on the asymptotic solution of the singularly perturbed boundary value problems posed by bohe abstract asymptotic solutions to two point boundary value problems for certain equations of the form g x f on 0 t 1 are obtained featuring an interior shock layer where the solution jumps from nearly x 0 to nearly x 1

h control of uncertain fuzzy continuous time systems a new kind of dynamical fuzzy model is proposed to represent the continuous time complex system which includes both linguistic information and system uncertainties a new stability analysis and control system design approach is developed for this kind of dynamical fuzzy model since the fuzzy model considers the norm bounded disturbance the controller design problem becomes a h control problem a constructive algorithm is developed to obtain the h feedback control law finally an example is given to illustrate the application of the method

slow motion manifolds far from the attractor in multistable reaction diffusion equations abstract we consider a scalar reaction diffusion equation with multistable nonlinearity with a particular symmetry by reduction to a family of transmission problems in r and by contraction arguments a manifold close to an invariant manifold formed by functions exhibiting a pattern of transition layers is constructed an approximation for the associated vector field is also provided this shows that the motion on those manifolds is exponentially slow as in the well known case of the bistable equation however in opposition to the bistable case some of these manifolds are far from the attractor since these manifolds correspond to metastable patterns this shows the importance of the transient motion toward the attractor and the importance of these manifolds in organizing that motion it is also shown that by a suitable perturbation we can obtain new equilibria on those manifolds

a class of nonlinear problems with perturbation both in boundary and interior points under appropriate conditions using the boundary perturbation theory and the technique of differential inequalities a class of nonlinear singularly perturbed problems with perturbation not only arising in the equation but also arising in interior points and boundary points is considered the existence of solution is proved by improving the structure of auxiliary functions in the literature the uniformly valid asymptotic expansion of the solution and its derivation for arbitrary order are obtained the conclusion in this paper richens and improves some early results

modeling identification and control of a class of nonlinear systems in this paper we propose a new fuzzy hyperbolic model for a class of complex systems which is difficult to model the fuzzy hyperbolic model is a nonlinear model in nature and can be easily derived from a set of fuzzy rules it can also be seen as a feedforward neural network model and so we can identify the model parameters by bp algorithm we prove that the stable controller can be designed based on linear system theory two methods of designing the controller for the fuzzy hyperbolic model are proposed the results of simulation support the effectiveness of the model and the control scheme

fuzzy control turns 50 in 2015 we celebrate the 50th anniversary of fuzzy sets ten years after the main milestones regarding its applications in fuzzy control in their 40th birthday were reviewed in fss see 1 ten years is at the same time a long period and short time thinking to the inner dynamics of research this paper presented for these 50 years of fuzzy sets is taking into account both thoughts a first part presents a quick recap of the history of fuzzy control from model free design based on human reasoning to quasi lpv linear parameter varying model based control design via some milestones and key applications the second part shows where we arrived and what the improvements are since the milestone of the first 40 years a last part is devoted to discussion and possible future research topics

brief delay dependent robust h control of uncertain linear state delayed systems this paper examines the problems of robust stabilization and robust h control for linear systems with a constant time delay in the state and subject to parameter uncertainty systems with norm bounded parameter uncertainty will be considered and attention is focused on the design of linear memoryless state feedback controllers we develop methods of robust stabilization and robust h control which are dependent on the size of the delay and are based on the solution of linear matrix inequalities the proposed methods can be easily extended to uncertain linear polytopic systems as well as to the case of multiple time delays

h quantized control for nonlinear networked control systems this paper presents a new approach to the problems of h analysis and synthesis for nonlinear networked control systems nncss with limited communication capacity where a nncs can be represented by a t s fuzzy model with two time varying quantizers neither free weighting matrices nor model transformations are employed in the derivation instead by constructing an improved lyapunov function and introducing an extended jessen s inequality an improved stability criteria is obtained the h controller is shown in terms of nonlinear matrix inequalities which can be computed through solving a convex optimization problem numerical examples are exploited to show the usefulness and effectiveness of the results obtained

h output feedback control design for uncertain fuzzy singularly perturbed systems an lmi approach this paper examines the problem of designing a robust h output feedback controller for a class of singularly perturbed systems described by a takagi sugeno fuzzy model based on a linear matrix inequality lmi approach lmi based sufficient conditions for the uncertain singularly perturbed nonlinear systems to have an h performance are derived to eliminate the ill conditioning caused by the interaction of slow and fast dynamic modes solutions to the problem are presented in terms of lmis which are independent of the singular perturbation the proposed approach does not involve the separation of states into slow and fast ones and it can be applied not only to standard but also to nonstandard singularly perturbed nonlinear systems a numerical example is provided to illustrate the design developed in this paper

using global invariant manifolds to understand metastability in the burgers equation with small viscosity the large time behavior of solutions to the burgers equation with small viscosity is described using invariant manifolds in particular a geometric explanation is provided for a phenomenon known as metastability which in the present context means that solutions spend a very long time near the family of solutions known as diffusive n waves before finally converging to a stable self similar diffusion wave more precisely it is shown that in terms of similarity or scaling variables in an algebraically weighted l 2 space the self similar diffusion waves correspond to a one dimensional global center manifold of stationary solutions through each of these fixed points there exists a one dimensional global attractive invariant manifold corresponding to the diffusive n waves thus metastability corresponds to a fast transient in which solutions approach this metastable manifold of diffusive n waves followed by a slow decay along this manifold and finally convergence to the self similar diffusion wave

stability and stabilization of a class of fuzzy time delay descriptor systems this paper studies a class of fuzzy time delay descriptor systems in the extended takagi sugeno t s fuzzy model sufficient conditions are derived for the stability and stabilization in terms of linear matrix inequalities lmis illustrative examples are given to show the effectiveness and the advantages of the present results

patterns of propagating pulses the complex dynamics that arise in certain nonlinear partial differential equations in time and in one space dimension are studied in the general case considered the equation admits a solitary wave in the form of a pulse tailing off exponentially fore and aft with possibly oscillatory character complicated solutions are described by a superposition of many such solitary structures in interaction the description is asymptotic in terms of a parameter that becomes exponentially small as the ratio of typical pulse separation to pulse width becomes large the outcome is a set of dynamical equations for the motion of the individual pulses with nearest neighbor interactions this system of ordinary differential equations odes admits a wide range of patterns both regular and chaotic the stability theory of such patterns is sketched and the continuum limit of the lattice dynamical equations of the pulses is given

on the speed rate of convergence of solutions to conservation laws with nonlinear diffusions abstract in this paper we analyze the long time behavior of solutions to conservation laws with nonlinear diffusion terms of different types saturating diffusions monotone and non monotone and singular nonlinear diffusions are considered in particular the cases of mean curvature type diffusions both in the euclidean space and in lorentz minkowski space enter in our framework after dealing with existence and stability of monotone steady states in a bounded interval of the real line with dirichlet boundary conditions we discuss the speed rate of convergence to the asymptotic limit as t finally in the particular case of a burgers flux function we show that the solutions exhibit the phenomenon of metastability

relaxed cal h _ infty stabilization conditions for discrete time fuzzy systems with interval time varying delays to derive less conservative delay and range dependent h infin stabilization conditions for discrete time takagi sugeno t s fuzzy systems with interval time varying delays the use of a fuzzy weighting dependent lyapunov krasovskii functional fwlkf in which all variables are set to be affinely or quadratically dependent on fuzzy weighting functions is proposed subsequently parameterized linear matrix inequality plmi based h infin stabilization conditions are derived by following the free weighting matrix approach to fully exploit the convexity of fuzzy weighting functions the derived plmis are sequentially replaced by a finite set of lmis by considering all possible conditions associated with fuzzy weighting functions

robust h sub spl infin control for uncertain discrete time delay fuzzy systems via output feedback controllers this work investigates the problem of robust output feedback h sub spl infin control for a class of uncertain discrete time fuzzy systems with time delays the state space takagi sugeno fuzzy model with time delays and norm bounded parameter uncertainties is adopted the purpose is the design of a full order fuzzy dynamic output feedback controller which ensures the robust asymptotic stability of the closed loop system and guarantees an h sub spl infin norm bound constraint on disturbance attenuation for all admissible uncertainties in terms of linear matrix inequalities lmis a sufficient condition for the solvability of this problem is presented explicit expressions of a desired output feedback controller are proposed when the given lmis are feasible the effectiveness and the applicability of the proposed design approach are demonstrated by applying this to the problem of robust h sub spl infin control for a class of uncertain nonlinear discrete delay systems

observer based robust h sub spl infin control for fuzzy systems using two step procedure this paper investigates both robust h sub spl infin analysis and synthesis problems involving observer based fuzzy control via linear matrix inequality methods for which efficient optimization techniques are available the observer and controller are capable of disturbance rejection in the presence of unknown but bounded disturbance we present results in a unified fashion applicable to both continuous and discrete time problems with or without uncertainty finally the validity and applicability of the approach are demonstrated by examples

shock layer movement for burgers equation this paper considers the motion of the shock layer exhibited by the solution of the initial boundary value problem for the equation epsilon u xx uu x u t with small values of epsilon 0 this burgers equation occurs as a model for a number of physical problems and is representative of many convection dominated evolution equations a specific example will be solved explicitly using the cole hopf transformation the result suggests a corresponding asymptotic approach which provides the shock layer location x epsilon t as the solution of an initial value problem that method which can be applied to a far wider class of equations also shows how the steady state shock location can be changed substantially by asymptotic exponentially small perturbations

quasilinear elliptic equations on noncompact riemannian manifolds abstract the existence of solutions to a class of quasilinear elliptic problems on noncompact riemannian manifolds with finite volume is investigated boundary value problems with homogeneous neumann conditions in possibly irregular euclidean domains are included as a special instance a nontrivial solution is shown to exist under an unconventional growth condition on the right hand side which depends on the geometry of the underlying manifold the identification of the critical growth is a crucial step in our analysis and entails the use of the isocapacitary function of the manifold a condition involving its isoperimetric function is also provided

a metastable flame front interface and carrier s problem metastable dynamics for a nonlocal pde modeling the upwards propagation of a flame front interface in a vertical channel is analyzed in the one dimensional case where the channel cross section is taken to be the slab 1

the singularly perturbed generalized dirichlet problems for semilinear elliptic equation of higher order the singularly perturbed generalized boundary value problems for the semilinear elliptic equation of higher order are considered under suitable conditions the existence uniqueness and asymptotic behavior of generalized solution for the dirichlet boundary value problems are studied

output feedback robust h sup spl infin control of uncertain fuzzy dynamic systems with time varying delay this paper presents an output feedback robust h sup spl infin control problem for a class of uncertain fuzzy dynamic systems with time varying delayed state the takagi sugeno fuzzy model is employed to represent an uncertain nonlinear systems with time varying delayed state using a single quadratic lyapunov function the globally exponential stability and disturbance attenuation of the closed loop fuzzy control system are discussed sufficient conditions for the existence of robust h sup spl infin controllers are given in terms of matrix inequalities constructive algorithm for design of robust h sup spl infin controller is also developed the resulting controller is nonlinear and automatically tuned based on fuzzy operation

new sufficient conditions for robust h fuzzy hyperbolic tangent control of uncertain nonlinear systems with time varying delay this paper considers the delay dependent robust h control problem based on fuzzy hyperbolic model fhm for a class of uncertain nonlinear systems with time varying delay firstly fhm modeling method is presented for uncertain nonlinear systems with time varying delay secondly the new delay dependent sufficient condition for the existence of a state feedback fuzzy hyperbolic tangent controller is proposed in terms of linear matrix inequalities lmis by constructing a novel lyapunov krasovskii functional the robust fhm based control law can guarantee that the closed loop system is robustly asymptotically stable with a prescribed h index as more information of the fhm and the size of time delay are taken into account the proposed conditions are new and less conservative finally three illustrative examples are given to show the effectiveness of using fhm based controllers

transition to turbulence small disturbances and sensitivity analysis i a motivating problem abstract for over 100 years researchers have attempted to predict transition to turbulence in fluid flows by analyzing the spectrum of the linearized navier stokes equations however for many simple flows this approach fails to match experimental results recently new scenarios for transition have been proposed that are based on the interaction of the linearized equations of motion with small disturbances to the flow system these new mostly linear theories have increased our understanding of the transition process but the role of nonlinearity has not been explored in detail this paper is the first of a two part work in which sensitivity analysis is used to study the effects of small disturbances on transition to turbulence in this part we study a highly sensitive one dimensional burgers equation as a motivating problem sensitivity analysis is used to predict the large changes in solutions in the presence of a small disturbance also sensitivity analysis is shown to provide more information about the disturbed nonlinear problem than a purely linear analysis of the problem in the second part of this work this analysis will be extended to the three dimensional navier stokes equations to show that small disturbances have great potential to trigger transition to turbulence

an adaptive partition of unity method for chebyshev polynomial interpolation for a function that is analytic on and around an interval chebyshev polynomial interpolation provides spectral convergence however if the function has a singularity close to the interval the rate of convergence is near one in these cases splitting the interval and using piecewise interpolation can accelerate convergence chebfun includes a splitting mode that finds an optimal splitting through recursive bisection but the result has no global smoothness unless conditions are imposed explicitly at the breakpoints an alternative is to split the domain into overlapping intervals and use an infinitely smooth partition of unity to blend the local chebyshev interpolants a simple divide and conquer algorithm similar to chebfun s splitting mode can be used to find an overlapping splitting adapted to features of the function the algorithm implicitly constructs the partition of unity over the subdomains this technique is applied to explicitly given functions as well as to the solutions of singularly pertur

h sub spl infin controller synthesis of fuzzy dynamic systems based on piecewise lyapunov functions and bilinear matrix inequalities this work presents an h sub spl infin controller design method for fuzzy dynamic systems based on techniques of piecewise smooth lyapunov functions and bilinear matrix inequalities it is shown that a piecewise continuous lyapunov function can be used to establish the global stability with h sub spl infin performance of the resulting closed loop fuzzy control systems and the control laws can be obtained by solving a set of bilinear matrix inequalities bmis two examples are given to illustrate the application of the proposed methods

delay dependent robust stabilization of uncertain systems with multiple state delays this paper deals with the problem of robust stabilization for uncertain systems with multiple state delays the parameter uncertainties are time varying and unknown but are norm bounded and the delays are time varying a new method for achieving robust stabilization is presented for a class of uncertain time delay systems via linear memoryless state feedback control the results depend on the size of the delays and are given in terms of several linear matrix inequalities

adaptive residual subsampling methods for radial basis function interpolation and collocation problems we construct a new adaptive algorithm for radial basis functions rbfs method applied to interpolation boundary value and initial boundary value problems with localized features nodes can be added and removed based on residuals evaluated at a finer point set we also adapt the shape parameters of rbfs based on the node spacings to prevent the growth of the conditioning of the interpolation matrix the performance of the method is shown in numerical examples in one and two space dimensions with nontrivial domains

large time behavior for conservation laws with source in a bounded domain here u u x t u r precise assumptions will be given later we are in particular interested in the asymptotic behavior of solutions to problem 1 3 equation of the form 1 is called reaction convection equation or balance law the correct setting to deal with for such equations is the one given by entropy solutions in the sense of kruz kov in 15 in such class it is well known that the cauchy problem has a unique solution continuously depending on initial data in l norm in this article we consider boundary conditions and we analyze the influence of such conditions on the whole solution as time goes on such conditions for equations of the form 1 were considered in 1 it turns out that in order to have existence uniqueness and continuous dependence conditions 3 have to be interpreted in a non classical fashion following 1 we look for entropy solutions of 1 such that their boundary values belong to appropriate sets details will be given later on article id jdeq 1999 3669 available online at http www idealibrary com on

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

supersensitivity due to uncertain boundary conditions summary we study the viscous burgers equation subject to perturbations on the boundary conditions two kinds of perturbations are considered deterministic and random for deterministic perturbations we show that small perturbations can result in o 1 changes in the location of the transition layer for random perturbations we solve the stochastic burgers equation using different approaches first we employ the jacobi polynomial chaos which is a subset of the generalized polynomial chaos for stochastic modeling converged numerical results are reported up to seven significant digits and we observe similar stochastic supersensitivity for the mean location of the transition layer subsequently we employ up to fourth order perturbation expansions we show that even with small random inputs the resolution of the perturbation method is relatively poor due to the larger stochastic responses in the output two types of distributions are considered uniform distribution and a truncated gaussian distribution with no tails various solution statistics including the spatial evolution of probability density function at steady state are studied copyright 2004 john wiley sons ltd

h sub spl infin output feedback control of discrete time fuzzy systems with application to chaos control this paper presents an observer based h sub spl infin output feedback synthesis method for discrete time fuzzy dynamic systems based on a piecewise lyapunov function the basic idea of the approach is to design an observer based piecewise linear output feedback control law to guarantee the global stability with h sub spl infin performance of the resulting closed loop fuzzy control systems it is shown that the controller parameters can be obtained by solving a set of linear matrix inequalities lmis that are numerically feasible with commercially available software application to control chaotic systems is given to illustrate the effectiveness and advantages of the proposed method

asymptotic numerical study of supersensitivity for generalized burgers equations this article addresses some asymptotic and numerical issues related to the solution of burgers equation varepsilon u xx u t u u x 0 on 1 1 subject to the boundary conditions u 1 1 delta u 1 1 and its generalization to two dimensions varepsilon delta u u t u u x u u y 0 on 1 1 times pi pi subject to the boundary conditions u x 1 1 delta u x 1 1 with 2 pi periodicity in y the perturbation parameters delta and varepsilon are arbitrarily small positive and independent when they approach 0 they satisfy the asymptotic order relation delta o s rm e a varepsilon for some constant a in 0 1 the solutions of these convection dominated viscous conservation laws exhibit a transition layer in the interior of the domain whose position as t to infty is supersensitive to the boundary perturbation algorithms are presented for the computation of the position of the transition layer at steady state the algorithms generalize to viscous conservation laws with a convex nonlinearity and are scalable in a parallel computing environment

a descriptor representation approach to observer based h control synthesis for discrete time fuzzy systems this work is concerned with the observer based h control synthesis problem of discrete time takagi sugeno t s fuzzy systems with external disturbances the objective is to find a new way to design the controller and observer guaranteeing a prescribed h performance of the fuzzy system by the descriptor representation approach two new conditions for observer based h control synthesis are proposed based on various lyapunov function candidates which are in the form of linear matrix inequalities lmis a numerical example will be given to show the efficiency of the proposed method

delay dependent stabilization of linear systems with time varying state and input delays the integral inequality method is a new way of tackling the delay dependent stabilization problem for a linear system with time varying state and input delays email protected t ax t a 1x t h 1 t b 1u t b 2u t h 2 t in this paper a new integral inequality for quadratic terms is first established then it is used to obtain a new state and input delay dependent criterion that ensures the stability of the closed loop system with a memoryless state feedback controller finally some numerical examples are presented to demonstrate that control systems designed based on the criterion are effective even though neither a b 1 nor a a 1 b 1 is stabilizable

robust stability and stabilization of uncertain t s fuzzy systems with time varying delay an input output approach an input output approach to the stability and stabilization of uncertain takagi sugeno t s fuzzy systems with time varying delay is proposed in this paper the time varying parameter uncertainties are assumed to be norm bounded and the delay is intervally time varying a novel method is employed to approximate the time varying delay based on which the considered system is transformed into a feedback interconnection form the new formulation of the system is comprised of a forward subsystem with constant time delay and a feedback subsystem embedding the uncertainties by applying the scaled small gain theorem to the converted system less conservative stability and stabilization criteria are obtained moreover the applicability of the proposed approach to the robust case is simpler since both delay and parameter uncertainties are processed in a unified framework numerical experiments are performed to illustrate the advantage of the proposed techniques

a new approach to fuzzy modeling and control of discrete time systems we present a new approach to fuzzy modeling and control of discrete time systems which is based on the formulation of a novel state space representation using the hyperbolic tangent function the new representation designated the hyperbolic model combines the advantages of fuzzy system theory and classical control theory on the one hand the hyperbolic model is easily derived from a set of mamdani type fuzzy rules on the other hand classical control theory can be applied to design controllers for the hyperbolic model that not only guarantee stability and robustness but are themselves equivalent to a set of mamdani type fuzzy rules thus this new approach combines the best of two worlds it enables linguistic interpretability of both the model and the controller and guarantees closed loop stability and robustness

on the exponentially slow motion of a viscous shock using formal asymptotic methods we study the internal layer behavior associated with the following viscous shock problem in the limit e 0 the convex nonlinearity f u satisfies f f for the steady problem we show that the method of matched asymptotic expansions fails to uniquely determine the location of the equilibrium shock layer solution this indeterminacy resulting from neglecting certain exponentially small effects is eliminated by using the projection method which exploits certain properties of the spectrum associated with the linearized operator for the time dependent problem we show that the viscous shock which is formed from initial data drifts towards the equilibrium solution on an exponentially long time interval of the order o ec e for some c 0 this exponentially slow behavior is analyzed by deriving an equation of motion for the location of the viscous shock for burgers equation f u u2 2 the results give an analytical characterization of the slow shock layer motion observed numerically in kreiss and kreiss see 11 we also show that the shock layer behavior is very sensitive to small changes in the boundary operator in addition using a wkb type method the slow viscous shock motion is studied numerically for small e the results comparing favorably with corresponding analytical results finally we relate the slow viscous shock motion to similar slow internal layer motion for the allen cahn equation

optimal fuzzy controller design local concept approach in this paper we present a global optimal and stable fuzzy controller design method for both continuous and discrete time fuzzy systems under both finite and infinite horizons first a sufficient condition is proposed which indicates that the global optimal effect can be achieved by the fuzzily combined local optimal controllers based on this sufficient condition we derive a local concept approach to designing the optimal fuzzy controller by applying traditional linear optimal control theory the stability of the entire closed loop continuous fuzzy system can be ensured by the designed optimal fuzzy controller the optimal feedback continuous fuzzy system can not only be guaranteed to be exponentially stable but also be stabilized to any desired degree also the total energy of system output is absolutely finite moreover the resultant feedback continuous fuzzy system possesses an infinite gain margin that is its stability is guaranteed no matter how large the feedback gain becomes two examples are given to illustrate the proposed optimal fuzzy controller design approach and to demonstrate the proved stability properties

parameter dependent lyapunov functional for stability of time delay systems with polytopic type uncertainties this note concerns the problem of the robust stability of a linear system with a time varying delay and polytopic type uncertainties in order to construct a parameter dependent lyapunov functional for the system we first devised a new method of dealing with a time delay system without uncertainties in this method the derivative terms of the state which is in the derivative of the lyapunov functional are retained and some free weighting matrices are used to express the relationships among the system variables and among the terms in the leibniz newton formula as a result the lyapunov matrices are not involved in any product terms of the system matrices in the derivative of the lyapunov functional this method is then easily extended to a system with polytopic type uncertainties numerical examples demonstrate the validity of the proposed criteria

state and output feedback control of interval type 2 fuzzy systems with mismatched membership functions this paper is concerned with the problems of state and output feedback control for interval type 2 it2 fuzzy systems with mismatched membership functions the it2 fuzzy model and the it2 state and output feedback controllers do not share the same membership functions a novel performance index which is expressed as an extended dissipativity performance is introduced to be a generalization of h infty l 2 l infty passive and dissipativity performances indexes first the it2 takagi sugeno fuzzy model and the controllers are constructed by considering the mismatched membership functions second on the basis of lyapunov stability theory the it2 fuzzy state and output feedback controllers are designed respectively to guarantee that the closed loop system is asymptotically stable with extended dissipativity performance the existence conditions of the two kinds of controllers are obtained in terms of convex optimization problems which can be solved by standard software finally simulation results are provided to illustrate the effectiveness of the proposed methods

improved delay dependent stability criteria for time delay systems this note provides an improved asymptotic stability condition for time delay systems in terms of a strict linear matrix inequality unlike previous methods the mathematical development avoids bounding certain cross terms which often leads to conservatism when time varying norm bounded uncertainties appear in a delay system an improved robust delay dependent stability condition is also given examples are provided to demonstrate the reduced conservatism of the proposed conditions

stable transition layers in a semilinear diffusion equation with spatial inhomogeneities in n dimensional domains we prove existence and establish the asymptotic behavior as e 0 of stable stationary solutions to the equation ut e d x u 1 u2 u a x for t x r where rn n 2 with neumann boundary condition the function a x c0 satisfies 1 a x 1 and vanishes on some hypersurfaces the results generalize to n dimensional domains and to variable diffusivity earlier paper by angenent et al j differential equations 67 1987 212

analysis and design of fuzzy control systems using dynamic fuzzy state space models a discrete time fuzzy control system which is composed of a dynamic fuzzy model and a fuzzy state feedback controller is proposed stability of the fuzzy control system is discussed and two sufficient conditions to guarantee the stability of the system are given in terms of uncertain linear system theory an algorithm is developed to check the stability condition the controller design method is divided into two procedures one is to get the state feedback matrix by linear system theory in every local rule map the other is to determine conditions of global stability by using a nonlinear analysis method two examples are used to show the design method

metastable patterns in solutions of ut ϵ2uxx f u we consider the equation in question on the interval 0 x 1 having neumann boundary conditions with f u f u where f is a double well energy density with equal minima at u 1 the only stable states of the system are patternless constant solutions but given two phase initial data a pattern of interfacial layers typically forms far out of equilibrium the ensuing nonlinear relaxation process is extremely slow patterns persist for exponentially long times proportional to exp a l where a f 1 and l is the minimum distance between layers physically a tiny potential jump across a layer drives its motion we prove the existence and persistence of these metastable patterns and characterise accurately the equations governing their motion the point of view is reminiscent of center manifold theory a manifold parametrising slowly evolving states is introduced a neighbourhood is shown to be normally attracting and the parallel flow is characterised to high relative accuracy proofs involve a detailed study of the dirichlet problem spectral gap analysis and energy estimates

robust h control for discrete time fuzzy systems via basis dependent lyapunov functions this paper deals with the robust h control problem for a class of discrete time fuzzy systems with uncertainty the uncertainty is assumed to be of structured linear fractional form by using basis dependent lyapunov function an h control design approach is developed the control design approach is facilitated by introducing some additional instrumental matrix variables these additional matrix variables decouple the lyapunov and the system matrices which makes the control design feasible the proposed approach leads to some sufficient results in the form of strict linear matrix inequalities lmis it is expected that the basis dependent results are less conservative than the basis independent ones due to the introduction of basis dependent lyapunov function finally numerical examples including the discrete chaotic lorenz system are also given to demonstrate the applicability of the proposed approach

improved approach to robust cal h _ infty stabilization of discrete time t s fuzzy systems with time varying delays this study is concerned with the robust stabilization problem for a class of discrete time takagi sugeno t s fuzzy systems with time varying delays to improve the conditions for the solvability of the stabilization problem a nonquadratic lyapunov krasovskii functional with a triple summation term is established and a nonparallel distributed compensation non pdc scheme is adopted along with the matrixtransformation technique in addition an appropriate free weightingmatrix method is proposed to exploit novel slack variables for null sum terms especially resulting from i xi 1 xi t xi 1 xi

on equivalence and efficiency of certain stability criteria for time delay systems in recent years there have been a number of new delay dependent stability criteria based on linear matrix inequalities published in the literature this note aims to theoretically establish the equivalence of seven of these stability criteria moreover the efficiency of these stability criteria is assessed based on the number of unknowns in the linear matrix inequalities

wang s multiplicity result for superlinear equations without the ambrosetti rabinowitz condition we consider a nonlinear elliptic equation driven by the sum of a p laplacian and a q laplacian where 1 q 2 p with a p 1 superlinear caratheodory reaction term which doesn t satisfy the usual ambrosetti rabinowitz condition using variational methods based on critical point theory together with techniques from morse theory we show that the problem has at leat three nontrivial solutions among them one is positive and one is negative

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

delay dependent lmi conditions for stability and stabilization of t s fuzzy systems with bounded time delay this paper studies the stability and stabilization problems for time delay nonlinear systems through takagi sugeno t s fuzzy model approach the time delays are assumed to be bounded but perhaps non smooth delay dependent conditions are presented in terms of lmis illustrative examples are given to show the effectiveness and merits of the present results

passivity analysis and passive control of fuzzy systems with time varying delays this paper is concerned with the passive controller design problem for a class of continuous time takagi sugeno t s fuzzy systems with both state and input delays the delays are assumed to be time varying and differentiable a notion of very strict passivity is adopted the purpose is to design a state feedback fuzzy controller such that the resulting closed loop system is very strictly passive vsp delay dependent conditions for the solvability of the addressed problem are obtained by applying recently developed techniques for time delay systems and fuzzy systems these conditions are expressed by means of strict linear matrix inequalities lmis that can be easily solved a numerical example and simulation results are provided to demonstrate the effectiveness of the proposed method

memoryless h controllers for discrete time systems with time delay this paper considers the problem of h stabilization of discrete time systems with state delays and exogenous bounded energy l 2 disturbances specifically an h state feedback control design problem for discrete time systems with time delay is addressed the principal result involves sufficient conditions in terms of a modified riccati equation for characterizing state feedback controllers that enforce a bound on h performance and guarantee closed loop stability in the face of system state delay

on some applications of the superposition principle with fourier basis this paper presents several applications of local fourier basis combined with corrector techniques via the superposition principle to compute solutions of boundary value problems our methodology is inspired by the well known corrector technique used in asymptotic singular perturbation theory see for example w eckhaus asymptotic analysis of singular perturbations north holland amsterdam 1979 we build solvers for time dependent boundary value problems and or singular perturbation problems using fourier expansions combined to additional convenient set of time independent basis functions to enforce the boundary conditions the algorithms are very well suited for parallel computing because they rely mainly on ffts and basis functions given analytically or computed in parallel once and for all our method can be spectral accurate for simple geometry we obtain in addition interesting new results for boundary value problems with complex geometry we describe in this paper the implementation of the method and the numerical results for many linear and nonlinear problems our goal is to test the advantages and the limits of our approach in order to motivate further theoretical investigations our method applied to steady one dimensional problems is similar to the work of israeli vozovoi and averbuch j sci comput 8 1993 pp 135 149 on domain decomposition with local fourier basis for the helmotz problem however our methodology for time dependent problem and or two space dimensions geometry is rather different in its spirit and complements previous investigations of israeli vozovoi and averbuch

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

a multiple lyapunov function approach to stabilization of fuzzy control systems this paper addresses stability analysis and stabilization for takagi sugeno fuzzy systems via a so called fuzzy lyapunov function which is a multiple lyapunov function the fuzzy lyapunov function is defined by fuzzily blending quadratic lyapunov functions based on the fuzzy lyapunov function approach we give stability conditions for open loop fuzzy systems and stabilization conditions for closed loop fuzzy systems to take full advantage of a fuzzy lyapunov function we propose a new parallel distributed compensation pdc scheme that feedbacks the time derivatives of premise membership functions the new pdc contains the ordinary pdc as a special case a design example illustrates the utility of the fuzzy lyapunov function approach and the new pdc stabilization method

further studies on relaxed stabilization conditions for discrete time two dimension takagi sugeno fuzzy systems this paper investigates the stabilization problem of discrete time two dimension 2 d takagi sugeno t s fuzzy systems based on a novel non parallel distributed compensation non pdc control scheme combined with a new non quadratic lyapunov function less conservative stabilization conditions are developed the proposed non quadratic lyapunov function is homogeneous polynomially parameter dependent on membership functions as the degree of the lyapunov function increases the conservatism of the obtained stabilization conditions is gradually reduced by exploiting the algebraic property of membership functions the stabilization conditions approach to exactness in the sense of convergence compared with the existing methods no slack variables are introduced in control synthesis and hence the same or less conservative results can be obtained with a lower computational cost a numerical example is given to illustrate the effectiveness of the proposed method

weak solution for neumann p q laplacian problem on riemannian manifold abstract we prove the existence of a nontrivial solution for a nonlinear p q laplacian problem with neumann boundary condition on a non compact riemannian manifold the idea is to reduce the problem in variational form which means to consider the critical points of the corresponding euler lagrange functional in an orlicz sobolev space

stable neural controller design for unknown nonlinear systems using backstepping we propose from an adaptive control perspective a neural controller for a class of unknown minimum phase feedback linearizable nonlinear system with known relative degree the control scheme is based on the backstepping design technique in conjunction with a linearly parametrized neural network structure the resulting controller however moves the complex mechanics involved in a typical backstepping design from off line to online with appropriate choice of the network size and neural basis functions the same controller can be trained online to control different nonlinear plants with the same relative degree with semi global stability as shown by the simple lyapunov analysis meanwhile the controller also preserves some of the performance properties of the standard backstepping controllers simulation results are shown to demonstrate these properties and to compare the neural controller with a standard backstepping controller

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

technical communique new results on delay dependent robust h control for systems with time varying delays this paper considers the problem of delay dependent robust h control for uncertain systems with time varying delays an improved delay dependent bounded real lemma brl for time delay systems is established in terms of a linear matrix inequality based on the obtained brl a delay dependent condition for the existence of a state feedback controller which ensures asymptotic stability and a prescribed h performance level of the closed loop system for all admissible uncertainties is proposed in terms of a matrix inequality

burgers equation with no flux boundary conditions and its application for complete fluid separation abstract burgers equation in a one dimensional bounded domain with no flux boundary conditions at both ends is proven to be exactly solvable cole hopf transformation converts not only the governing equation to the heat equation with an extra damping but also the nonlinear mixed boundary conditions to dirichlet boundary conditions the average of the solution v is conserved consequently from an arbitrary initial condition solutions converge to the equilibrium solution which is unique for the given v the problem arises naturally as a continuum limit of a network of certain micro devices each micro device imperfectly separates a target fluid component from a mixture of more than one component and its input output concentration relationships are modeled by a pair of quadratic maps the solvability of the initial boundary value problem is used to demonstrate that such a network acts as an ideal macro separator separating out the target component almost completely another network is also proposed which leads to a modified burgers equation with a nonlinear diffusion coefficient

robust disturbance attenuation of nonlinear systems using output feedback and state dependent scaling this paper presents an approach to output feedback stabilization with l 2 disturbance attenuation for nonlinear systems in the presence of dynamic uncertainties a new formulation of state dependent scaling is introduced into the output feedback design which unifies treatment of nonlinear and linear gains the effect of disturbance on the controlled output which is allowed to be any function of output measurements can be always attenuated to an arbitrarily small level with global asymptotic stability if the plant belongs to a wide class of triangular systems whose uncertainties do not necessarily have finite linear gains the uncertain dynamics is not limited to input to state stable systems either the approach is not only a natural extension of popular approaches in robust linear control but also advantageous to numerical computation which is applicable to non triangular systems as well as triangular systems

internal layers small eigenvalues and the sensitivity of metastable motion on a semi infinite domain an analytical characterization of exponentially slow internal layer motion for the allen cahn equation and for a singularly perturbed viscous shock problem is given the results extend some previous results that were restricted to a finite geometry for these slow motion problems we show that the slow dynamics associated with the semi infinite domain are not preserved even qualitatively by imposing a commonly used form of artificial boundary condition to truncate the semi infinite domain to a finite domain this extreme sensitivity to boundary conditions and domain truncation is a direct result of the exponential ill conditioning of the underlying linearized problem for burgers equation many of the analytical results are verified by calculating certain explicit solutions some related ill conditioned internal layer problems are examined

h disturbance attenuation for state delayed systems in this note the differential game and dissipation inequality are applied to the disturbance attenuation or h control for linear systems with delayed state firstly a simple sufficient condition on the existence of a suboptimal h state feedback controller is given which is independent of delay and an observer based dynamic output feedback solution is presented in terms of riccati inequalities or riccati equations secondly a sufficient condition on the existence of a delay dependent state feedback is presented and the criterion is presented by a matrix inequality which can be solved by numerical methods

the keller segel model with logistic sensitivity function and small diffusivity the keller segel model is the classical model for chemotaxis of cell populations it consists of a drift diffusion equation for the cell density coupled to an equation for the chemoattractant here a variant of this model is studied in one dimensional position space where the chemotactic drift is turned off for a limiting cell density by a logistic term and where the chemoattractant density solves an elliptic equation modeling a quasi stationary balance of reaction and diffusion with production of the chemoattractant by the cells the case of small cell diffusivity is studied by asymptotic and numerical methods on a time scale characteristic for the convective effects convergence of solutions to weak entropy solutions of the limiting nonlinear hyperbolic conservation law is proven numerical and analytic evidence indicates that solutions of this problem converge to irregular patterns of cell aggregates separated by entropic shocks from vacuum regions as time tends to infinity close to each of these p

global regularity for the 2d boussinesq equations with partial viscosity terms abstract in this paper we prove the global in time regularity for the 2d boussinesq system with either the zero diffusivity or the zero viscosity we also prove that as diffusivity viscosity tends to zero the solutions of the fully viscous equations converge strongly to those of zero diffusion viscosity equations our result for the zero diffusion system in particular solves the problem no 3 posed by moffatt in r l ricca ed kluwer academic publishers dordrecht the netherlands 2001 pp 3 10

new delay dependent stabilization conditions of t s fuzzy systems with constant delay this paper focuses on the problem of robust control for takagi sugeno t s fuzzy systems with time delay the delay dependent stability analysis and controller synthesis have been addressed the free weighting matrix method has been used for stability analysis and controller synthesis new and less conservative delay dependent stability conditions are proposed in terms of linear matrix inequalities lmi finally some examples are given to illustrate the effectiveness of the proposed approaches

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

a numerical method based on finite difference for boundary value problems for singularly perturbed delay differential equations abstract a boundary value problem for second order singularly perturbed delay differential equation is considered when the delay argument is sufficiently small to tackle the delay term the researchers m k kadalbajoo k k sharma numerical analysis of singularly perturbed delay differential equations with layer behavior appl math comput 157 2004 11 28 r e o malley jr singular perturbation methods for ordinary differential equations springer verlag new york 1991 used taylor s series expansion and presented an asymptotic as well as numerical approach to solve such type boundary value problem but the existing methods in the literature fail in the case when the delay argument is bigger one because in this case the use of taylor s series expansion for the term containing delay may lead to a bad approximation in this paper to short out this problem we present a numerical scheme for solving such type of boundary value problems which works nicely in both the cases i e when delay argument is bigger one as well as smaller one to handle the delay argument we construct a special type of mesh so that the term containing delay lies on nodal points after discretization the proposed method is analyzed for stability and convergence to demonstrate the efficiency of the method and how the size of the delay argument and the coefficient of the delay term affects the layer behavior of the solution several test examples are considered

mode independent fuzzy fault tolerant variable sampling stabilization of nonlinear networked systems with both time varying and random delays this paper develops a fault tolerant variable sampling control vsc scheme for a class of nonlinear networked control systems ncss with time varying state and random network delays an uncertain continuous takagi sugeno t s fuzzy system with both state and input varying delays in the presence of possible actuator faults is obtained equivalently on the basis of the input delay methodology a tighter bounding lemma is proposed so as to gain less conservative closed loop stability criteria delay dependent conditions in terms of linear matrix inequalities are derived for the mode independent fault tolerant stabilizing controller of the resulting markovian network based system by employing a novel stochastic lyapunov krasovskii l k functional an illustrative example is simulated to show the validity of the obtained results

dirichlet problems for fully anisotropic elliptic equations the existence of a non trivial bounded solution to the dirichlet problem is established for a class of nonlinear elliptic equations involving a fully anisotropic partial differential operator the relevant operator depends on the gradient of the unknown through the differential of a general convex function this function need not be radial nor have a polynomial type growth besides providing genuinely new conclusions our result recovers and embraces in a unified framework several contributions in the existing literature and augments them in various special instances

slow travelling waves on a finite interval for burgers type equations abstract in this paper we study for small positive e the slow motion of the solution for evolution equations of burgers type with small diffusion u t eu xx f u x u x 0 u 0 x u 1 t u on the bounded spatial domain 1 1 f is a smooth nonpositive function having only a finite number of zeros at least two between u and u all of finite order the initial and boundary value problem has a unique asymptotically stable equilibrium solution that attracts all solutions starting with continuous initial data u 0 on an interval 1 c 0 e 1 c 0 e c 0 0 the differential equation has slow speed travelling wave solutions generated by profiles that satisfy the boundary conditions of during a long but finite time interval such travelling waves suitably describe the slow long term behaviour of the solution of evolution problem their speed characterizes the local velocity of the slow motion with algebraic precision w r t e in general and with exponential precision if f has only two zeros of first order located at u and u a solution that starts near a travelling wave moves in a small neighbourhood of such a travelling wave during a long time interval 0 t if f has zeros of order higher than 1 the equilibrium and the travelling wave are multi shock solutions of this situation differs strongly from the case where f has only a first order zero at both u studied by the authors in a previous paper in this paper we consider multi shock solutions of moreover we improve some results of the previous paper allowing a larger ball of initial data

novel delay dependent robust h control of uncertain systems with distributed time varying delays this paper investigates the problem of delay dependent robust h control for a class of uncertain systems with distributed time varying delays the aim is to design a delay dependent robust h control which ensures robust asymptotic stability of the system the delay derivative dependent robust h control criteria are obtained in terms of linear matrix inequalities lmis numerical examples are given to illustrate the effectiveness of the proposed method the results are also compared with the existing results to show the conservativeness

technical communique robust stabilization of uncertain input delayed systems using reduction method this paper concerns a robust stabilization problem that arises when applying the so called reduction method to multiple input delayed systems with parametric uncertainties a robust stabilizing controller that can be constructed easily by solving convex problems in terms of linear matrix inequalities is presented numerical examples are provided to show that in many cases the proposed controller is less conservative and easier to obtain than the existing controllers

relaxed stability conditions for continuous time t s fuzzy control systems via augmented multi indexed matrix approach this paper is concerned with the problem of developing an advanced strategy to reduce the conservatism in stability analysis and control synthesis of continuous time takagi sugeno t s fuzzy systems a novel augmented multi indexed matrix approach is proposed to implement new right hand side slack variables technique for the homogenous polynomial setting combining with the finsler lemma with homogenous matrix lagrange multipliers convergent linear matrix inequality lmi relaxations for stability analysis are proposed by using the generalization of the polya theorem for the case of positive polynomials with matrix valued coefficients a new type of state feedback controller namely the homogeneous polynomially nonquadratic control law hpnqcl is developed to conceive less conservative stabilization conditions the obtained stability and stabilization conditions are further relaxed by using the proposed right hand side slack variables technique moreover the advantages over the existing control schemes are certificated in theory three numerical examples are also provided to illustrate the effectiveness of the proposed methods