lmi based robust control of fractional order uncertain linear systems this paper concerns with the method of observer based control and static output feedback control for fractional order uncertain systems with the fractional commensurate order a 0 a 1 and a email protected email protected 2 via linear matrix inequality lmi approach respectively first the sufficient conditions for robust asymptotical stability of the closed loop control systems are presented next by using matrix s singular value decomposition svd and lmi technics the existence condition and method of designing a robust stabilizing controller for such fractional order control systems are derived unlike previous methods the results are obtained in terms of lmi which can be easily obtained by matlab s lmi toolbox finally two numerical examples demonstrate the validity of this approach

spherical unitary highest weight representations in this paper we give an almost complete classification of the h spherical unitary highest weight representations of a hermitian lie group g where g h is a symmetric space of cayley type

on temporal logics with data variable quantifications although data values are available in almost every computer system reasoning about them is a challenging task due to the huge data size or even infinite data domains temporal logics are the well known specification formalisms for reactive and concurrent systems various extensions of temporal logics have been proposed to reason about data values mostly in the last decade among them one natural idea is to extend temporal logics with variable quantifications ranging over an infinite data domain grumberg kupferman and sheinvald initiated the research on this topic recently and obtained several interesting results however there is still a lack of systematic investigation on the theoretical aspects of the variable extensions of temporal logics our goal in this paper is to fill this gap around this goal we make the following choices 1 we consider the variable extensions of two widely used temporal logics linear temporal logic ltl and computation tree logic ctl and allow arbitrary nestings of variable quantifications with boolean and temporal operators the resulting logics are called respectively variable ltl in brief vltl and variable ctl in brief vctl 2 we investigate the decidability and complexity of both the satisfiability and model checking problems over both finite and infinite words trees in particular we obtain the following results existential variable quantifiers or one single universal quantifier in the beginning already entail the undecidability of the satisfiability problems of both vltl and vctl over both finite and infinite words trees if only existential path quantifiers are used in vctl then the satisfiability problem over finite trees is decidable no matter which variable quantifiers are available for vltl formulae with one single universal variable quantifier in the beginning if the occurrences of the non parameterized atomic propositions are guarded by the positive occurrences of the quantified variables then its satisfiability problem becomes decidable over both finite and infinite words based on these results of the satisfiability problem we deduce the un decidability results of the model checking problem

spherical characters on p adic symmetric spaces symmetric spaces over local fields and the harmonic analysis of their class one representations arise as the local calculation of jacquet s theory of the relative trace formula there is an extensive literature at the real place but few general results for p adic fields are known the objective here is to carry over to symmetric spaces as much as possible of queens and the prerequisite results of howe and to provide counterexamples for those things which do not generalize we derive the weyl integration formula local constancy of the spherical character on the regular set howe s conjecture for groups the germ expansion for spherical characters at the origin and a spherical version of howe s kirillov theory for compact p adic groups we find that the density property of regular orbital integrals fails some of the basic ideas are nascent in hakim s thesis written under herve jacquet

robust stability and stabilization of fractional order interval systems with the fractional order alpha the 0 alpha 1 case this technical note firstly presents a sufficient and necessary condition for the robust asymptotical stability of fractional order interval systems with the fractional order satisfying 0 1 and then a sufficient condition for the robust asymptotical stabilization of such fractional order interval systems is derived all the results are obtained in terms of linear matrix inequalities finally two illustrative examples are given to show that our results are effective for checking the robust stability and designing the robust stabilizing controller for fractional order interval systems

fonctions orbitales surgc gr formule d inversion des integrales orbitales et formule de plancherel resume soitgun groupe de lie semi simple complexe connexe et simplement connexe d algebre de lie g soithune forme reelle degd algebre de lie h apres une etude generale des fonctions orbitales surg h nous construisons des series de fonctions orbitales propres sous l action de l algebre des operateurs differentielsg invariant surg h en utilisant les resultats de p harinck base de la serie la plus continue de fonctions generalisees spheriques surg c g r prepublication concernant les fonctions generalisees spheriques surg h nous demontrons la formule d inversion des integrales orbitales d une fonction de classec a support compact surg h nous en deduisons la formule de plancherel pour l espace symetriqueg h letgbe a complex connected and simply connected semisimple lie group with lie algebra g lethbe a real form ofgwith lie algebra h after a general study of orbital functions ong h we construct series of orbital functions which are eigen for the action ofg invariant differential operators ong h using the results harinck base de la serie la plus continue de fonctions generalisees spheriques surg c g r prepublication about spherical generalized functions ong h we prove the inversion formula for orbital integrals of ac function with compact support ong h we deduce the plancherel formula for the symmetric spaceg h

robust stability and stabilization of fractional order interval systems an lmi approach this technical note presents necessary and sufficient conditions for the stability and stabilization of fractional order interval systems the results are obtained in terms of linear matrix inequalities two illustrative examples are given to show that our results are effective and less conservative for checking the robust stability and designing the stabilizing controller for fractional order interval systems

base de la serie la plus continue de fonctions generalisees spheriques surgc gr resume soit g un groupe de lie semi simple complexe connexe et simplement connexe d algebre de lie g soit h une forme reelle de g d algebre de lie h on suppose que h admet une sous algebre de cartan de type compact t pour un element regulier du dual de t on construit une base de l espace des fonctions generalisees spheriques sur g h propres sous l action de l algebre des operateurs differentiels g invariants sur g h pour le caractere defini par on etudie ensuite le prolongement meromorphe en et la croissance des elements de cette base ces fonctions generalisees sont ensuite exprimees en terme de coefficients de representations de g ces resultats sont generalises a d autres series de fonctions generalisees spheriques let g be a complex connected and simply connected semisimple lie group with lie algebra g let h be a real form of g with lie algebra h we suppose that h admits a cartan subalgebra t of compact type for a regular element of the dual of h we construct a basis of the space of spherical generalized functions f such that for all g invariant differential operator d on g h we have d f d f where is the character defined by then we study the meromorphic continuation and the growth of the element of this basis we give these functions in terms of coefficients of representations of g these results are generalized to other series of spherical generalized functions

robust stability test of a class of linear time invariant interval fractional order system using lyapunov inequality this paper provides a new analytical robust stability checking method of fractional order linear time invariant interval uncertain system this paper continues the authors previous work yangquan chen hyo sung ahn i podlubny robust stability check of fractional order linear time invariant systems with interval uncertainties in proceedings of the ieee conference on mechatronics and automation niagara falls canada july 2005 pp 210 215 where matrix perturbation theory was used for the new robust stability checking lyapunov inequality is utilized for finding the maximum eigenvalue of a hermitian matrix through numerical examples the usefulness and the effectiveness of the newly proposed method are verified

robust asymptotical stability of fractional order linear systems with structured perturbations this paper considers the robust asymptotical stability problem of fractional order linear systems with structured perturbations which are more general than the investigated fractional order interval systems based on the kronecker product and m analysis necessary and sufficient conditions for the robust asymptotical stability are established by transforming such a problem into checking the nonsingularity of a class of uncertain matrices furthermore the robustness bounds with respect to parametric perturbations to preserve the asymptotical stability are given in terms of the structured singular values finally illustrative examples are given to show the effectiveness of the proposed approach

stabilization of multi group models with multiple dispersal and stochastic perturbation via feedback control based on discrete time state observations abstract this paper focuses on the multi group models with multiple dispersal and stochastic perturbation mgmds the effect of both multiple dispersal among groups and stochastic perturbation are taken into consideration the stabilization of mgmds is investigated via feedback control based on the discrete time state observations in addition a systematic method is given to construct a global lyapunov function for mgmds by means of graph theory and lyapunov method some sufficient conditions are obtained to ensure the stabilization in the sense of mean square asymptotical stability an upper bound of the duration between two consecutive state observations is estimated moreover to show the applicability of our results the main theory is employed to a stochastic coupled oscillators finally a numerical example is given to illustrate the effectiveness and feasibility of the theoretical results

on the meromorphic extension of the spherical functions on noncompactly causal symmetric spaces abstract we determine integral formulas for the meromorphic extension in the parameter of the spherical functions on a noncompactly causal symmetric space the main tool is bernstein s theorem on the meromorphic extension of complex powers of polynomials the regularity properties of are deduced in particular the possible poles of are located among the translates of the zeros of the bernstein polynomial the translation parameter depends only on the structure of the symmetric space the expression of the bernstein polynomial is conjectured the relation between the bernstein polynomial and the product formula of the c function is analyzed the conjecture is verified in the rank one case the explicit formulas obtained in this case yield a detailed description of singularities of in the general higher rank case the integral formulas are applied to find asymptotic estimates for the spherical functions in the appendix the spherical functions on noncompactly causal symmetric spaces are regarded as a special instance of harish chandra type expansions associated with roots systems with arbitrary multiplicities we study expansions obtained by taking averages over arbitrary parabolic subgroups of the weyl group of the root system the possible singularities are located in this general context

discussion on barbalat lemma extensions for conformable fractional integrals in this paper the barbalat type lemmas for conformable fractional order integrals which can be used to conclude the convergence of a function to zero is discussed

technical communique on the robustness of linear systems with nonlinear uncertain parameters the present paper studies the stability robustness problem of an uncertain state space system we propose a new uncertain state space model which allows second order uncertain parameters the uncertainty in the model appears in the form of a combination of additive perturbation and multiplicative perturbation it is shown that the model has a strong practical background a robustness criterion based on the model is derived an example shows advantages of the proposed approach

meromorphic extension of the spherical functions on a class of ordered symmetric spaces we discuss a conjecture of olafsson and pasquale published in j funct anal 181 2001 346 this conjecture gives the bernstein sato polynomial associated with the poisson kernel of the ordered or non compactly causal symmetric spaces the bernstein sato polynomials allow to locate the singularities of the spherical functions on the considered spaces we prove that this conjecture does not hold in general and propose a slight improvement of it finally we prove that the new conjecture holds for a class of ordered symmetric spaces called both the makarevic spaces of type i and the satellite cones

robust stability and stabilization of fractional order linear systems with polytopic uncertainties robust stability and stabilization of fractional order uncertain linear systems with order 0 1 and 1 2 are considered in the paper a new polytopic type uncertain state space model for fractional order linear systems is addressed which allows second order uncertain parameters the uncertainty in the fractional order model appears in terms of a polytope of matrices some sufficient criteria for the robust asymptotical stable and stabilization for such fractional order uncertain linear systems are derived all the results are obtained in terms of linear matrix inequalities lmis numerical examples are presented to demonstrate the validity and feasibility of the obtained results

technical communique necessary and sufficient stability condition of fractional order interval linear systems this paper establishes a necessary and sufficient stability condition of fractional order interval linear systems it is supposed that the system matrix a is an interval uncertain matrix and fractional commensurate order belongs to email protected email protected 2 using the existence condition of hermitian p p for a complex lyapunov inequality we prove that the fractional order interval linear system is robust stable if and only if there exists hermitian matrix p p such that a certain type of complex lyapunov inequality is satisfied for all vertex matrices the results are directly extended to the robust stability condition of fractional order interval polynomial systems

nonlinear impulsive problems for fractional differential equations and ulam stability in this paper the first purpose is treating cauchy problems and boundary value problems for nonlinear impulsive differential equations with caputo fractional derivative we introduce the concept of piecewise continuous solutions for impulsive cauchy problems and impulsive boundary value problems respectively by using a new fixed point theorem we obtain many new existence uniqueness and data dependence results of solutions via some generalized singular gronwall inequalities the second purpose is discussing ulam stability for impulsive fractional differential equations some new concepts in stability of impulsive fractional differential equations are offered from different perspectives some applications of our results are also provided

fourier and poisson transformation associated to a semisimple symmetric space soit g un groupe de lie semisimple connexe contenu dans un groupe de lie semisimple simplement connexe dont l algebre de lie est la complexification de celle de g soit une involution non triviale de g et une involution de cartan commutant avec soit h un groupe point fixe de on etudie les representations h spheriques de dimension finie de g contenant un vecteur k fixe ou k est un sous groupe compact maximal stable de g sous representations de dimension finie de le noyau de poisson la distribution u i la transformation de fourier et poisson formules integrales

finite state unification automata and relational languages abstract we define the new notion of a finite state unification automaton a device for finite state recognition of relational languages by means of unification transitions words in such a language are formed by composing base relations and have the general form r i 1 x j 1 x k 1 r i n x j n x k n for some n generation of such languages by regarding horn clauses as grammers has been considered before but to the best of our knowledge recognizing such languages by suitably designed automata is a new approach the main result presented is a pumping lemma forming a necessary condition for finite state recognizability some example results about such automata are given

holomorphic h spherical distribution vectors in principal series representations let g h be a semisimple symmetric space the main tool to embed a principal series representation of g into l2 g h are the h invariant distribution vectors if g h is a non compactly causal symmetric space then g h can be realized as a boundary component of the complex crown in this article we construct a minimal g invariant subdomain h of with g h as shilov boundary let be a spherical principal series representation of g we show that the space of h invariant distribution vectors of which admit a holomorphic extension to h is one dimensional furthermore we give a spectral definition of a hardy space corresponding to those distribution vectors in particular we achieve a geometric realization of a multiplicity free subspace of l2 g h mc in a space of holomorphic functions

vecteurs distributions h invariants pour les series principales generalisees d espaces symetriques reductifs et prolongement meromorphe d integrales d eisenstein

the cos λ and sin λ transforms as intertwining operators between generalized principal series representations of sl n 1 k abstract in this article we connect topics from convex and integral geometry with well known topics in representation theory of semisimple lie groups by showing that the cos and sin transforms on the grassmann manifolds gr p k su n 1 k s u p k u n 1 p k are standard intertwining operators between certain generalized principal series representations induced from a maximal parabolic subgroup p p of sl n 1 k the index p indicates the dependence of the parabolic on p the general results of knapp and stein 1971 1980 20 21 and vogan and wallach 1990 44 then show that both transforms have meromorphic extension to c and are invertible for generic c furthermore known methods from representation theory combined with a selberg type integral allow us to determine the k spectrum of those operators

robust stabilization of uncertain linear systems quadratic stabilizability and h sup infinity control theory the problem of robustly stabilizing a linear uncertain system is considered with emphasis on the interplay between the time domain results on the quadratic stabilization of uncertain systems and the frequency domain results on h sup infinity optimization a complete solution to a certain quadratic stabilization problem in which uncertainty enters both the state and the input matrices of the system is given relations between these robust stabilization problems and h sup infinity control theory are explored it is also shown that in a number of cases if a robust stabilization problem can be solved via lyapunov methods then it can be also be solved via h sup infinity control theory based methods

finite memory automata abstract a model of computation dealing with infinite alphabets is proposed this model is based on replacing the equality test by substitution it appears to be a natural generalization of the classical rabin scott finite state automata and possesses many of their closure and decision properties also when restricted to finite alphabets the model is equivalent to finite state automata

two variable logic on data trees and xml reasoning motivated by reasoning tasks for xml languages the satisfiability problem of logics on data trees is investigated the nodes of a data tree have a label from a finite set and a data value from a possibly infinite set it is shown that satisfiability for two variable first order logic is decidable if the tree structure can be accessed only through the child and the next sibling predicates and the access to data values is restricted to equality tests from this main result decidability of satisfiability and containment for a data aware fragment of xpath and of the implication problem for unary key and inclusion constraints is concluded

robust stability for fractional order systems with structured and unstructured uncertainties the issues of robust stability for uncertain fractional order systems of two types of order a 0 1 are dealt with in this paper for the polytope type uncertainty case a less conservative sufficient condition for robust stability is given for the norm bounded uncertainty case a sufficient and necessary condition for robust stability is presented both of these conditions can be checked by solving sets of linear matrix inequalities two numerical examples are presented to confirm the proposed conditions

the holomorphic discrete series for affine symmetric spaces i abstract let x g h be an affine symmetric space we study part of the discrete spectrum of l2 x for x of hermitian type a notion we define in analogy with the group case in particular we find intertwining operators from the scalar holomorphic discrete series of g which is automatically of hermitian type into l2 x the multiplicity of this series is then shown to be one by a uniqueness result for the intertwining operators finally we investigate the complexification x c of x and show that the discrete series in question admits holomorphic continuation into a certain domain in x c