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

delay dependent robust h control for t s fuzzy system with interval time varying delay this paper is concerned with the problem of robust h control for uncertain t s fuzzy systems with interval time varying delay that is the delay is assumed to be a time varying function belonging to an interval by defining new lyapunov functions and making use of novel techniques to achieve delay dependence new conditions for the existence of robust h controller are obtained based on the parallel distributed compensation pdc method in this article all the conditions are shown in terms of linear matrix inequalities lmis which can be solved efficiently by using the lmi optimization techniques two numerical examples are given to illustrate the less conservatism of the proposed method

resonant suppression of turing patterns by periodic illumination we study the resonant behavior of turing pattern suppression in a model of the chlorine dioxide iodine malonic acid reaction with periodic illumination the results of simulations based on integration of partial differential equations display resonance at the frequency of autonomous oscillations in the corresponding well stirred system the resonance in turing pattern suppression is sharper at lower complexing agent concentration and is affected by the waveform of the periodic driving force square wave on off periodic forcing is more effective in suppressing turing patterns than sinusoidal forcing we compare the dynamics of periodically forced turing patterns with the dynamics of periodically forced nonhomogeneous states in a system of two identical coupled cells bifurcation analysis based on numerical continuation of the latter system gives good predictions for the boundaries of the major resonance regions of the periodically forced patterns

spatiotemporal chaos stimulated by transverse hopf instabilities in an optical bilayer system we study two dimensional spatiotemporal dynamics in an optical system of two identical nonlinear films irradiated from both sides by equal plane waves and show that a wide variety of chaotic behaviors can be obtained near the subcritical pitchfork bifurcation point the regimes arising in the vicinity of asymmetrical steady state depend on stability of the symmetrical steady state at the same driving field on interactions of hopf and turing instabilities occurring at the asymmetrical branch of solutions and on a transverse wave number of the hopf instability band center the wave number is controlled by a phase shift of the field passed between two films and the relative order of the turing and hopf bifurcations is controlled by a diffusion of charge carrier in a semiconductor media chaotic oscillating patterns are formed mainly by transverse hopf modes rising due to a time delay in the system

spatiotemporal dynamics near a codimension two point spatiotemporal dynamics resulting from the interaction of two instabilities breaking respectively spatial and temporal symmetries are studied in the framework of the amplitude equation formalism the corresponding bifurcation scenarios feature steady hopf bistability with corresponding localized structures but also different types of mixed states some of these mixed modes result from self induced subharmonic instabilities of the pure steady and hopf modes the bifurcation schemes are then used to organize the results of numerical simulations of a one dimensional reaction diffusion model these dynamics are relevant to experimental chemical systems featuring a codimension two turing hopf point but also to any experimental setup where homogeneous temporal oscillations and spatial patterns are obtained for nearby values of parameters s1063 651x 96 03707 5

brief paper on almost sure stability of continuous time markov jump linear systems in this paper we study the almost sure stability of continuous time jump linear systems with a finite state markov form process a sufficient condition for almost sure stability is derived that refers to the statistics of the transition matrix over m switches it is shown that if the system is exponentially almost sure stable there exists a finite m such that the criterion is satisfied in order to evaluate the expected value appearing in the condition an efficient monte carlo algorithm is worked out

a stabilization algorithm for a class of uncertain linear systems abstract this paper presents an algorithm for the stabilization of a class of uncertain linear systems the uncertain systems under consideration are described by state equations which depend on time varying unknown but bounded uncertain parameters the construction of the stabilizing controller involves solving a certain algebraic riccati equation furthermore the solution to this riccati equation defines a quadratic lyapunov function which is used to establish the stability of the closed loop system this leads to a notion of quadratic stabilizability it is shown that the stabilization procedure will succeed if and only if the given uncertain linear system is quadratically stabilizable the paper also deals with a notion of overbounding for uncertain linear systems this procedure enables the stabilization algorithm to be applied to a larger class of uncertain linear systems also included in the paper are results which indicate the degree of conservativeness introduced by this overbounding process

further results on exponential estimates of markovian jump systems with mode dependent time varying delays this technical note studies the problem of exponential estimates for markovian jump systems with mode dependent interval time varying delays a novel lyapunov krasovskii functional lkf is constructed with the idea of delay partitioning and a less conservative exponential estimate criterion is obtained based on the new lkf illustrative examples are provided to show the effectiveness of the proposed results

new approach to delay dependent stability analysis and stabilization for continuous time fuzzy systems with time varying delay this paper is concerned with delay dependent stability analysis and stabilization problems for continuous time takagi and sugeno t s fuzzy systems with a time varying delay a new method for the delay dependent stability analysis and stabilization is suggested which is less conservative than other existing ones first based on a fuzzy lyapunov krasovskii functional lkf a delay dependent stability criterion is derived for the open loop fuzzy systems in the derivation process some free fuzzy weighting matrices are introduced to express the relationships among the terms of the system equation and among the terms in the leibniz newton formula then a delay dependent stabilization condition based on the so called parallel distributed compensation pdc scheme is worked out for the closed loop fuzzy systems the proposed stability criterion and stabilization condition are represented in terms of linear matrix inequalities lmis and compared with the existing ones via two examples finally application to control of a truck trailer is also given to illustrate the effectiveness of the proposed design method

robust h_ infty fuzzy control approach for a class of markovian jump nonlinear systems this paper addresses the problem of stabilizing a class of nonlinear systems subject to markovian jump parameters using a robust stochastic fuzzy controller with hinfin performance the class of jump nonlinear systems considered is described by a fuzzy model composed of two levels a crisp level which represents the jumps and a fuzzy level which represents the system nonlinearities considering the approximation error between the fuzzy model and the jump nonlinear system as norm bounded uncertainties we develop a systematic technique based on a coupled lyapunov function to obtain a robust stochastic fuzzy controller which guarantees the l2 gain of the closed loop system in respect to external inputs to be equal to or less than a prescribed value a simulation example on an industrial power plant operating in a cogeneration scheme is presented to illustrate the effectiveness of the proposed stabilizing controller in reducing oscillations as well as maintaining a desired operation condition in the presence of fluctuations in the local load

delay dependent guaranteed cost control for t s fuzzy systems with time delays this study introduces a guaranteed cost control method for nonlinear systems with time delays which can be represented by takagi sugeno t s fuzzy models with time delays the state feedback and generalized dynamic output feedback approaches are considered the generalized dynamic output feedback controller is presented by a new fuzzy controller architecture which is of dual indexed rule base it considers both the dynamic part and the output part of t s fuzzy model which guarantees that the controller without any delay information can stabilize time delay t s fuzzy systems based on delay dependent lyapunov functional approach some sufficient conditions for the existence of state feedback controller are provided via parallel distributed compensation pdc first second the corresponding conditions are extended into the generalized dynamic output feedback closed loop system via so called generalized pdc technique the upper bound of time delay can be obtained using convex optimization such that the system can be stabilized for all time delays whose sizes are not larger than the bound the minimizing method is also proposed to search the suboptimal upper bound of guaranteed cost function the effectiveness of the proposed method can be shown by the simulation examples

technical communique absolute stability of time delay systems with sector bounded nonlinearity this paper deals with the problem of absolute stability of time delay systems with sector bounded nonlinearity some new delay dependent stability criteria are obtained and formulated in the form of linear matrix inequalities lmis neither model transformation nor bounding technique for cross terms is involved through derivation of the stability criteria numerical examples show that the results obtained in this paper improve the estimate of the stability limit over some existing result

robust output feedback stabilization for uncertain discrete time fuzzy markovian jump systems with time varying delays this paper provides a delay dependent approach to the design of fuzzy dynamic output feedback controllers for uncertain discrete time fuzzy markovian jump systems with interval time varying delays first by a fuzzy basis dependent and mode dependent lyapunov functional a stochastic stability condition is derived by using the finsler s lemma second in terms of linear matrix inequalities lmis a delay dependent sufficient condition is presented under which there exists a fuzzy output feedback controller such that the resulting closed loop system is robustly stochastically stable a desired controller can be constructed when these lmis are feasible finally the effectiveness of the proposed design method is demonstrated by a simulation example

amplitude equations for reaction diffusion systems with cross diffusion using taylor series expansion multiscaling and further expansion in powers of a small parameter we develop general amplitude equations for two variable reaction diffusion systems with cross diffusion terms in the cases of hopf and turing instabilities we apply this analysis to the oregonator and brusselator models and find that inhibitor cross diffusion induced by the activator and activator cross diffusion induced by the inhibitor have opposite effects in the two models as a result of the different structure of their community matrices our analysis facilitates finding regions of supercritical and subcritical bifurcations as well as wave and antiwave domains and domains of turbulent waves in the case of hopf instability

secure steganographic communication algorithm based on self organizing patterns a secure steganographic communication algorithm based on patterns evolving in a beddington de angelis type predator prey model with self and cross diffusion is proposed in this paper small perturbations of initial states of the system around the state of equilibrium result in the evolution of self organizing patterns small differences between initial perturbations result in slight differences also in the evolving patterns it is shown that the generation of interpretable target patterns cannot be considered as a secure mean of communication because contours of the secret image can be retrieved from the cover image using statistical techniques if only it represents small perturbations of the initial states of the system an alternative approach when the cover image represents the self organizing pattern that has evolved from initial states perturbed using the dot skeleton representation of the secret image can be considered as a safe visual communication technique protecting both the secret image and communicating parties

on designing of sliding mode control for stochastic jump systems in this note we consider the problems of stochastic stability and sliding mode control for a class of linear continuous time systems with stochastic jumps in which the jumping parameters are modeled as a continuous time discrete state homogeneous markov process with right continuous trajectories taking values in a finite set by using linear matrix inequalities lmis approach sufficient conditions are proposed to guarantee the stochastic stability of the underlying system then a reaching motion controller is designed such that the resulting closed loop system can be driven onto the desired sliding surface in a limited time it has been shown that the sliding mode control problem for the markovian jump systems is solvable if a set of coupled lmis have solutions a numerical example is given to show the potential of the proposed techniques

forced patterns near a turing hopf bifurcation we study time periodic forcing of spatially extended patterns near a turing hopf bifurcation point a symmetry based normal form analysis yields several predictions including that i weak forcing near the intrinsic hopf frequency enhances or suppresses the turing amplitude by an amount that scales quadratically with the forcing strength and ii the strongest effect is seen for forcing that is detuned from the hopf frequency to apply our results to specific models we perform a perturbation analysis on general two component reaction diffusion systems which reveals whether the forcing suppresses or enhances the spatial pattern for the suppressing case our results are consistent with features of previous experiments on the chlorine dioxide iodine malonic acid chemical reaction however we also find examples of the enhancing case which has not yet been observed in experiment numerical simulations verify the predicted dependence on the forcing parameters

stably embedded surfaces of bounded integral curvature we study the effect of simultaneous bounds on the local l1 norms of the second fundamental form and of the gauss curvature on the geometry of surfaces embedded in a riemannian manifold m such bounds are natural since together with an area bound they amount to a local bound on the area of the manifold of unit normals to living in the sphere bundle of m the main technical point is that given a sequence of surfaces i with uniform local bounds of this type converging in the hausdorff metric topology to a surface 0 the length space structures of the i converge to that of 0 i e distances do not collapse it follows that under suitable local topological conditions the surface 0 is a manifold of bounded integral curvature mbc in the sense of alexandrov under all smooth complete changes of the metric on m in particular the boundary of a convex set with nonempty interior in any smooth complete m3 is mbc our method is to construct local coordinates for smoothly embedded surfaces satisfying w1 bv bounds based solely on curvature integrals in the process we demonstrate a regularity property for cut loci of surfaces

brief paper a delay decomposition approach to l2 l filter design for stochastic systems with time varying delay this paper investigates the problem of l 2 l filter design for a class of stochastic systems with time varying delay the addressed problem is the design of a full order linear filter such that the error system is asymptotically mean square stable and a prescribed l 2 l performance is satisfied in order to develop a less conservative filter design a new lyapunov krasovskii functional lkf is constructed by decomposing the delay interval into multiple equidistant subintervals and a new integral inequality is established in the stochastic setting then based on the lkf and integral inequality the delay dependent conditions for the existence of l 2 l filters are obtained in terms of linear matrix inequalities lmis the resulting filters can ensure that the error system is asymptotically mean square stable and the peak value of the estimation error is bounded by a prescribed level for all possible bounded energy disturbances finally two examples are given to illustrate the effectiveness of the proposed method

finite time h fuzzy control of nonlinear markovian jump delayed systems with partly uncertain transition descriptions abstract this paper addresses a finite time h fuzzy control problem for a class of nonlinear markovian jump delayed systems with partly uncertain transition descriptions which is represented as a takagi sugeno t s fuzzy model a new homogeneous polynomial of partly uncertain transition rates is chosen free matrix based and double integral forms of the wirtinger based integral inequalities are employed to make the proposed approach less conservative then sufficient conditions are derived such that the fuzzy nonlinear makovian jump delayed system exhibits stochastic finite time boundedness finally two numerical examples are given to illustrate the effectiveness of the proposed design methodology

spatiotemporal dynamics near a supercritical turing hopf bifurcation in a two dimensional reaction diffusion system pattern formation in semiconductor heterostructures is studied on the basis of a spatially two dimensional model of reaction diffusion type in particular we investigate the neighborhood of a codimension two turing hopf instability by analytical methods amplitude equations are derived which predict the absence of mixed modes but extended ranges of bistability between homogeneous oscillatory states and hexagonal turing patterns our results are confirmed by numerical simulations the features are not confined to a neighborhood of the bifurcation point so that the conclusions of the weakly nonlinear analysis explain the observations in large portions of the parameter space at least qualitatively

simple and superlattice turing patterns in reaction diffusion systems bifurcation bistability and parameter collapse abstract we use equivariant bifurcation theory to investigate pattern selection at the onset of a turing instability in a general two component reaction diffusion system the analysis is restricted to patterns that periodically tile the plane in either a square or hexagonal fashion both simple periodic patterns stripes squares hexagons and rhombs and superlattice patterns are considered the latter correspond to patterns that have structure on two disparate length scales the short length scale is dictated by the critical wave number from linear theory while the periodicity of the pattern is on a larger scale analytic expressions for the coefficients of the leading nonlinear terms in the bifurcation equations are computed from the general reaction diffusion system using perturbation theory we show that no matter how complicated the reaction kinetics might be the nonlinear reaction terms enter the analysis through just four parameters moreover for hexagonal problems all patterns bifurcate unstably unless a particular degeneracy condition is satisfied and at this degeneracy we find that the number of effective system parameters drops to two allowing a complete characterization of the possible bifurcation results at this degeneracy for example we find that rhombs squares and superlattice patterns always bifurcate unstably we apply these general results to some specific model equations including the lengyel epstein cima model to investigate the relative stability of patterns as a function of system parameters and to numerically test the analytical predictions

fuzzy guaranteed cost control for nonlinear systems with time varying delay this paper focuses on the problem of guaranteed cost control for takagi sugeno t s fuzzy systems with time varying delayed state a linear quadratic cost function is considered as a performance index of the closed loop fuzzy system then the guaranteed cost control of the closed loop fuzzy system is discussed and the sufficient conditions are provided for the construction of a guaranteed cost controller via state feedback and observer based output feedback when these conditions which are given in terms of the feasibility of linear matrix inequalities lmis are satisfied the designed state feedback controller and observer based controller gain matrices can be obtained via a convex optimization problem two illustrative examples are provided to demonstrate the effectiveness of the approaches proposed in this paper

parameterized linear matrix inequality techniques in fuzzy control system design this paper proposes different parameterized linear matrix inequality plmi characterizations for fuzzy control systems these plmi characterizations are in turn relaxed into pure lmi programs which provides tractable and effective techniques for the design of suboptimal fuzzy control systems the advantages of the proposed methods over earlier ones are then discussed and illustrated through numerical examples and simulations

robust h fuzzy control for uncertain nonlinear markovian jump systems with time varying delay this paper investigates the problem of robust h fuzzy control for a class of uncertain nonlinear markovian jump systems with time varying delay the class of systems under consideration is described by the takagi sugeno fuzzy model the goal of the paper is to design a mode dependent fuzzy state feedback controller such that the closed loop system is stochastically stable with a prescribed h performance of disturbance attenuation for all admissible parameter uncertainties in order to obtain a less conservative control design a new stochastic lyapunov krasovskii functional is first constructed by decomposing the delay interval into multiple equidistant subintervals then by employing this functional a delay decomposition approach to the design of robust h fuzzy controllers is developed in terms of linear matrix inequalities finally two examples are given to illustrate the merit and usability of the proposed design method

a delay decomposition approach to fuzzy markovian jumping genetic regulatory networks with time varying delays in this paper we investigated the asymptotic stability of fuzzy markovian jumping genetic regulatory networks with time varying delays by delay decomposition approach the genetic regulatory networks are composed of s modes and the network switches from one mode to another according to a markovian chain with known transition probabilities purpose of this work is to establish some easy to verify conditions under which the dynamics of the true concentrations of the messenger ribonucleic acid mrna and protein is asymptotically stable irrespective of the norm bounded modeling errors a new lyapunov krasovskii functional lkf is constructed by nonuniformly dividing the whole delay intervals into multiple segments choosing proper functionals with different weighting matrices corresponding to different segments in the lkfs employing these new lkfs for the case of constant time delays and time varying delays some new delay dependent stability criteria are established with markovian jumping parameters by t s fuzzy model maximum admissible upper bounds maubs for the time varying delays are determined all the conditions presented here are in the form of linear matrix inequalities lmi which are efficiently solved by the lmi toolbox in matlab numerical examples are given to show the effectiveness of the proposed method

analysis and synthesis of nonlinear time delay systems via fuzzy control approach takagi sugeno ts fuzzy models 1985 1992 can provide an effective representation of complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning applied to a set of linear input output i o submodels in this paper the ts fuzzy model approach is extended to the stability analysis and control design for both continuous and discrete time nonlinear systems with time delay the ts fuzzy models with time delay are presented and the stability conditions are derived using lyapunov krasovskii approach we also present a stabilization approach for nonlinear time delay systems through fuzzy state feedback and fuzzy observer based controller sufficient conditions for the existence of fuzzy state feedback gain and fuzzy observer gain are derived through the numerical solution of a set of coupled linear matrix inequalities an illustrative example based on the cstr model is given to design a fuzzy controller

brief paper new results on stabilization of markovian jump systems with time delay this paper studies the problem of stochastic stabilization for a class of markovian jump systems with time delay a new delay dependent stochastic stability criterion on the stochastic stability of the system is derived based on a novel lyapunov krasovskii functional lkf approach the equivalence and superiority to existing results are demonstrated then a state feedback controller which guarantees the stochastic stability of the closed loop system is designed illustrative examples are provided to show the reduced conservatism and effectiveness of the proposed techniques

brief paper a discrete delay decomposition approach to stability of linear retarded and neutral systems this paper is concerned with stability of linear time delay systems of both retarded and neutral types by using some new simple quadratic lyapunov krasovskii functionals these lyapunov krasovskii functionals consist of two parts one part comes from some existing lyapunov krasovskii functionals employed in han q l 2005a absolute stability of time delay systems with sector bounded nonlinearity automatica 41 2171 2176 han q l 2005b a new delay dependent stability criterion for linear neutral systems with norm bounded uncertainties in all system matrices international journal of systems science 36 469 475 the other part is constructed by uniformly dividing the discrete delay interval into multiple segments and choosing proper functionals with different weighted matrices corresponding to different segments then using these new simple quadratic lyapunov krasovskii functionals some new discrete delay dependent stability criteria are derived for both retarded systems and neutral systems it is shown that these criteria for retarded systems and neutral systems are always less conservative than the ones in han 2005a and han 2005b cited above respectively numerical examples also show that the results obtained in this paper significantly improve the estimate of the discrete delay limit for stability over some other existing results

delay dependent robust h sub spl infin control for t s fuzzy systems with time delay this paper focuses on the problem of delay dependent robust fuzzy control for a class of nonlinear delay systems via state feedback the takagi sugeno t s fuzzy model is adopted for representing a nonlinear system with time delayed state a delay dependent stabilization criterion is first presented then the methods of robust stabilization and robust h sub spl infin control are developed which are dependent on the size of the delay and are based on the solutions of linear matrix inequalities lmis finally a design example of robust h sub spl infin controller for uncertain nonlinear systems is given to illustrate the effectiveness of the approaches proposed in this paper

delay dependent robust stability and h control for jump linear systems with delays abstract this paper considers robust stochastic stability stabilization and h control problems for a class of jump linear systems with time delays by using some zero equations neither model transformation nor bounding for cross terms is required to obtain the delay dependent results which are given in terms of linear matrix inequalities lmis maximum sizes of time delays are also studied for system stability furthermore solvability conditions and corresponding h control laws are given which provide robust stabilization with a prescribed h disturbance attenuation level numerical examples show that the proposed methods are much less conservative than existing results

robust h_ infty control for uncertain takagi sugeno fuzzy systems with interval time varying delay this paper is concerned with the problem of robust hinfin control for a class of uncertain time delay fuzzy systems the time delay is assumed to be a time varying continuous function belonging to a given interval which means that the lower and upper bounds for the time varying delay are available no restriction on the derivative of the time varying delay is needed which allows the time delay to be a fast time varying function the takagi sugeno t s uncertain fuzzy model with interval time varying delay is adopted based on the lyapunov krasovskii functional approach some delay dependent conditions for the existence of robust hinfin controller are formulated in the form of linear matrix inequalities lmis when these lmis are feasible an hinfin controller is presented a numerical example is given to demonstrate the effectiveness of the proposed method

extreme points of the distance function on convex surfaces we first see that in the sense of baire categories many convex surfaces have quite large cut loci and infinitely many relative maxima of the distance function from a point then we find that on any convex surface all these extreme points lie on a single subtree of the cut locus with at most three endpoints finally we confirm both in the sense of measure and in the sense of baire categories steinhaus conjecture that almost all points admit a single farthest point on the surface

generic spatiotemporal dynamics near codimension two turing hopf bifurcations the coupling of spatial and temporal symmetry breaking instabilities is studied in a two variable reaction diffusion model describing semiconductor transport a variety of spatiotemporal patterns corresponding to pure hopf and turing modes localized patterns and mixed turing hopf modes including subharmonic spatiotemporal spiking are found by organizing the results in a time scale versus space scale diagram and by comparing them with a chemical reaction diffusion model it is shown that such behavior is generic for a class of extended nonlinear dynamic systems near codimension two turing hopf bifurcations

the lipschitz continuity of the distance function to the cut locus let n be a closed submanifold of a complete smooth riemannian manifold m and uv the total space of the unit normal bundle of n for each v c uv let p v denote the distance from n to the cut point of n on the geodesic y with the velocity vector tyv 0 v the continuity of the function p on uv is well known in this paper we prove that p is locally lipschitz on which p is bounded in particular if m and n are compact then p is globally lipschitz on uy therefore the canonical interior metric 6 may be introduced on each connected component of the cut locus of n and this metric space becomes a locally compact and complete length space let n be an immersed submanifold of a complete cc riemannian manifold m and 7 uv n the unit normal bundle of n for each positive integer k and vector v c uv let a number k v denote the parameter value of fy where 7yv denotes the geodesic for which the velocity vector is v at t 0 such that yv ak v is the k th focal point conjugate point for the case in which n is a point of n along y counted with focal or conjugate multiplicities a unit speed geodesic segment 0 a m emanating from n is called an n segment if t d n y t on 0 a by the first variation formula an n segment is orthogonal to n a point 7y to on an n segment 7y v e uv is called a cut point of n if there is no n segment properly containing y o to for each v c uv let p v denote the distance from n to the cut point on y of n whitehead 27 investigated the structure of the conjugate locus and the cut locus of a point on a real analytic finsler manifold he determined the structure of the conjugate locus around a conjugate point for which the conjugate multiplicity is locally constant on its neighborhood cf also 25 and proved the continuity of the function p in compact symmetric spaces t sakai 19 and m takeuchi 23 determined the detailed structure of the cut locus of a point the detailed structure of the cut locus of a point in a 2 dimensional riemannian manifold has been investigated by poincare myers and others 7 11 13 hartman first tried to show the absolute continuity of the function p when m is 2 dimensional he proved in 8 that if p is of bounded variation then p is absolutely continuous recently hebda 11 and the first named author 13 independently proved ambrose s problem by showing that p is absolutely continuous on a closed arc on which p is bounded when n is a point in a 2 dimensional riemannian manifold therefore the cut locus of a point in a compact 2 dimensional received by the editors october 14 1998 and in revised form april 13 1999 2000 mathematics subject classification primary 53c22 secondary 28a78 supported in part by a grant in aid for scientific research from the ministry of education science sports and culture japan 2000 american mathematical society

stability and stabilization of delayed t s fuzzy systems a delay partitioning approach this paper proposes a new approach namely the delay partitioning approach to solving the problems of stability analysis and stabilization for continuous time delay takagi sugeno fuzzy systems based on the idea of delay fractioning a new method is proposed for the delay dependent stability analysis of fuzzy time delay systems due to the instrumental idea of delay partitioning the proposed stability condition is much less conservative than most of the existing results the conservatism reduction becomes more obvious with the partitioning getting thinner based on this the problem of stabilization via the so called parallel distributed compensation scheme is also solved both the stability and stabilization results are further extended to time delay fuzzy systems with time varying parameter uncertainties all the results are formulated in the form of linear matrix inequalities lmis which can be readily solved via standard numerical software the advantage of the results proposed in this paper lies in their reduced conservatism as shown via detailed illustrative examples the idea of delay partitioning is well demonstrated to be efficient for conservatism reduction and could be extended to solving other problems related to fuzzy delay systems

robust h control of takagi sugeno fuzzy systems with state and input time delays this paper addresses the robust h fuzzy control problem for nonlinear uncertain systems with state and input time delays through takagi sugeno t s fuzzy model approach the delays are assumed to be interval time varying delays and no restriction is imposed on the derivative of time delay based on lyapunov krasoviskii functional method delay dependent sufficient conditions for the existence of an h controller are proposed in linear matrix inequality lmi format illustrative examples are given to show the effectiveness and merits of the proposed fuzzy controller design methodology

stabilization of continuous time jump linear systems we investigate almost sure and moment stabilization of continuous time jump linear systems with a finite state markov jump form process we first clarify the concepts of spl delta moment stabilizability exponential spl delta moment stabilizability and stochastic spl delta moment stabilizability we then present results on the relationships among these concepts coupled riccati equations that provide necessary and sufficient conditions for mean square stabilization are given in detail and an algorithm for solving the coupled riccati equations is proposed moreover we show that individual mode controllability implies almost sure stabilizability which is not true for other types of stabilizability finally we present some testable sufficient conditions for spl delta moment stabilizability and almost sure stabilizability

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

infinite horizon h control for nonlinear stochastic markov jump systems with x u v dependent noise via fuzzy approach in this paper the h control problem is studied for nonlinear stochastic markov jump systems with state control and external disturbance dependent noise x u v dependent noise for short a sufficient condition is derived for the infinite horizon h control of such systems in terms of a set of coupled second order hamilton jacobi inequalities hjis in general it is difficult to solve these coupled hjis by using fuzzy approach the infinite horizon h control design for nonlinear stochastic markov jump systems is developed via solving a set of linear matrix inequalities lmis instead of hjis two numerical examples are presented to illustrate the effectiveness of the proposed design methods

geodesics in large planar maps and in the brownian map we study geodesics in the random metric space called the brownian map which appears as the scaling limit of large planar maps in particular we completely describe geodesics starting from the distinguished point called the root and we characterize the set s of all points that are connected to the root by more than one geodesic the set s is dense in the brownian map and homeomorphic to a non compact real tree furthermore for every x in s the number of distinct geodesics from x to the root is equal to the number of connected components of s x in particular points of the brownian map can be connected to the root by at most three distinct geodesics our results have applications to the behavior of geodesics in large planar maps