infinitely many small solutions for a modified nonlinear schrodinger equations abstract in the present paper we study the modified nonlinear schrodinger equations mnse without any growth condition on the nonlinear term we obtain the existence of infinitely many small solutions for mnse by a dual approach

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

a class of minimization problems related to quasilinear equations abstract for a class of minimization problems related to quasilinear equations we establish the existence and nonexistence of minimizers by a minimization argument and the pohozaev type identity

infinitely many solutions for quasilinear schrodinger equation with critical exponential growth in rn abstract this paper shows the existence of infinitely many solutions for the quasilinear equations of the form 0 1 n u v x u n 2 u n u 2 u k x u q 2 u h u x r n where n u is the n laplacian operator n 3 0 1 q n k l r n n n q and h is an odd continuous function having critical exponential growth the potential function v x c r n and 0 inf x r n v x sup x r n v x using mountain pass theorem and some special techniques we demonstrate that there exists 0 0 such that problem 0 1 admits infinitely many high energy solutions provided that 0 0

technical communique further studies on lmi based relaxed stabilization conditions for nonlinear systems in takagi sugeno s form this paper further studies stabilization of nonlinear systems represented by a takagi sugeno t s discrete fuzzy model by extending a nonquadratic lyapunov function and applying a nonparallel distributed compensation non pdc law a new stabilization conclusion is presented that is a generalization of some previous results in the literature the new conclusion under a special situation is also suitable for a pdc law which presents to be more relaxed than some existing results an example is provided to demonstrate the effectiveness of the new conclusions

a new lmi based approach to relaxed quadratic stabilization of t s fuzzy control systems this paper proposes a new quadratic stabilization condition for takagi sugeno t s fuzzy control systems the condition is represented in the form of linear matrix inequalities lmis and is shown to be less conservative than some relaxed quadratic stabilization conditions published recently in the literature a rigorous theoretic proof is given to show that the proposed condition can include previous results as special cases in comparison with conventional conditions the proposed condition is not only suitable for designing fuzzy state feedback controllers but also convenient for fuzzy static output feedback controller design the latter design work is quite hard for t s fuzzy control systems based on the lmi based conditions derived one can easily synthesize controllers for stabilizing t s fuzzy control systems since only a set of lmis is involved the controller design is quite simple and numerically tractable finally the validity and applicability of the proposed approach are successfully demonstrated in the control of a continuous time nonlinear system

convergent lmi relaxations for quadratic stabilizability and mathscr h _ infty control of takagi sugeno fuzzy systems this paper investigates the quadratic stabilizability of takagi sugeno t s fuzzy systems by means of parallel distributed state feedback compensators using finsler s lemma a new design condition assuring the existence of such a controller is formulated as a parameter dependent linear matrix inequality lmi with extra matrix variables and parameters in the unit simplex algebraic properties of the system parameters and recent results of positive polynomials are used to construct lmi relaxations that differently from most relaxations in the literature provide certificates of convergence to solve the control design problem due to the degrees of freedom obtained with the extra variables the conditions presented in this paper are an improvement over earlier results based only on polya s theorem and can be viewed as an alternative to the use of techniques based on the relaxation of quadratic forms an extension to cope with guaranteed h infin attenuation levels is also given with proof of asymptotic convergence to the global optimal controller under quadratic stability the efficiency of the proposed approach in terms of precision and computational effort is demonstrated by means of numerical comparisons with other methods from the literature

generalized nonquadratic stability of continuous time takagi sugeno models this paper provides generalized nonquadratic stability conditions for continuous time nonlinear models in the takagi sugeno ts form obtained by sector nonlinearity approach should global quadratic stability fail for a given nonlinear model the proposed approach allows the obtaining of progressively better estimations of the stability domain via local asymptotic conditions in the form of linear matrix inequalities lmis which are efficiently solved by convex optimization techniques illustrative examples are presented to emphasize the broadening capabilities of the new stability analysis

asymptotically necessary and sufficient conditions for stability and performance in fuzzy control applications of polya s theorem stability and performance requirements in fuzzy control of takagi sugeno systems are usually stated as fuzzy summations i e sums of terms related to lyapunov functions which are weighted by membership functions or products of them this paper presents an application to fuzzy control of polya s theorems on positive forms on the standard simplex the result provides a set of progressively less conservative sufficient conditions for proving positivity of fuzzy summations such conditions are less and less conservative as a complexity parameter n increases particular cases of such conditions are those in c h fang y s liu s w kau l hong c h lee a new lmi based approach to relaxed quadratic stabilization of t s fuzzy control systems ieee trans fuzzy systems 14 2006 286 397 x liu q zhang new approaches to h controller designs based on fuzzy observers for t s fuzzy systems via lmi automatica 39 9 2003 1571 1582 with n 2 and 3 respectively the proposed conditions are asymptotically exact i e necessary and sufficient when n tends to infinity or equivalently when a tolerance parameter tends to zero

a descriptor system approach to fuzzy control system design via fuzzy lyapunov functions there has been a flurry of research activities in the analysis and design of fuzzy control systems based on linear matrix inequalities lmis this paper presents a descriptor system approach to fuzzy control system design using fuzzy lyapunov functions the design conditions are still cast in terms of lmis but the proposed approach takes advantage of the redundancy of descriptor systems to reduce the number of lmi conditions which leads to less computational requirement to obtain relaxed lmi conditions new types of fuzzy controller and fuzzy lyapunov function are proposed a salient feature of the lmi conditions derived in this paper is to relate the feasibility of the lmis to the switching speed of each linear subsystem to be exact to the lower bounds of time derivatives of membership functions to illustrate the validity and applicability of the proposed approach two design examples are provided the first example shows that the lmi conditions based on the fuzzy lyapunov function are less conservative than those based on a common standard lyapunov function the second example illustrates the utility of the fuzzy lyapunov function approach in comparison with a piecewise lyapunov function approach

lmi based relaxed nonquadratic stabilization conditions for nonlinear systems in the takagi sugeno s form this paper presents the stabilization analysis for a class of nonlinear systems that are represented by a takagi and sugeno ts discrete fuzzy model takagi and sugeno ieee trans systems man cybern 15 1 1985 116 the main result given here concerns their stabilization using new control laws and new nonquadratic lyapunov functions new relaxed conditions and linear matrix inequality based design are proposed that allow outperforming previous results found in the literature two examples are also provided to demonstrate the efficiency of the approaches

further studies on control synthesis of discrete time t s fuzzy systems via useful matrix equalities this paper is concerned with further studies on the control synthesis of discrete time nonlinear systems in the takagi sugeno t s fuzzy form to do this a novel slack variable technique is presented by developing some useful matrix equalities which are homogenous polynomially parameter dependent on both the current time normalized fuzzy weighting functions and the past time normalized fuzzy weighting functions under the framework of homogenous matrix polynomials the algebraic properties of both the current time normalized fuzzy weighting functions and the past time normalized fuzzy weighting functions are collected for the first time into sets of united collection matrices consequently the relaxation quality of control synthesis of discrete time t s fuzzy systems is improved i e the convergence of asymptotically necessary and sufficient stabilization conditions is further sped up finally a numerical example is provided to illustrate the effectiveness of the proposed result

on relaxed lmi based designs for fuzzy regulators and fuzzy observers relaxed conditions for stability of nonlinear continuous and discrete time systems given by fuzzy models are presented a theoretical analysis shows that the proposed methods provide better or at least the same results of the methods presented in the literature numerical results exemplify this fact these results are also used for fuzzy regulators and observers designs the nonlinear systems are represented by fuzzy models proposed by takagi and sugeno 1985 the stability analysis and the design of controllers are described by linear matrix inequalities that can be solved efficiently using convex programming techniques the specification of the decay rate constrains on control input and output are also discussed

observer design of discrete time t s fuzzy systems via multi instant homogenous matrix polynomials this paper is concerned with the design of observer for discrete time nonlinear systems in the takagi sugeno t s fuzzy form under the framework of multi instant homogenous matrix polynomials a novel fuzzy observer and a new lyapunov function which are homogenous polynomially parameter dependent on both the current time normalized fuzzy weighting functions and the m steps past time normalized fuzzy weighting functions are proposed for conceiving less conservative observer design conditions since the algebraic properties of both the current time normalized fuzzy weighting functions and the m steps past time normal ized fuzzy weighting functions are fully considered the relaxation quality of the fuzzy observer design of discrete time t s fuzzy systems is significantly improved in particular some existing fuzzy lyapunov functions and fuzzy observers are special cases of the lyapunov function and the fuzzy observer given in this paper respectively finally a numerical example is provided to illustrate the effectiveness of the proposed approach index terms discrete time system homogenous matrix polynomials multi instant observer design takagi sugeno t s fuzzy model

positive solutions for a class of singular quasilinear schrodinger equations with critical sobolev exponent abstract we prove the existence of positive solutions of the following singular quasilinear schrodinger equations at critical growth u c x u u 2 u 2 2 u u q 2 u u 2 2 u u d 1 2 r n via variational methods where 0 c r n r 0 0 1 2 2 q 2 it is interesting that we do not need to add a weight function to control u q 2 u

control synthesis of discrete time t s fuzzy systems based on a novel non pdc control scheme this paper proposes relaxed stabilization conditions of discrete time nonlinear systems in the takagi sugeno t s fuzzy form by using the algebraic property of fuzzy membership functions a novel nonparallel distributed compensation non pdc control scheme is proposed based on a new class of fuzzy lyapunov functions thus relaxed stabilization conditions for the underlying closed loop fuzzy system are developed by applying a new slack variable technique in particular some existing fuzzy lyapunov functions and non pdc control schemes are special cases of the new lyapunov function and fuzzy control scheme respectively finally two numerical examples are provided to illustrate the effectiveness of the proposed method

robust filter for nonlinear stochastic partial differential systems in sensor signal processing fuzzy approach this study addresses a robust h filter design problem for nonlinear stochastic partial differential systems nspdss with random external disturbance and measurement noise in the spatiotemporal domain for nspdss a robust h filter design through a set of sensor measurements needs to solve a complex second order hamilton jacobi integral inequality hjii in order to simplify the design procedure a fuzzy stochastic partial differential system based on a fuzzy interpolation approach is proposed to approximate the nspds then a fuzzy stochastic spatial state space model is developed to represent the fuzzy stochastic partial differential system via the semidiscretization finite difference scheme and the kronecker product based on this model a robust h filter design is proposed to achieve the robust state estimation via solving linear matrix inequalities lmis instead of a second order hjii the proposed robust fuzzy h filter efficiently attenuates the effect of spatiotemporal external disturbances and measurement noise on the state estimation of nspdss from the area energy point of view finally a robust h state estimation example of heat transfer system is given to illustrate the design procedure and to confirm the h filtering performance of the proposed robust filter design method

existence of radial bounded solutions for some quasilinear elliptic equations in rn abstract we study the quasilinear equation p div a x u u p 2 u 1 p a t x u u p u p 2 u g x u i n r n with n 3 p 1 where a x t a t x t a t x t and g x t are caratheodory functions on r n r suitable assumptions on a x t and g x t set off the variational structure of p and its related functional j is c 1 on the banach space x w 1 p r n l r n in order to overcome the lack of compactness we assume that the problem has radial symmetry then we look for critical points of j restricted to x r subspace of the radial functions in x following an approach which exploits the interaction between x and the norm on w 1 p r n we prove the existence of at least one weak bounded radial solution of p by applying a generalized version of the ambrosetti rabinowitz mountain pass theorem

new stability and stabilization conditions for t s fuzzy systems with time delay this paper is concerned with the problem of the stability analysis and stabilization for takagi sugeno t s fuzzy systems with time delay a new lyapunov krasovskii functional containing the fuzzy line integral lyapunov function and the simple functional is chosen by using a recently developed wirtinger based integral inequality and introducing slack variables less conservative conditions in terms of linear matrix inequalities lmis are derived several examples are given to show the advantages of the proposed results

solutions for a class of quasilinear schrodinger equations with critical sobolev exponents in this paper we study a class of quasilinear schrodinger equations involving a critical exponent which arises in plasma physics by using the change of variable and variational approaches combining the concentration compactness principle the existence of a positive solution which has a local maximum point and decays exponentially is obtained

ground states for a class of critical quasilinear coupled superlinear elliptic systems abstract in this work we consider the following class of quasilinear coupled systems u a x u u 2 u g u x u 2 u v x r n v b x v v 2 v h v x v 2 v u x r n where n 3 and a b r n r are positive potentials r n r is a nonnegative continuous function 0 and 2 satisfying 2 2 on the nonlinear terms we assume that g h are in c 1 class which are superlinear functions at infinity and at the origin we deal with nonlinearities g and h being subcritical or critical the coupling term is a subcritical function which is superlinear at infinity our main theorem is stated without the well known ambrosetti rabinowitz condition at infinity using a change of variable we turn the quasilinear coupled system into a nonlinear coupled system where we establish a variational approach based on nehari method

new approaches to relaxed quadratic stability condition of fuzzy control systems this paper deals with the quadratic stability conditions of fuzzy control systems that relax the existing conditions reported in the previous literatures two new conditions are proposed and shown to be useful in analyzing and designing fuzzy control systems the first one employs the s procedure to utilize information regarding the premise parts of the fuzzy systems the next one enlarges the class of fuzzy control systems whose stability is ensured by representing the interactions among the fuzzy subsystems in a single matrix and solving it by linear matrix inequality the relationships between the suggested stability conditions and the conventional well known stability conditions reported in the previous literatures are also discussed and it is shown in a rigorous manner that the second condition of this paper includes the conventional conditions finally some examples and simulation results are presented to illustrate the effectiveness of the stability conditions

ground state solutions for the quasilinear schrodinger equation abstract this paper is concerned with the quasilinear schrodinger equation u a x 1 u 1 2 u 2 u u p u 0 x r n with a x 0 having a potential well and 4 p 1 2 2 by using the variational method and the concentration compactness method in orlicz space we prove the existence of a ground state solution which localizes near the potential well int a 1 0 for large enough

a new fuzzy lyapunov function approach for a takagi sugeno fuzzy control system design in this paper a new fuzzy lyapunov function approach is presented for a class of continuous time takagi sugeno fuzzy control system the proposed fuzzy lyapunov function is formulated as a line integral of a fuzzy vector which is a function of the state and it can be regarded as the work done from the origin to the current state in the fuzzy vector field unlike the approaches using a fuzzy blending of multiple quadratic lyapunov functions the time derivatives of membership functions do not appear in the proposed approach the effectiveness of the proposed approach is shown through numerical examples

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

petri net representation of switched fuzzy systems switched fuzzy systems can be used to describe the hybrid systems with fuzziness however the languages to describe the switching logic and the fuzzy subsystems are in general different and this difference makes the system analysis and implementation hard in this paper we use differential petri net dpn as a unified model to represent both the discrete logic and fuzzy dynamic processes to exam the rationality of the representation we prove the correctness of the representation for the discrete part and estimate the approximation accuracy of the representation for the dynamic part our work provides a way to analyze the switched fuzzy systems by checking the pn and to use the pn model for further system implementation we demonstrate the benefits of our work via a case study

non autonomous perturbations for a class of quasilinear elliptic equations on r abstract this paper is concerned with the existence of two positive solutions for a class of quasilinear elliptic equations on r involving the p laplacian with a non autonomous perturbation the first solution is obtained as a local minimum in a neighborhood of 0 and the second one by a mountain pass argument the special features of the problem here is the complex structure of the linear part which in particular oblige to work into the space w 1 p r then one faces problems in the convergence of the sequences of derivatives u n u

selective hbox scr h _2 and hbox scr h _ infty stabilization of takagi sugeno fuzzy systems this paper presents new results concerning the stability analysis and design of state feedback controllers for continuous time takagi sugeno t s fuzzy systems via fuzzy lyapunov functions the membership functions of the t s fuzzy systems are modeled in a space that is defined by the cartesian product of simplexes called a multisimplex if the time derivatives of the membership functions are bounded the bounds are used to construct a polytope that models the space of the time derivatives of the membership functions linear matrix inequality lmi relaxations that are based on polynomial matrices are provided for stability analysis and controller design extensions for the design of control laws that minimize upper bounds to h2 and h norms are also given the main novelty of this method is that it allows one to synthesize control gains which depends only on some premise variables that are selected by the designer numerical experiments illustrate the flexibility and advantages of the proposed method

solutions for a quasilinear schrodinger equation a dual approach abstract we consider quasilinear stationary schrodinger equations of the form 1 u u 2 u g x u x r n introducing a change of unknown we transform the search of solutions u x of 1 into the search of solutions v x of the semilinear equation 2 v 1 1 2f 2 v g x f v x r n where f is suitably chosen if v is a classical solution of 2 then u f v is a classical solution of 1 variational methods are then used to obtain various existence results

parameter dependent lmis in robust analysis characterization of homogeneous polynomially parameter dependent solutions via lmi relaxations this note investigates the robust stability of uncertain linear time invariant systems in polytopic domains by means of parameter dependent linear matrix inequality pd lmi conditions exploiting some algebraic properties provided by the uncertainty representation a systematic procedure to construct a family of finite dimensional lmi relaxations is provided the robust stability is assessed by means of the existence of a lyapunov function more specifically a homogeneous polynomially parameter dependent lyapunov hppdl function of arbitrary degree for a given degree if an hppdl solution exists a sequence of relaxations based on real algebraic properties provides sufficient lmi conditions of increasing precision and constant number of decision variables for the existence of an hppdl function which tend to the necessity alternatively if an hppdl solution of degree exists a sequence of relaxations which increases the number of variables and the number of lmis will provide an hppdl solution of larger degree the method proposed can be applied to determine homogeneous parameter dependent matrix solutions to a wide variety of pd lmis by transforming the infinite dimensional lmi problem described in terms of uncertain parameters belonging to the unit simplex in a sequence of finite dimensional lmi conditions which converges to the necessary conditions for the existence of a homogeneous polynomially parameter dependent solution of arbitrary degree illustrative examples show the efficacy of the proposed conditions when compared with other methods from the literature

continuous takagi sugeno s models reduction of the number of lmi conditions in various fuzzy control design technics fuzzy models of the takagi sugeno type enable representation of a wide class of nonlinear models conditions about their stabilization can be derived systematically usually these conditions are written as linear matrix inequality lmi problems in this paper we use a collection of properties concerning matrices to extend the area of solutions involving the feedback control laws we will work out with continuous fuzzy models and supply results about the stabilization the regulator problem and also hinfin control solutions based on a reduced number of decision variables implying a reduced number of lmi conditions are also proposed we show that a good tradeoff can been obtained

multiple solutions for a class of singular quasilinear problems abstract in this paper we use sub supersolution and minimax methods to show the existence and multiplicity of solutions for the following class of singular quasilinear problems u u 2 u a x u h x u in u 0 in u 0 on where is a bounded smooth domain of r n n 3 the function a x is nonnegative 0 is a constant and the nonlinearity h x u is continuous in our first result the nonlinearity h has an arbitrary polynomial growth and we obtain the existence of a solution for the problem via sub supersolution method for the second result h has subcritical growth and we show the existence of a second solution by applying the mountain pass theorem

technical communique reducing conservativeness in recent stability conditions of ts fuzzy systems in this correspondence a new simple strategy for reducing the conservativeness in stability analysis of continuous time takagi sugeno fuzzy systems based on fuzzy lyapunov functions is proposed this new strategy generalizes previous results

multiple solutions for quasilinear schrodinger equations involving critical exponent by using lions second concentration compactness principle and concentration compactness principle at infinity to prove that the ps condition holds locally and by minimax methods and the krasnoselski genus theory we establish the multiplicity of solutions for a class of quasilinear schrodinger equations arising from physics

existence of positive solutions for a class of quasilinear schrodinger equations on rn abstract in this paper we study the following quasilinear schrodinger equation of the form u v x u 1 2 u 2 u u p 1 u u q 1 u x r n where n 3 2 2 n q p 2 2 n n 2 1 r n under appropriate assumptions on v x we establish the existence of ground state solutions by a minimization argument

on a nonhomogeneous and singular quasilinear equation involving critical growth in r2 abstract this paper establishes sufficient conditions for the existence and multiplicity of solutions for nonhomogeneous and singular quasilinear equations of the form u v x u u 2 u g x u x a h x in r 2 where a 0 2 v x is a continuous positive potential bounded away from zero and which can be large at infinity the nonlinearity g x s is allowed to enjoy the critical exponential growth with respect to the trudinger moser inequality and the nonhomogeneous term h belongs to l q r 2 for some q 1 2 by combining variational arguments in a nonstandard orlicz space context with a singular version of the trudinger moser inequality we obtain the existence of two distinct solutions when h q is sufficiently small schrodinger equations of this type have been studied as models of several physical phenomena

maximal reductions in the baker hausdorff formula a preliminary expression for the baker hausdorff formula is found up to ninth order i e a series expansion of z in terms of multiple commutators where ez exey with x and y noncommuting up to ninth degree in x y by means of complete sets of linear relations between multiple commutators maximal reduction of the number of different multiple commutators in the series are obtained

ground state solutions for generalized quasilinear schrodinger equations without ar condition abstract in this paper we study the following generalized quasilinear schrodinger equations div g 2 u u g u g u u 2 v x u h x u x r n where n 3 g r r is an even differentiable function satisfying lim t g t t 1 0 for some 1 h x t is a given function behaving like t 2 1 at infinity which does not satisfy the a r condition combining the change of variables and the monotone method developed by jeanjean in 16 we obtain the existence of positive ground state solutions for the given problem

on the existence of standing wave solutions for a class of quasilinear schrodinger systems abstract in this paper minimax methods in a suitable orlicz space are employed to establish the existence of standing wave solutions for a class of quasilinear schrodinger systems involving subcritical nonlinearities the systems considered here can model an interaction phenomena in plasma physics

a class of quasilinear schrodinger equations with critical or supercritical exponents abstract we study the existence of nontrivial solutions for the following quasilinear schrodinger equations u v x u 2 u 2 u l u x r n where v r n r and l u involves critical or supercritical exponents

critical exponents and solitary wave solutions for generalized quasilinear schrodinger equations abstract this paper is concerned with the solitary wave solutions for a generalized quasilinear schrodinger equation in r n involving critical exponents which have appeared from plasma physics as well as high power ultashort laser in matter we find the related critical exponents for a generalized quasilinear schrodinger equation and obtain its solitary wave solutions by using a change of variables and variational argument

nodal soliton solutions for quasilinear schrodinger equations with critical exponent this paper is concerned with constructing nodal radial solutions for quasilinear schrodinger equations in rn with critical growth which have appeared as several models in mathematical physics for any given integer k 0 by using a change of variables and minimization argument we obtain a sign changing minimizer with k nodes of a minimization problem since the critical exponent appears and the lower order term may change sign we should use more delicate arguments

multiple solutions for quasilinear schrodinger equations with a parameter abstract in this paper we study the following quasilinear schrodinger equations of the form u v x u u 2 u 2 2 u g x u x r n where 1 1 2 v c r n r g c r n r r using some special techniques the existence of positive solutions negative solutions and sequence of high energy solutions are studied

a systematic approach to improve multiple lyapunov function stability and stabilization conditions for fuzzy systems this paper presents a systematic approach for decreasing conservativeness in stability analysis and control design for takagi sugeno ts systems this approach is based on the idea of multiple lyapunov functions together with simple techniques for introducing slack matrices unlike some previous approaches based on multiple lyapunov functions both the stability and the stabilization conditions are written as linear matrix inequality lmi problems the proposed approach reduces the number of inequalities and guarantees extra degrees of freedom to the lmi problems numeric examples illustrate the effectiveness of this method

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

quasilinear schrodinger equations with nonlinearities interacting with high eigenvalues it is the established existence and multiplicity of solutions for quasilinear schrodinger equations where the nonlinear term is 3 superlinear or 3 asymptotically linear at infinity in an appropriate sense the main difficulty arises from the fact that the nonlinearity has an interaction with high eigenvalues for the linear eigenvalue problem under these conditions we consider a local linking theorem together with a compactness result in order to ensure our main results we consider two distinct eigenvalues problems and some kind of crossing of eigenvalues it is the established existence and multiplicity of solutions for quasilinear schrodinger equations where the nonlinear term is 3 superlinear or 3 asymptotically linear at infinity in an appropriate sense the main difficulty arises from the fact that the nonlinearity has an interaction with high eigenvalues for the linear eigenvalue problem under these conditions we consider a local linking theorem together with a compactness result in order to ensure our main results we consider two distinct eigenvalues problems and some kind of crossing of eigenvalues

an approach to observer design of continuous time takagi sugeno fuzzy model with bounded disturbances this paper addresses the problem of designing the observer for a class of nonlinear systems by using the t s takagi sugeno fuzzy model first two lemmas are obtained to demonstrate how to design the observer then based on the non quadratic lyapunov function a new method is proposed to locally stabilize the t s fuzzy system the new method can be applied to any t s models no matter whether the rules are even or odd naturally the new method is extended to get some lmis linear matrix inequalities to design the observer for practical reason the disturbances considered in this paper are bounded by magnitude and energy finally three examples are given to illustrate the effectiveness of the new approach

local analysis of continuous time takagi sugeno fuzzy system with disturbances bounded by magnitude or energy a lagrange multiplier method abstract this paper is concerned with the problem of computing the bounds of disturbances for continuous time takagi sugeno fuzzy model two kinds of disturbances are investigated by applying the non parallel distributed compensation non pdc law non quadratic lyapunov function and lagrange multiplier method one is bounded by magnitude the other is bounded by energy if the exogenous disturbances are bounded by magnitude the maximal value of the magnitude under which the closed loop system can be controlled is obtained by solving an optimization problem on the other hand if the disturbances are bounded by energy except for the maximal bound some conditions are derived to get two local regions a smaller and a bigger such that all the trajectories starting from the smaller region will remain in the bigger one which is required to be contained in a specific compact set where the original system can be represented as t s model exactly in the end the effectiveness of the proposed results is demonstrated by two examples

parameter dependent lyapunov functions for discrete time systems with time varying parametric uncertainties abstract in this paper we consider discrete time systems with polytopic time varying uncertainty we look for a class of parameter dependent lyapunov functions which are quadratic on the system state and depend in a polytopic way on the uncertain parameter we show that extending the new discrete time stability condition proposed by de oliveira et al systems control lett 36 1999 135 to the case of time varying uncertainty leads to a necessary and sufficient condition for the computation of such a lyapunov function this allows to check asymptotic stability of the system under study the obtained linear matrix inequalities condition can also be used to cope with the control synthesis problem

existence of solutions to a class of asymptotically linear schrodinger equations in rn via the pohozaev manifold abstract in this study we investigate the nonexistence of a least energy solution and the existence of a positive solution for a class of nonhomogeneous asymptotically linear schrodinger equations in r n via the pohozaev manifold after changing the variables the quasilinear operator becomes a semilinear nonhomogeneous operator the technique used employs variational methods that are constrained to the pohozaev manifold which are combined with the splitting lemma

nonquadratic stabilization conditions for a class of uncertain nonlinear discrete time ts fuzzy models a new approach the discrete time uncertain nonlinear models are considered in a takagi sugeno form and their stabilization is studied through a non quadratic lyapunov function the classical conditions consider a one sample variation here the main results are obtained considering k samples variation i e deltak v x t v x t k v x t the results are shown to always include the classical cases and several examples illustrate the effectiveness of the approach

quasilinear elliptic equations involving the n laplacian with critical exponential growth in rn abstract this paper shows the existence of nontrivial solutions for the quasilinear equations of the form n u v x u n 2 u n u 2 u h u in r n where n is the n laplacian operator v is a continuous function bounded from below away from zero and h u is a continuous function having critical exponential growth

existence of solution for a class of quasilinear schrodinger equation in rn with zero mass abstract in this paper we use variational methods to establish a berestycki lions type result for two classes of quasilinear schrodinger equations in r n in the zero mass situation

soliton solutions for quasilinear schrodinger equations the critical exponential case abstract quasilinear elliptic equations in r 2 of second order with critical exponential growth are considered by using a change of variable the quasilinear equations are reduced to semilinear equations whose respective associated functionals are well defined in h 1 r 2 and satisfy the geometric hypotheses of the mountain pass theorem using this fact we obtain a cerami sequence converging weakly to a solution v in the proof that v is nontrivial the main tool is the concentration compactness principle p l lions the concentration compactness principle in the calculus of variations the locally compact case part i and ii ann inst h poincare anal non lineaire 1 1984 109 145 223 283 combined with test functions connected with optimal trudinger moser inequality

new stability conditions based on piecewise fuzzy lyapunov functions and tensor product transformations improvements of recent stability conditions for continuous time takagi sugeno t s fuzzy systems are proposed the key idea is to bring together the so called local transformations of membership functions and new piecewise fuzzy lyapunov functions by relying on these special local transformations the associated linear matrix inequalities that are used to prove the system s stability can be relaxed without increasing the number of conditions in addition to enhance the usefulness of the proposed methodology one can choose between two different sets of conditions characterized by independence or dependence on known bounds of the membership functions time derivatives a standard example is presented to illustrate that the proposed method is able to provide substantial improvements in some cases

semiclassical ground states for quasilinear schrodinger equations with three times growth abstract in this paper we study the quasilinear schrodinger equation 2 u v x u 2 u u 2 q x u 3 u h 1 r 3 where 0 is a parameter v and q are positive bounded functions for the equation with three times growth we establish the existence of ground states for small using the method of nehari manifold we also describe the concentration phenomena of ground states as 0

an efficient approach for reducing the conservatism of lmi based stability conditions for continuous time t s fuzzy systems this paper deals with reducing the conservatism of stability conditions for continuous time t s fuzzy systems previous stability conditions are relaxed by further exploring the properties of the time derivatives of normalized fuzzy weighting functions and by introducing more slack matrix variables by relying on analysis of the positive and negative characteristics of the time derivatives of normalized fuzzy weighting functions some redundant terms are removed from the problem formulation furthermore more slack matrix variables are introduced to enlarge the design space consequently less conservative stability conditions are obtained finally a well known numerical example is provided to illustrate the effectiveness of the proposed result

fuzzy control design of nonlinear systems under unreliable communication links in this study we propose a systematic homogenous polynomial approach for fuzzy control design of discrete time takagi sugeno fuzzy systems under unreliable communication links a novel delayed fuzzy control scheme which is homogenous polynomially parameter dependent on both the current normalized fuzzy weighting function and the one step past normalized fuzzy weighting function is designed to accomplish the assignment of relaxed control synthesis in contrast to the existing methods the closed loop controlled system is stochastically stable in the mean square sense with less conservative stabilization conditions finally simulation results are provided to verify the advantage and the effectiveness of the proposed approach

local stability analysis of continuous time takagi sugeno fuzzy systems a fuzzy lyapunov function approach this paper proposes a strategy to estimate invariant subsets of the domain of attraction da for asymptotically stable zero equilibrium points of continuous time takagi sugeno t s fuzzy systems specifically by using lyapunov s stability theory and the linear matrix inequality lmi technique sufficient conditions for proving the local stability are provided in terms of single parameter minimization problems subject to lmi constraints or eigenvalue problems which are solvable via convex optimizations the fuzzy lyapunov functions flfs expressed by the so called multi dimensional fuzzy summations are employed to characterize invariant subsets of the da as sublevel sets of the flfs to compute a larger inner estimate of the da an iterative lmi algorithm is also developed finally illustrative examples show the efficacy of the approach

an approach to fuzzy control of nonlinear systems stability and design issues presents a design methodology for stabilization of a class of nonlinear systems first the authors represent a nonlinear plant with a takagi sugeno fuzzy model then a model based fuzzy controller design utilizing the concept of the so called parallel distributed compensation is employed the main idea of the controller design is to derive each control rule so as to compensate each rule of a fuzzy system the design procedure is conceptually simple and natural moreover the stability analysis and control design problems can be reduced to linear matrix inequality lmi problems therefore they can be solved efficiently in practice by convex programming techniques for lmis the design methodology is illustrated by application to the problem of balancing and swing up of an inverted pendulum on a cart

reduced order dynamic output feedback control of continuous time t s fuzzy systems the problem of reduced order dynamic output feedback control design for continuous time takagi sugeno fuzzy systems with h guaranteed cost is addressed the proposed approach is based on a line integral fuzzy lyapunov function with arbitrary polynomial dependence on the premise variables allowing the membership functions modeled as multi simplexes to vary arbitrarily the controller is obtained by transforming the problem into a static output feedback control design problem solved by means of a two stages linear matrix inequality procedure the main appeal of the approach is that the order of the output feedback controller as well as the dependence of the premise variables are customizable for control implementation purposes examples illustrate the flexibility of the method and also that the proposed strategy can provide less conservative results when compared to other methods for full order dynamic output feedback controllers from the literature of continuous time takagi sugeno fuzzy systems

fuzzy regulators and fuzzy observers relaxed stability conditions and lmi based designs this paper presents new relaxed stability conditions and lmi linear matrix inequality based designs for both continuous and discrete fuzzy control systems they are applied to design problems of fuzzy regulators and fuzzy observers first takagi and sugeno s fuzzy models and some stability results are recalled to design fuzzy regulators and fuzzy observers nonlinear systems are represented by takagi sugeno s ts fuzzy models the concept of parallel distributed compensation is employed to design fuzzy regulators and fuzzy observers from the ts fuzzy models new stability conditions are obtained by relaxing the stability conditions derived in previous papers lmi based design procedures for fuzzy regulators and fuzzy observers are constructed using the parallel distributed compensation and the relaxed stability conditions other lmi s with respect to decay rate and constraints on control input and output are also derived and utilized in the design procedures design examples for nonlinear systems demonstrate the utility of the relaxed stability conditions and the lmi based design procedures

on the generalized local stability and local stabilization conditions for discrete time takagi sugeno fuzzy systems in this paper local stability and local stabilization problems are considered for discrete time nonlinear systems represented by takagi sugeno t s fuzzy systems improved methods to assess the local stability design locally stabilizing control laws and estimate the domain of attraction are developed in terms of single parameter minimization problems subject to linear matrix inequality lmi constraints the improvement is achieved by applying a convergent lmi relaxation technique to prove positivity of homogeneous polynomial parameter dependent matrices of arbitrary degree with variables in the simplex we also take advantage of the recently developed parameter variation modeling technique to deal with the case that the variation rate of the membership functions of the t s fuzzy systems is bounded and less than one finally several illustrative examples demonstrate the validity and efficiency of the proposed method

soliton solutions for quasilinear schrodinger equations ii abstract for a class of quasilinear schrodinger equations we establish the existence of ground states of soliton type solutions by a variational method

multiplicity of nonnegative solutions for quasilinear schrodinger equations abstract the paper deals with existence and multiplicity of nonnegative weak solutions for quasilinear schrodinger equations involving nonlinearities with possibly supercritical growth at infinity and indefinite sign an appropriate change of variables reduces the quasilinear problem into a semilinear one variational and sub super methods are applied in order to obtain the main results of the paper

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

progressively better estimates of the domain of attraction for nonlinear systems via piecewise takagi sugeno models this paper introduces a novel approach for stability analysis and controller design of nonlinear models both continuous and discrete time based on an exact piecewise takagi sugeno representation which generalizes the sector nonlinearity methodology the motivation behind this work lies on the fact that piecewise induced takagi sugeno representations have smaller variations than single ones covering the whole modeling area thus increasing the chances of finding piecewise solutions for stability analysis or controller synthesis moreover this relaxation is shown to produce progressively better estimations of the domain of attraction via easy to implement algorithms that demand much less computational effort than other recent approaches in the literature examples are provided to highlight the advantages of the contributions over the existing methods

blow up phenomena and asymptotic profiles of ground states of quasilinear elliptic equations with h1 supercritical nonlinearities abstract this paper is concerned with asymptotic profiles of ground states for a class of quasilinear schrodinger equations with h 1 supercritical nonlinearities we study the blow up rate of ground states by using the dual variational structure of equations as well as various variational methods

positive solution to a class of relativistic nonlinear schrodinger equation abstract using a change of variables we convert a quasilinear elliptic equation into a semilinear one then by jeanjean s result 6 we get a bounded ps sequence for the corresponding functional and show the existence of positive nontrivial solution

uniqueness of the ground state solutions of quasilinear schrodinger equations abstract we are concerned with the uniqueness result of positive solutions for a class of quasilinear elliptic equation arising from plasma physics we convert a quasilinear elliptic equation into a semilinear one and show the unique existence of positive radial solution for original equation under the suitable conditions on the power of nonlinearity and quasilinearity we also investigate the non degeneracy of a positive radial solution for a converted semilinear elliptic equation

relaxed stabilization conditions for continuous time takagi sugeno fuzzy control systems this paper deals with the stabilization of continuous time takagi sugeno t s fuzzy control systems based on fuzzy lyapunov functions and nonparallel distributed compensation non pdc control laws new stabilization conditions are represented in the form of linear matrix inequalities lmis the theoretical proof shows that the proposed conditions can provide less conservatism than the existing results in the literature moreover in order to demonstrate the effectiveness of the non pdc control laws the problem of h controller design for t s fuzzy systems is also studied simulation examples are given to illustrate the merits of the proposed methods

technical communique new dilated lmi characterizations for continuous time multiobjective controller synthesis this paper provides new dilated linear matrix inequality lmi characterizations for continuous time controller synthesis the dilated lmis enable us to parametrize controllers without involving the lyapunov variables in the parametrizations taking advantage of this feature we can readily design multiobjective controllers with non common lyapunov variables whereas we are forced to employ a common one in the well known lyapunov shaping paradigm in particular it is shown that the proposed dilated lmi based approach to h 2 d stability synthesis encompasses the corresponding lyapunov shaping paradigm as a special case in this sense the results of this paper can be viewed as partial counterparts of those obtained in the discrete time setting

nonquadratic stabilization of continuous t s fuzzy models lmi solution for a local approach this paper is concerned with nonquadratic stabilization design problem for continuous time nonlinear models in the takagi sugeno t s form obtained by sector nonlinearity approach most of the previous results found in the literature intended to establish global nonquadratic stabilization conditions which are hard to uphold due to the difficulty of handling time derivatives of the membership function by changing the paradigm of global stabilization for something less restrictive a local solution to overcome infeasible quadratic stabilization conditions is offered in this paper it is shown that the derived local nonquadratic conditions actually lead to reasonable advantages over the existing quadratic approach as well as some previous nonquadratic attempts moreover conditions for the solvability of state feedback controller design given here are written in the form of linear matrix inequalities lmis which can be efficiently solved by convex optimization techniques simulation examples are given to demonstrate the validity and applicability of the proposed approaches

h2 and h fuzzy filters with memory for takagi sugeno discrete time systems abstract this paper is concerned with the problem of h 2 and h fuzzy filter design for takagi sugeno t s discrete time systems the novelty of the proposed method in the context of t s fuzzy systems is the inclusion of an arbitrary number of past information states and measurements in the structure of the filter producing a t s fuzzy filter with memory linear matrix inequality relaxations based on multi polynomial fuzzy lyapunov functions are proposed for the filter design providing filters that attain lower bounds for the h 2 and h performance criteria when compared to other approaches available in the fuzzy literature that employ memoryless filters the advantages of the proposed approach are illustrated by numerical examples

piecewise quadratic stability of fuzzy systems presents an approach to stability analysis of fuzzy systems the analysis is based on lyapunov functions that are continuous and piecewise quadratic the approach exploits the gain scheduling nature of fuzzy systems and results in stability conditions that can be verified via convex optimization over linear matrix inequalities examples demonstrate the many improvements over analysis based on a single quadratic lyapunov function special attention is given to the computational aspects of the approach and several methods to improve the computational efficiency are described

soliton solutions for quasilinear schrodinger equations with critical growth in this paper we establish the existence of standing wave solutions for quasilinear schrodinger equations involving critical growth by using a change of variables the quasilinear equations are reduced to semilinear one whose associated functionals are well defined in the usual sobolev space and satisfy the geometric conditions of the mountain pass theorem using this fact we obtain a cerami sequence converging weakly to a solution v in the proof that v is nontrivial the main tool is the concentration compactness principle due to p l lions together with some classical arguments used by h brezis and l nirenberg 1983 in 9

a generalised integral polynomial lyapunov function for nonlinear systems abstract this work generalises the line integral lyapunov function in rhee won 2006 for stability analysis of continuous time nonlinear models expressed as fuzzy systems the referred result applied only to takagi sugeno representations and required memberships to be a tensor product of functions of a single state these are generalised here so that membership arguments can be arbitrary polynomials of the state variables in this way systems for which earlier results cannot be applied are now covered both the modelling and the integral terms appearing in the lyapunov functions are generalised to a fuzzy polynomial case illustrative examples show the advantage of the proposed method against previous literature even in the ts case

solutions for a class of quasilinear choquard equations with hardy littlewood sobolev critical nonlinearity abstract in this article we consider the quasilinear choquard equation with critical nonlinearity in r n e 2 u v x u e 2 u u 2 r n u 2 2 x y d y u 2 2 2 u h x u u where 0 n n 3 2 2 n n 2 is the critical exponent in the sense of hardy littlewood sobolev inequality e is a real parameter by using a change of variables the quasilinear equations are reduced to a semilinear one whose associated functionals are well defined in the usual sobolev space and satisfy the geometric conditions of the mountain pass theorem under suitable assumptions on v and h we investigate the existence and multiplicity of solutions for the above problem by using the mountain pass theorem and index theory in order to overcome the lack of compactness we apply the concentration compactness principle