stability analysis and synthesis of nonlinear time delay systems via linear takagi sugeno fuzzy models abstract this paper concerns with the stability analysis and synthesis of nonlinear retarded systems via linear takagi sugeno ts fuzzy model approach first the ts fuzzy models with time delay are present and the stability conditions are derived using lyapunov razumikhin functional approach then a stabilization approach for nonlinear retarded systems through fuzzy state feedback and fuzzy observer based controller is proposed it shows that the analysis results provide an efficient technique for the design of fuzzy controllers sufficient conditions for the existence of fuzzy state feedback gain and fuzzy observer gain of the time delay systems are derived through the numerical solution of a set of coupled linear matrix inequalities

metriques de carnot cartheodory et quasiisometries des espaces symetriques de rang un we exhibit a rigidity property of the simple groups sp n 1 and f7 20 which implies mostow rigidity this property does not extend to o n 1 and u n 1 the proof relies on quasiconformal theory applied in the cr setting extensions are given to a class of solvable lie groups as a byproduct a result on quasiisometries of infinite nilpotent groups is obtained dans cet article on etablit une propriete de rigidite des groupes simples de rang un sp n 1 n 2 2 et fqui entraine la rigidite de mostow 1 theoreme toute quasiisornwtrie de 1 espace hyperbolique quaternionien hhn n 2 resp du plan hyperbolique de cayley cah2 est d distance bornee d une isometrie i e differe d une isomnetrie par une application qui diplace les points d une distance bornee une application f entre espaces metriques est une quasiisometrie s il existe des constantes l et c telles que l image de f soit c dense et que pour tous x y c d x y d fx fy ld x y c l une quasiisometrie entre des g et g est une sorte d isomorphisme virtuel dans la categorie topologique en effet cela correspond a une action de g sur un fibre principal c de groupe g sur une base compacte cf ra un isomorphisme entre sous groupes cocompacts covolume fini suffit pour les groupes simples de rang un de groupes de lie s etend en une quasiisometrie des espaces symetriques ou des groupes de lie si celle ci est proche d une isometrie des espaces symetriques resp un isomorphisme des groupes de lie les sous groupes sont conjugues c est la rigidite de mostow m2 la propriete ci dessus ne s etend pas aux groupes o n 1 et u n 1 en effet paragraphe 11 7 ceux ci ont beaucoup de quasiisometries au moins this content downloaded from 207 46 13 92 on sun 20 nov 2016 04 26 46 utc all use subject to http about jstor org terms

theorems about the attractor for incompressible non newtonian flow driven by external forces that are rapidly oscillating in time but have a smooth average this paper discusses the incompressible non newtonian fluid with rapidly oscillating external forces g x t g x t t possessing the average g 0 x t as 0 where 0 0 then we establish that the hausdorff distance between the uniform attractors a v and a 0 v in space v is also less than o as 0 finally we show a a v for each 0 0

constrained mpc algorithm for uncertain time varying systems with state delay in this note we present a model predictive control mpc algorithm for uncertain time varying systems with input constraints and state delay uncertainty is assumed to be polytopic and delay is assumed to be unknown but with a known upper bound for a memoryless state feedback mpc law we define an optimization problem that minimizes a cost function and relaxes it to two other optimization problems by finding an upper bound of the cost function one is solvable and the other is not we prove equivalence and feasibilities of the two optimization problems under a certain assumption on the weighting matrix based on these properties and optimality we show that feasible mpc from the optimization problems stabilizes the closed loop system then we present an improved mpc algorithm that includes relaxation procedures of the assumption on the weighting matrix and stabilizes the closed loop system finally a numerical example illustrates the performance of the proposed algorithm

robust guaranteed cost control for uncertain linear differential systems of neutral type in this paper the robust guaranteed cost control problem for a class of uncertain linear differential systems of neutral type with a given quadratic cost functions is investigated the uncertainty is assumed to be norm bounded and time varying nonlinear the problem is to design a state feedback control laws such that the closed loop system is robustly stable and the closed loop cost function value is not more than a specified upper bound for all admissible uncertainty and time delay a criterion for the existence of such controllers is derived based on the matrix inequality approach combined with the lyapunov method a parameterized characterization of the robust guaranteed cost controllers is given in terms of the feasible solutions to the certain matrix inequalities a numerical example is given to illustrate the proposed method

an improved l2 decay for weak solutions of a boussinesq system in exterior domains abstract the algebraic decay for the total kinetic energy of weak solutions of the viscous boussinesq system in an exterior domain is given by means of the spectral analysis method of the stokes operator which gives a positive answer to the l 2 decay question in 11

general receding horizon control for linear time delay systems a general receding horizon control rhc or model predictive control mpc for time delay systems is proposed the proposed rhc is obtained by minimizing a new cost function that includes two terminal weighting terms which are closely related to the closed loop stability the general solution of the proposed rhc is derived using the generalized riccati method furthermore an explicit solution is obtained for the case where the horizon length is less than or equal to the delay size a linear matrix inequality lmi condition on the terminal weighting matrices is proposed under which the optimal cost is guaranteed to be monotonically non increasing it is shown that the monotonic condition of the optimal cost guarantees closed loop stability of the rhc simulations demonstrate that the proposed rhc effectively stabilizes time delay systems

robust constrained predictive control of uncertain norm bounded linear systems a novel robust predictive control algorithm is presented for uncertain discrete time input saturated linear systems described by structured norm bounded model uncertainties the solution is based on the minimization at each time instant of a semi definite convex optimization problem subject to a number of lmi feasibility constraints which grows up only linearly with the control horizon length n the general case of arbitrary n is considered closed loop stability and feasibility retention over the time are proved and comparisons with robust multi model polytopic mpc algorithms are reported

robust constrained model predictive control using linear matrix inequalities abstract the primary disadvantage of current design techniques for model predictive control mpc is their inability to deal explicitly with plant model uncertainty in this paper we present a new approach for robust mpc synthesis that allows explicit incorporation of the description of plant uncertainty in the problem formulation the uncertainty is expressed in both the time and frequency domains the goal is to design at each time step a state feedback control law that minimizes a worst case infinite horizon objective function subject to constraints on the control input and plant output using standard techniques the problem of minimizing an upper bound on the worst case objective function subject to input and output constraints is reduced to a convex optimization involving linear matrix inequalities lmis it is shown that the feasible receding horizon state feedback control design robustly stabilizes the set of uncertain plants several extensions such as application to systems with time delays problems involving constant set point tracking trajectory tracking and disturbance rejection which follow naturally from our formulation are discussed the controller design is illustrated with two examples

existence and uniqueness of solutions for a class of non newtonian fluids with singularity and vacuum abstract the aims of this paper are to discuss existence and uniqueness of local solutions for a class of non newtonian fluids with singularity and vacuum in one dimensional bounded intervals there are two important points in this paper one is that we allow the initial vacuum another one is that the viscosity term of momentum equation is with singularity and fully nonlinearity

pullback attractors for a non autonomous incompressible non newtonian fluid this paper studies the pullback asymptotic behavior of solutions for a non autonomous incompressible non newtonian fluid in two dimensional 2d bounded domains we first prove the existence of pullback attractors av in space v has h2 regularity see notation in section 2 and ah in space h has l2 regularity for the cocycle corresponding to the solutions of the fluid then we verify the regularity of the pullback attractors by showing av ah which implies the pullback asymptotic smoothing effect of the fluid in the sense that the solutions become eventually more regular than the initial data

existence regularity and decay rate of solutions of non newtonian flow the existence and the regularity of young measure valued solutions to non newtonian flows are considered furthermore the uniqueness of solutions and their asymptotic behavior are given

asymptotic stability of non newtonian flows with large perturbation in r2 consider asymptotic stability of weak solutions for the incompressible non newtonian fluid motion in whole spaces r 2 we shall show that although the initial data disturbance from u are large every perturbed flow v with the energy inequality converges asymptotically to u as v t u t 0 as t

delay dependent guaranteed cost stabilization criterion for neutral delay differential systems matrix inequality approach abstract in this paper we address the problem of the guaranteed cost stabilization for a class of neutral delay differential systems with a given quadratic cost function based on the lyapunov method delay dependent criteria which are expressed in terms of matrix inequalities are proposed to guarantee the asymptotic stability of the system the matrix inequalities can be easily solved by various efficient optimization algorithms

uniform attractor for a two dimensional nonautonomous incompressible non newtonian fluid abstract we discuss the long time behavior of solutions for a two dimensional 2d nonautonomous incompressible non newtonian fluid in 2d bounded domains when the external force g 0 x t is translation compact tr c in l loc 2 r h we obtain the existence and reveal the structure of the uniform attractor for the processes associated to the fluid by constructing skew product flow on the extended phase space when g 0 l b 2 is properly small we establish that there exists a unique bounded asymptotically stable solution to the fluid

regularity of trajectory attractor and upper semicontinuity of global attractor for a 2d non newtonian fluid abstract there are two results within this paper the one is the regularity of trajectory attractor and the trajectory asymptotic smoothing effect of the incompressible non newtonian fluid on 2d bounded domains for which the solution to each initial value could be non unique the other is the upper semicontinuity of global attractors of the addressed fluid when the spatial domains vary from m to r l l where m m 1 is an expanding sequence of simply connected bounded and smooth subdomains of such that m as m that is let a and a m be the global attractors of the fluid corresponding to and m respectively we establish that for any neighborhood o a of a the global attractor a m enters o a if m is large enough

random attractor for the ladyzhenskaya model with additive noise this paper studies the dynamical behavior of the ladyzhenskaya model with additive noise with some conditions we prove that the generated random dynamical system has a compact random attractor which is a random compact set absorbing any bounded nonrandom subset of the phase space

l2 compact uniform attractors for a nonautonomous incompressible non newtonian fluid with locally uniformly integrable external forces in distribution space we consider the long time behavior of solutions for a two dimensional nonautonomous incompressible non newtonian fluid with external forces in distribution space when the external force g0 x t is locally uniformly integrable see definition 3 1 in lloc2 r w we prove the existence of l2 compact uniform attractor in space h and reveal its structure for the families of processes corresponding to the fluid moreover if g0 lb2 r w is properly small we establish the unique existence of bounded asymptotically stable solutions and give two interesting corollaries

robust memory state feedback model predictive control for discrete time uncertain state delayed systems in this paper we propose a memory state feedback model predictive control mpc law for a discrete time uncertain state delayed system with input constraints the model uncertainty is assumed to be polytopic and the delay is assumed to be unknown but with a known upper bound we derive a sufficient condition for cost monotonicity in terms of lmi which can be easily solved by an efficient convex optimization algorithm a delayed state dependent quadratic function with an estimated delay index is considered for incorporating mpc problem formulation the mpc problem is formulated to minimize the upper bound of infinite horizon cost that satisfies the sufficient conditions therefore a less conservative sufficient conditions in terms of linear matrix inequality lmi can be derived to design a more robust mpc algorithm a numerical example is included to illustrate the effectiveness of the proposed method

analytical solutions to a class of non newtonian fluids with free boundaries we study analytical solutions to a class of non newtonian fluids with free boundaries for suitable non newtonian fluids we construct a class of analytical solutions in r with both continuous density condition and the stress free condition across the free boundaries separating the fluid from vacuum such solutions exhibit interesting new information such as the formation of vacuum as time tends to infinitely and explicit regularities and large time decay estimates of the velocity field

large time behavior to the system of incompressible non newtonian fluids in r2 abstract in this paper the authors study the large time behavior for the weak solutions to a class system of the incompressible non newtonian fluids in r 2 it is proved that the weak solutions decay in l 2 norm at 1 t 1 2 and the estimate for the decay rate is sharp in the sense that it coincides with the decay rate of a solution to the heat equation

quasi flats and rigidity in higher rank symmetric spaces in this paper we use elementary geometrical and topological methods to study some questions about the coarse geometry of symmetric spaces our results are powerful enough to apply to noncocompact lattices in higher rank symmetric spaces such as sl n 2 n 3 theorem 8 1 is a major step towards the proof of quasiisometric rigidity of such lattices e we also give a different and effective proof of the theorem of kleiner leeb on the quasi isometric rigidity of higher rank symmetric spaces kl

uniform attractors for nonautonomous incompressible non newtonian fluid with locally uniform integrable external forces this paper discusses the long time behavior of solutions for a two dimensional 2d nonautonomous incompressible non newtonian fluid in 2d bounded domains when the external force g0 x t is locally uniform integrable see definition 1 1 in lloc2 r h the authors obtain the existence and structure of uniform attractors in space v for the family of processes associated with the fluid moreover when g0 lb2 is properly small they provide some interesting corollaries

technical communique a synthesis approach of on line constrained robust model predictive control a new method to address constrained robust model predictive control mpc for systems with polytopic description rpc spd is proposed this is motivated by two previous techniques one is the well known robust mpc that parameterizes the infinite horizon control moves into a single linear state feedback law the other is a nominal on line mpc that splits the infinite horizon control moves into a set of free control moves over a fixed horizon and a state feedback law in the terminal region the basic idea here is to adopt the rationale of the second technique to improve feasibility and optimality of the first one a parameter dependent lyapunov function is developed for establishing the closed loop stability the performance of the controller is demonstrated by an example

differentiability of lipschitz functions on banach spaces abstract the main result of this note says that if the norm of a banach space e is differentiable frechet gateaux or in some intermediate sense away from the origin then every locally lipschitz function defined on an open subset g of e is differentiable in the same sense at every point of some subset of g dense in g as the main corollary we prove that every lipschitz function on an asplund space is frechet differentiable on a dense set moreover in all these results the mean value theorem for the points of differentiability which is equivalent to the possibility of computing the clarke subdifferential from the points of differentiability is shown to hold

global classical solution to a one dimensional compressible non newtonian fluid with large initial data and vacuum abstract because of the stronger nonlinearity and degeneracies of the density due to the momentum equation and appearance of vacuum there are few results until now about global existence of classical solution to a compressible non newtonian fluid in this paper the global in time existence and uniqueness of classical solution to the initial boundary value problem is established for a one dimensional compressible non newtonian fluid with large initial data and vacuum our analysis is based on some delicate energy estimates together with the iterate method being used ingeniously

trajectory attractor and global attractor for a two dimensional incompressible non newtonian fluid the authors construct the trajectory attractor and global attractor for an autonomous two dimensional non newtonian fluid

quasi actions on trees i bounded valence given a bounded valence bushy tree t we prove that any cobounded quasi action of a group g on t is quasiconjugate to an action of g on another bounded valence bushy tree t this theorem has many applications quasi isometric rigidity for fundamental groups of finite bushy graphs of coarse pd n groups for each fixed n a generalization to actions on cantor sets of sullivan s theorem about uniformly quasiconformal actions on the 2 sphere and a characterization of locally compact topological groups which contain a virtually free group as a cocompact lattice finally we give the first examples of two finitely generated groups which are quasi isometric and yet which cannot act on the same proper geodesic metric space properly discontinuously and cocompactly by isometries

a new discrete time robust stability condition a new robust stability condition for uncertain discrete time systems with convex polytopic uncertainty is given it enables to check stability using parameter dependent lyapunov functions which are derived from lmi conditions it is shown that this new condition provides better results than the classical quadratic stability besides the use of a parameter dependent lyapunov function this condition exhibits a kind of decoupling between the lyapunov and the system matrices which may be explored for control synthesis purposes a numerical example illustrates the results

coarse differentiation of quasi isometries i spaces not quasi isometric to cayley graphs in this paper we prove that certain spaces are not quasi isometric to cayley graphs of nitely generated groups in particular we answer a question of woess and prove a conjecture of diestel and leader by showing that certain homogeneous graphs are not quasi isometric to a cayley graph of a nitely generated group this paper is the rst in a sequence of papers proving results announced in our 2007 article quasi isometries and rigidity of solvable groups in particular this paper contains many steps in the proofs of quasi isometric rigidity of lattices in sol and of the quasi isometry classication of lamplighter groups the proofs of those results are completed in coarse dierentiation of quasi isometries ii rigidity for lattices in sol and lamplighter groups the method used here is based on the idea of coarse dierentiation introduced in our 2007 article

predictive control for sector bounded nonlinear model and its application to solid oxide fuel cell systems in this paper a nonlinear model predictive control method is presented for solid oxide fuel cell systems for realistic modeling a sector bounded nonlinear model with input constraint is considered as a performance index we consider one horizon cost function that is represented by the weighted sum of state control input and nonlinear function by minimizing the upper bound of the cost function the optimized control input sequences are obtained for cost monotonicity a terminal inequality condition is derived in terms of a finite number of linear matrix inequalities lmis by using augmented vector feedback law which consists of state and sector bounded nonlinear function in order to show the effectiveness of the proposed method the sector bounded nonlinear model is derived for the solid oxide fuel cell systems and the system performance is verified by applying the proposed mpc algorithm to the systems

regularity criterion for generalized newtonian fluids in bounded domains abstract the regularity of a non newtonian flow in a domain with a boundary cannot be treated easily because of the nonlinear viscosity term and the global property of the pressure a distance function was used in a previous study to obtain a strong solution in the present study using the distance function idea we obtain serrin type regularity criteria for the vorticity and the velocity with regard to non newtonian equations with shear dependent viscosity in a bounded domain

on the asymptotic geometry of abelian by cyclic groups gromov s polynomial growth theorem gro81 states that the property of having polynomial growth characterizes virtually nilpotent groups among all finitely generated groups gromov s theorem inspired the more general problem see e g gdlh91 of understanding to what extent the asymptotic geometry of a finitelygenerated solvable group determines its algebraic structure in short are solvable groups quasi isometrically rigid in general they aren t very recently a dioubina dio99 has found a solvable group which is quasi isometric to a group which is not virtually solvable these groups are finitely generated but not finitely presentable in the opposite direction first steps in identifying quasi isometrically rigid solvable groups which are not virtually nilpotent were taken for a special class of examples the solvable baumslagsolitar groups in fm98 and fm99b the goal of the present paper is to show that a much broader class of solvable groups the class of finitely presented nonpolycyclic abelian bycyclic groups is characterized among all finitely generated groups by its quasi isometry type we also give a complete quasi isometry classification of the groups in this class such a classification for nilpotent groups remains a major open question motivated by these results we offer a conjectural picture of quasi isometric classification and rigidity for polycyclic abelianby cyclic groups in 10 1

implementation of stabilizing receding horizon controls for time varying systems in this paper a new stabilizing receding horizon control rhc scheme is proposed for linear discrete time varying systems which can be easily implemented by using linear matrix inequality lmi optimization the control scheme is based on the minimization of the finite horizon cost with a finite terminal weighting matrix the resulting stabilizing rhc scheme leads to time varying finite terminal weighting matrices even for time invariant systems which is more general than in the case of using constant matrices based on the proposed scheme another implementation method is also discussed for easy computation and numerical feasibility consideration of lmi optimization although the second method does not guarantee the closed loop stability theoretically through a simulation example the effectiveness of the proposed schemes is illustrated

output feedback model predictive control for lpv systems using parameter dependent lyapunov function in this paper we consider a robust dynamic output feedback model predictive controller mpc design for linear parameter varying lpv systems according to the proposed mpc algorithm the control law is computed based on linear matrix inequality lmi at each sampling time by solving convex optimization problem also a new parameter dependent lyapunov function is proposed to get a less conservative condition for stability of the system the effectiveness of the result proposed is verified via a numerical example

on the design of nonfragile guaranteed cost controller for a class of uncertain dynamic systems with state delays in this article the nonfragile guaranteed cost control problem is studied for a class of uncertain dynamic systems with multiple time delays and controller gain variation the multiple time varying delays are considered the uncertainty is nonlinear time varying and is bounded in magnitude for all admissible uncertainties time delays and controller gain variations the problem is to design a memoryless state feedback control laws such that the closed loop system is asymptotically stable and the closed loop cost function value is not more than a specified upper bound of a given cost function several criteria for the existence of such controllers are derived using the lyapunov method a feature of the proposed method is that an upper bound on the guaranteed cost is minimized by solving a convex optimization problem with linear matrix inequalities a numerical example is given to illustrate the proposed method