems of dissipativity analysis and dissipativity based controller design for markovian jump systems with both time varying delays and norm bounded parametric uncertainties improved delay dependent conditions for the system concerned to be strictly dissipative are established by using a mode dependent lyapunov krasovskii functional and introducing some slack variables these conditions are expressed by means of linear matrix inequalities lmis which are easy to check it is also shown that these conditions are less conservative than those obtained by using the existing methods the dissipativity synthesis problem is considered and on the basis of the obtained dissipativity conditions both the state feedback and dynamic output feedback controllers are designed to guarantee the strict dissipativity of the closed loop systems numerical examples are provided to demonstrate the utility of the developed methods

character generators for unitary and symplectic groups combinatorial algorithms for computing the character generators of u n su n and sp 2n c are described these algorithms produce relatively compact nested expressions for the character generators moreover the terms appearing in these expressions all have positive coefficients this feature is not shared by the expression for the character generator which uses the weyl character formula