a critical p biharmonic system with negative exponents abstract in this paper we are devoted to the study of critical p biharmonic system with a parameter which involves strongly coupled critical nonlinearities and negative exponents we prove that there exists a positive constant such that the above problem admits at least two solutions if 0

radial symmetry of positive solutions in nonlinear polyharmonic dirichlet problems we extend the symmetry result of gidas ni nirenberg to semilinear polyharmonic dirichlet problems in the unit ball in the proof we develop a new variant of the method of moving planes relying on fine estimates for the green function of the polyharmonic operator we also consider minimizers for subcritical higher order sobolev embeddings for embeddings into weighted spaces with a radially symmetric weight function we show that the minimizers are at least axially symmetric this result is sharp since we exhibit examples of minimizers which do not have full radial symmetry

design of fuzzy control systems with guaranteed stability abstract this paper addresses the analysis and design of fuzzy control systems the fuzzy systems are represented by a family of local state space models with aggregation the controller is designed by considering each local state feedback controller and a compensating controller the compensating controller is based on the well known variable structure control theory it is shown that this controller guarantees global stability of the closed loop fuzzy system the issues of a state observer for the fuzzy system is also addressed a numerical example and an example of nonlinear system control are given for demonstration of the performance of the method

a procedure for simultaneously stabilizing a collection of single input linear systems using non linear state feedback control abstract this paper considers the problem of simultaneously stabilizing a finite collection of single input linear systems this stabilization is achieved using a single non linear state feedback controller the stability of the resulting closed loop system is established using a collection of quadratic lyapunov functions the main result of this paper is a sufficient condition for simultaneous stabilizability furthermore when this sufficient condition is satisfied the paper gives a formula for constructing the stabilizing feedback control law the paper includes an example in which the stabilization procedure is applied to the stabilization of an f4e fighter aircraft

fuzzy stability criterion of a class of nonlinear systems abstract a fuzzy stability criterion of a class of nonlinear systems is discussed in accordance with the definition of stability in the sense of lyapunov first a sufficient condition that guarantees stability of a fuzzy system is given in terms of lyapunov s direct method two concepts for stability of fuzzy systems are defined locally stable and globally table second a construction procedure for lyapunov functions is presented finally the construction procedure is applied to the fuzzy stability criterion of a class of nonlinear systems that can be approximated by fuzzy systems

global bifurcation and nodal solutions for fourth order problems with sign changing weight in this paper we shall establish unilateral global bifurcation result for a class of fourth order eigenvalue problems with sign changing weight under some natural hypotheses on perturbation function we show that m k n 0 is a bifurcation point of the above problems and there are two distinct unbounded continua c k n and c k n consisting of the bifurcation branch c k n from m k n 0 where m k n is the kth positive or negative eigenvalue of the linear problem corresponding to the above problems email protected as the applications of the above result we study the existence of nodal solutions for a class of fourth order eigenvalue problems with sign changing weight moreover we also establish the sturm type comparison theorem for fourth order problems with sign changing weight

existence and multiplicity of nontrivial solutions for a class of modified nonlinear fourth order elliptic equations on r n in this paper we study the following fourth order elliptic equation of the form 2 u u v x u 2 u 2 u h x u x r n where 2 is the biharmonic operator 0 n 6 v c r n r and h c r n r r under appropriate assumptions on v x and h x u some existence and multiplicity results for nontrivial solutions are obtained via variational methods

on the partial differential equations of electrostatic mems devices iii refined touchdown behavior abstract this paper is a continuation of n ghoussoub y guo on the partial differential equations of electrostatic mems devices stationary case siam j math anal 38 2007 1423 1449 and n ghoussoub y guo on the partial differential equations of electrostatic mems devices ii dynamic case nodea nonlinear differential equations appl 2008 in press where we analyzed nonlinear parabolic problem u t u f x 1 u 2 on a bounded domain of r n with dirichlet boundary conditions this equation models a simple electrostatic micro electromechanical system mems device consisting of a thin dielectric elastic membrane with boundary supported at 0 above a rigid ground plate located at 1 here u is modeled to describe dynamic deflection of the elastic membrane when a voltage represented here by is applied the membrane deflects towards the ground plate and a snap through touchdown must occur when it exceeds a certain critical value pull in voltage creating a so called pull in instability which greatly affects the design of many devices in an effort to achieve better mems design the material properties of the membrane can be technologically fabricated with a spatially varying dielectric permittivity profile f x in this work some a priori estimates of touchdown behavior are established based on which the refined touchdown profiles are obtained by adapting self similar method and center manifold analysis applying various analytical and numerical techniques some properties of touchdown set such as compactness location and shape are also discussed for different classes of varying permittivity profiles

on the stability of fuzzy systems studies the global asymptotic stability of a class of fuzzy systems it demonstrates the equivalence of stability properties of fuzzy systems and linear time invariant lti switching systems a necessary and sufficient condition for the stability of such systems are given and it is shown that under the sufficient condition a common lyapunov function exists for the lti subsystems a particular case when the system matrices can be simultaneously transformed to normal matrices is shown to correspond to the existence of a common quadratic lyapunov function a constructive procedure to check the possibility of simultaneous transformation to normal matrices is provided

high energy solutions and nontrivial solutions for fourth order elliptic equations abstract in this paper we study the existence of nontrivial solutions and infinitely many high energy solutions for a class of nonlinear fourth order elliptic equations in r n via variational methods three main theorems are obtained

on the critical dimension of a fourth order elliptic problem with negative exponent we study the regularity of the extremal solution of the semilinear biharmonic equation 2u u 1 u 2 on a ball b rn under navier boundary conditions u u 0 on b where 0 is a parameter while 0 0 are fixed constants it is known that there exists such that for there is no solution while for 0 and it is singular supbu 1 for n 9 0 and 0 with small our proof for the singularity of extremal solutions in dimensions n 9 is based on certain improved hardy rellich inequalities

universality in orbit spaces of compact linear groups if p1 x p q x is a minimal integrity basis of the ideal of polynomial invariants of a compact coregular linear groupg the orbit map open image in new window yields a diffeomorphic image open image in new window of the orbit spacer n g starting from this fact we point out some properties which are common to the orbit space of all the compact coregular linear groups of transformations ofr n in particular we show that a contravariant metric matrix hat p p can be defined in the interior of open image in new window as a polynomial function of p1 p q we prove that the matrix hat p p which characterizes the set open image in new window as it is positive semi definite only forp open image in new window can be determined as a solution of a canonical differential equation which for every compact coregular linear group depends only on the numberq and on the degrees of the elements of the minimal integrity bases this allows to determine all the isomorphism classes of the orbit spaces of the compact coregular linear groups through a determination of the equivalence classes of the corresponding matrices hat p p forq 3 orbit spaces with dimensions 3 the solutions hat p p of the canonical equation are explicitly determined and the number of their equivalence classes is shown to be finite it is also shown that with a convenient choice of the minimal integrity basis the polynomial matrix elements of hat p p have only integer coefficients arguments are given in favour of the conjecture that our conclusions hold true for all values ofq our results are relevant and lead to universality properties in the physics of spontaneous symmetry breaking

improved l2 gain performance controller synthesis for takagi sugeno fuzzy system in this paper an improved l2 gain performance controller synthesis is proposed for takagi sugeno t s fuzzy system the t s fuzzy controller can be easily derived by a three step procedure with the linear matrix inequalities lmis technique first a new t s fuzzy model structure is presented which includes the original t s fuzzy plant with stable pre and post filters on the input and output of the original plant second by using this structure the l2 gain performance controller design problem can be easily transformed into standard lmis formulation compared with the previous results it not only gives us a simple structure of the t s fuzzy controller but also provides us effective lmis based conditions which include a small number of unknown matrix variables consequently less value of l2 gain performance of the closed loop system can be obtained third an augmented t s fuzzy controller which guarantees l2 gain performance is obtained for the original t s fuzzy plant which is composed of the t s controller derived from step two and two stable pre and post filters finally some numerical examples are demonstrated to show the effectiveness of the proposals

multiplicity of solutions for a fourth order problem with exponential nonlinearity abstract let b be the unit ball in r n n 5 and n be the exterior unit normal vector on the boundary we consider radial solutions to 2 u e u in b u 0 and u n 0 on b where 0 we show that there exists a unique s 0 such that if s there is a radial singular solution if 5 n 12 then for s there exist infinitely many regular radial solutions and as s the number of such solutions goes to infinity if n 13 we prove uniqueness of smooth radial solutions we derive similar results for the same equation with navier boundary conditions

polyharmonic k hessian equations in rn abstract this work is focused on the study of the nonlinear elliptic higher order equation m u s k u f x r n where the k hessian s k u is the kth elementary symmetric polynomial of eigenvalues of the hessian matrix of the solution and the datum f belongs to a suitable functional space this problem is posed in r n and we prove the existence of at least one solution by means of topological fixed point methods for suitable values of m n questions related to the regularity of the solutions and extensions of these results to the nonlocal setting are also addressed on the way to construct these proofs some technical results such as a fixed point theorem and a refinement of the critical sobolev embedding which could be of independent interest are introduced

robust design of rule based fuzzy controllers this paper deals with the design of stable and robust rule based fuzzy control systems new expressions to compute indices which provide a measure of the stability and robustness of fuzzy control systems are presented the relation between the modification of the rules and the stability is studied through the so called sensitivity indices the paper presents procedures that make use of these indices to improve the design of fuzzy control systems including the modification of the rules to obtain the global stability of an unstable system with multiple attractors and to improve the dynamic behavior or the robustness of a non linear plant an example with a fuzzy controller for a system with non linear damping and saturation in the actuation is presented to illustrate the design procedure

brief paper quadratic boundedness via dynamic output feedback for constrained nonlinear systems in takagi sugeno s form this paper studies output feedback stabilization of takagi sugeno fuzzy systems with input or state constraint and bounded noise a dynamic output feedback controller is adopted rather than a controller based on the state observer the notion of quadratic boundedness specified by a common lyapunov matrix which is novel in fuzzy control is invoked to handle the noise under the proposed controller the state of the closed loop system is stabilizing to an ellipsoid specified by this common lyapunov matrix two numerical examples are given to show the effectiveness of the controller

robust h control of multiple time delay uncertain nonlinear system using fuzzy model and adaptive neural network in this paper a robust control method which combines fuzzy model based control with adaptive neural network control is presented for a class of uncertain nonlinear system with multiple time delay the fuzzy t s model with multiple time delay is adopted for the approximate modeling of the nonlinear system with some unknown uncertainties and fuzzy model based h control law is designed by means of lmi method a full adaptive rbf neural network is added to the fuzzy h control in order to guarantee the robust stability of the controlled system the effect of the unknown uncertainties and the error caused by fuzzy modeling can be overcome by adaptive tuning of the weights centers and widths of the rbf neural network on line and no constraint or matching conditions are required the stability of the designed closed loop system is thus proved the proposed method is applied to a multiple time delay nonlinear chaotic system and the simulation results show that the proposed method cannot only stabilize the chaos systems but has strong robustness against uncertainties and external disturbance

the regularity and stability of solutions to semilinear fourth order elliptic problems with negative exponents we examine the regularity of the extremal solution of the nonlinear eigenvalue problem on a general bounded domain in n with navier boundary condition u u on firstly we prove the extremal solution is smooth for any p 1 and n 4 which improves the result of guo and wei discrete contin dynam syst a 34 2014 2561 2580 secondly if p 3 n 3 we prove that any radial weak solution of this nonlinear eigenvalue problem is smooth in the case which completes the result of davila et al math annalen 348 2009 143 193 finally we also consider the stability of the entire solution of 2 u l u p in n with u 0

trajectory stabilization of a model car via fuzzy control abstract this paper deals with trajectory stabilization of a computer simulated model car via fuzzy control stability conditions of fuzzy systems are given in accordance with the definition of stability in the sense of lyapunov first we approximate a computer simulated model car whose dynamics is nonlinear by t s takagi and sugeno fuzzy model fuzzy control rules which guarantee stability of the control system under a condition are derived from the approximated fuzzy model the simulation results show that the fuzzy control rules effectively realize trajectory stabilization of the model car along a given reference trajectory from all initial positions under a condition and the dynamics of the approximated fuzzy model agrees well with that of the model car

a note on nonlinear biharmonic equations with negative exponents abstract in this paper we study radially symmetric entire solutions of 2 u u q u 0 in r 3 we find the asymptotic behavior of these solutions for any q 1 and prove that for any q 3 there exists a solution with exactly linear growth

on a p biharmonic problem with no flux boundary condition the study of fourth order partial differential equations has flourished in the last years however a p biharmonic problem with no flux boundary condition has never been considered before not even for constant p this is an important step further since surfaces that are impermeable to some contaminants are appearing quite often in nature hence the significance of such boundary condition by relying on several variational arguments we obtain the existence and the multiplicity of weak solutions to our problem we point out that although we use a mountain pass type theorem in order to establish the multiplicity result we do not impose an ambrosettirabinowitz type condition nor a symmetry condition on our nonlinearity f

nonlinear decentralized state feedback controller for uncertain fuzzy time delay interconnected systems abstract in this paper the perturbed continuous time interconnected system with time delay is represented by an equivalent takagi sugeno type fuzzy model having r i rules for each subsystem based on lyapunov stability theorem and razumikhin theorem the nonlinear decentralized state feedback fuzzy controllers are proposed to stabilize the whole perturbed fuzzy time delay interconnected system asymptotically under using this nonlinear controller the design methods only consider the r i fuzzy rules rather than r i r i rules for each subsystem that is we can remove the negative effect of the coupled terms therefore these approaches can be less conservative moreover if all the time delays of each subsystem are the same for all rules we shall propose less conservative criteria these criteria do not need the solution of a lyapunov equation or a riccati equation we also do not need to find a common positive matrix p to satisfy any inequality the so called matching condition for the interconnection matrices and perturbations are not needed finally a numerical example is given to illustrate the control design and its effectiveness

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

multiplicity of solutions for a fourth order equation with power type nonlinearity let b be the unit ball in mathbb r n n 3 and n be the exterior unit normal vector on the boundary we consider radial solutions to delta 2 u lambda 1 rm sign p u p quad rm in b quad u 0 quad frac partial u partial n 0 quad rm on partial b where 0 for positive p we assume 5 n 12 and p frac n 4 n 4 or n 13 and frac n 4 n 4 0 such that if s there exists a radial weakly singular solution for s there exist infinitely many regular radial solutions and the number of radial regular solutions goes to infinity as s

a new proof of i guerra s results concerning nonlinear biharmonic equations with negative exponents abstract here we give a self contained new proof of the asymptotic behavior of the radially symmetric entire solution of 2 u u p in r 3 these results were obtained by i guerra in 4 our proof is much more direct and simpler

compactness along the branch of semistable and unstable solutions for an elliptic problem with a singular nonlinearity we study the branch of semistable and unstable solutions i e those whose morse index is at most 1 of the dirichlet boundary value problem u f x 1 u 2 on a bounded domain n which models among other things a simple electrostatic microelectromechanical system mems device we extend the results of 11 relating to the minimal branch by obtaining compactness along unstable branches for 1 n 7 on any domain and for a large class of permittivity profiles f we also show the remarkable fact that powerlike profiles f x x can push back the critical dimension n 7 of this problem by establishing compactness for the semistable branch on the unit ball also for n 8 and as long as as a byproduct we are able to follow the second branch of the bifurcation diagram and prove the existence of a second solution for in a natural range in all these results the conditions on the space dimension and on the power of the profile are essentially sharp 2007 wiley periodicals inc

inequalities defining orbit spaces the orbit space of a representation of a compact lie group has a natural semialgebraic structure we describe explicit ways of finding the inequalities defining this structure and we give some applications

some singular equations modeling mems in the past fifteen years mathematical models for microelectromechanical systems mems have been the subject of several studies in particular due to the interesting qualitative properties they feature still most research is devoted to an illustrative but simplified model which is deduced from a more complex model when the aspect ratio of the device vanishes the so called vanishing or small aspect ratio model the analysis of the aforementioned complex model involving a moving boundary has started only recently and an outlook of the results obtained so far in this direction is provided in this survey

analysis and design of fuzzy controller and fuzzy observer this paper addresses the analysis and design of a fuzzy controller and a fuzzy observer on the basis of the takagi sugeno t s fuzzy model the main contribution of the paper is the development of the separation property that is the fuzzy controller and the fuzzy observer can be independently designed a numerical simulation and an experiment on an inverted pendulum system are described to illustrate the performance of the fuzzy controller and the fuzzy observer

symmetry breaking patterns and extended morse theory an indirect topological method is considered which constrains the possible breaking patterns of a lie group symmetry for higgs landau systems the application of the method and its efficiency are discussed

an elementary proof that the biharmonic green function of an eccentric ellipse changes sign p r garabedian showed in 1951 that the green function for the biharmonic boundary value problem with vanishing dirichlet data changes sign in case the domain is a sufficiently eccentric ellipse this refuted a conjecture made by j hadamard in 1908 the proof of garabedian was based on kernel functions the present note gives an elementary proof

comments on robust stabilization of a class of uncertain nonlinear systems via fuzzy control quadratic stabilizability h sup spl infin control theory and linear matrix inequalities this paper presents stability analysis for a class of uncertain nonlinear systems and a method for designing robust fuzzy controllers to stabilize the uncertain nonlinear systems first a stability condition for takagi and sugeno s fuzzy model is given in terms of lyapunov stability theory next new stability conditions for a generalized class of uncertain systems are derived from robust control techniques such as quadratic stabilization h sup spl infin control theory and linear matrix inequalities the derived stability conditions are used to analyze the stability of takagi and sugeno s fuzzy control systems with uncertainty which can be regarded as a generalized class of uncertain nonlinear systems the design method employs the so called parallel distributed compensation important issues for the stability analysis and design are remarked finally three design examples of fuzzy controllers for stabilizing nonlinear systems and uncertain nonlinear systems are presented

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

orbit spaces of compact coregular simple lie groups with 2 3 and 4 basic polynomial invariants effective tools in the analysis of invariant potentials the coregular real representations of the compact simple lie groups are classified and the equalities and inequalities defining their orbit spaces are determined in the case of 2 3 and 4 basic polynomial invariants the results are obtained making use of the classification of the complex coregular simple lie groups given by g w schwarz and of the determination of all the allowable metric matrices for q dimensional q 4 orbit spaces of compact coregular linear groups recently obtained by the present authors the results are used to determine in a rigorous way the minima of two so 10 and e6 invariant higgs potentials

existence of radial solutions to biharmonic k hessian equations abstract this work presents the construction of the existence theory of radial solutions to the elliptic equation 2 u 1 k s k u f x x b 1 0 r n provided either with dirichlet boundary conditions u n u 0 x b 1 0 or navier boundary conditions u u 0 x b 1 0 where the k hessian s k u is the k th elementary symmetric polynomial of eigenvalues of the hessian matrix and the datum f l 1 b 1 0 while r we prove the existence of a caratheodory solution to these boundary value problems that is unique in a certain neighborhood of the origin provided is small enough moreover we prove that the solvability set of is finite giving an explicity bound of the extreme value

quadratic stability analysis of the takagi sugeno fuzzy model the nonlinear dynamic takagi sugeno fuzzy model with offset terms is analyzed as a perturbed linear system a sufficient criterion for the robust stability of this nominal system against nonlinear perturbations guarantees quadratic stability of the fuzzy model the criterion accepts a convex programming formulation of reduced computational cost compared to the common lyapunov matrix approach parametric robust control techniques suggest synthesis tools for stabilization of the fuzzy system application examples on fuzzy models of nonlinear plants advocate the efficiency of the method the examples demonstrate reduced conservatism compared to norm based criteria

structure identification of fuzzy model abstract the problems of structure identification of a fuzzy model are formulated a criterion for the verification of a structure is discussed using the criterion an algorithm for identifying a structure is suggested further a successive identification algorithm of the parameters is suggested the proposed methods are applied to an example

bessel pairs and optimal hardy and hardy rellich inequalities we give necessary and sufficient conditions on a pair of positive radial functions v and w on a ball b of radius r in rn n 1 so that the following inequalities hold for all u in c 0 infty b label one int limits b v x nabla u 2 dx geq int limits b w x u 2dx label two int limits b v x delta u 2 dx geq int limits b w x nabla u 2 dx n 1 int limits b left frac v x x 2 frac v r x x right nabla u 2dx this characterization makes a very useful connection between hardy type inequalities and the oscillatory behaviour of certain ordinary differential equations and helps in the identification of a large number of such couples v w that we call bessel pairs as well as the best constants in the corresponding inequalities this allows us to improve extend and unify many results old and new about hardy and hardy rellich type inequalities such as those obtained by caffarelli et al compos math 53 259 275 1984 brezis and vazquez revista mat univ complutense madrid 10 443 469 1997 wang and willem j funct anal 203 550 568 2003 adimurthi et al proc am math soc 130 489 505 2002 and many others

stability analysis and design of fuzzy control systems abstract the stability analysis and the design technique of fuzzy control systems using fuzzy block diagrams are discussed first we show the concept of fuzzy blocks and consider the connection problems of fuzzy blocks diagrams we derive some theorems and corollaries with respect to two basic types of connections of fuzzy blocks in order to preserve some properties in a connection of fuzzy blocks continuous piecewise polynomial membership functions are defined secondly a sufficient condition which guarantees the stability of fuzzy systems is obtained in terms of lyapunov s direct method we give an important fact based on this condition thirdly we propose a new design technique of a fuzzy controller the fuzzy block diagrams and the stability analysis are applied to the design problems of a model based fuzzy controller

stability analysis and stabilization of fuzzy state space models abstract a new stability test method for linguistic fuzzy state space models is proposed in this paper this method allows the determination of stability of fuzzy models by applying the lyapunov function to each rule a gradient based algorithm is suggested to simplify the stability tests using this algorithm the lyapunov equation can be updated towards the direction where the stability can be determined more correctly an additional gradient based stabilizing algorithm is also derived which allows a systematic approach to find stabilizing controls by updating the lyapunov equations towards the direction where unstable eigenvalues are decreased examples demonstrate the convenience of the stability test and the two suggested gradient based algorithms

classification of radial solutions for semilinear elliptic systems with nonlinear gradient terms abstract we are concerned with the classification of positive radial solutions for the system u v p v f u where p 0 and f c 1 0 is a nondecreasing function such that f t 0 for all t 0 we show that in the case where the system is posed in the whole space r n such solutions exist if and only if 1 0 s f t d t p 2 p 1 d s this is the counterpart of the keller osserman condition for the case of single semilinear equation similar optimal conditions are derived in case where the system is posed in a ball of r n if f t t q q 1 using dynamical system techniques we are able to describe the behaviour of solutions at infinity in case where the system is posed in the whole r n or around the boundary in case of a ball

on solutions of second and fourth order elliptic equations with power type nonlinearities abstract we study second and fourth order semilinear elliptic equations with a power type nonlinearity depending on a power p and a parameter 0 for both equations we consider dirichlet boundary conditions in the unit ball b r n regularity of solutions strictly depends on the power p and the parameter we are particularly interested in the radial solutions of these two problems and many of our proofs are based on an ordinary differential equation approach

radial singular solutions for a fourth order equation with negative exponents abstract in this paper we consider the radial singular solution of 2 u 1 u p in r n with u 0 p 0 by using some elementary ordinary differential equation arguments we prove the above equation admits no radial singular solution for n 3 p 3 in addition the exact asymptotic behaviors of the radial singular solution as r 0 is established for p 1 n 4 which have a significant difference with the explicit singular solution as a product the singularity of any radial singular solution is of type ii if p 1 n 4

fuzzy observer based fuzzy control design for nonlinear systems with persistent bounded disturbances to date nonlinear l gain control problems have not been solved by the conventional control methods for the nonlinear dynamic systems with persistent bounded disturbances this study introduces a fuzzy control design to deal with the nonlinear l gain output feedback control problem first the takagi and sugeno t s fuzzy model is employed to approximate the nonlinear dynamic system next based on the fuzzy model a fuzzy observer based fuzzy controller is developed to minimize the upper bound of l gain of the closed loop system under some linear matrix inequality lmi constraints therefore the nonlinear l gain control problem is transformed into a suboptimal control problem i e to minimize the upper bound of the l gain of the closed loop system subject to some lmi constraints in this situation the nonlinear l gain output feedback control problem can be easily solved by a lmi based optimization method the proposed methods which efficiently attenuate the peak of perturbation due to persistent bounded disturbances extend the l gain control problems from linear dynamic systems to nonlinear dynamic systems

a fourth order model for mems with clamped boundary conditions the dynamical and stationary behaviors of a fourth order equation in the unit ball with clamped boundary conditions and a singular reaction term are investigated the equation arises in the modeling of microelectromechanical systems mems and includes a positive voltage parameter lambda it is shown that there is a threshold value lambda 0 of the voltage parameter such that no radially symmetric stationary solution exists for lambda lambda while at least two such solutions exist for lambda in 0 lambda local and global well posedness results are obtained for the corresponding hyperbolic and parabolic evolution problems as well as the occurrence of finite time singularities when lambda lambda

existence and multiplicity of solutions for a class of fourth order elliptic equations in r n abstract in this paper we study the existence and multiplicity of nontrivial solutions for the following fourth order elliptic equations 2 u u v x u f x u in r n u h 2 r n via variational methods two main theorems are obtained

relaxed stability and stabilization conditions for a t s fuzzy discrete system it is known that the stability condition of a t s fuzzy discrete system depends on the existence of the common matrix p which satisfies all lyapunov inequalities in general the common matrix p can be found by means of linear matrix inequalities lmi method however if the number of rules of a fuzzy system is large the common matrix p may not exist or may not be found even using lmi therefore in this paper the state space is divided into several subregions and the local common matrix p j for each subregion j is found then the number of lyapunov inequalities to be satisfied by the corresponding local common matrix p j becomes much fewer such that the stability condition of the fuzzy system is more relaxed the similar derivation is also extended to solve the stabilization problem of the t s fuzzy discrete system with parallel distributed compensation

control laws for takagi sugeno fuzzy models abstract this work presents control laws for fuzzy models of takagi sugeno ts sugeno and kang fuzzy sets and systems 28 1988 15 33 takagi and sugeno ieee trans systems man cybernet 15 1 1985 116 132 these laws are not directly put in the classical form called pdc for parallel distributed compensation wang et al ieee trans fuzzy systems 4 1 1996 14 23 on a particular family of ts fuzzy models the approach allows to reduce the conservatism of results found in the literature tanaka et al ieee trans fuzzy systems 6 2 1998 1 16 this approach utilizes the state space representation according to that remark observers are also considered and a separation principle is also given though results are provided mainly for the continuous case they are also provided for the discrete case an example in both cases illustrates the results obtained

flat bases of invariant polynomials and p matrices of e7 and e8 let g be a compact group of linear transformations of a euclidean space v the g invariant c functions can be expressed as c functions of a finite basic set of g invariant homogeneous polynomials sometimes called an integrity basis the mathematical description of the orbit space v g depends on the integrity basis too it is realized through polynomial equations and inequalities expressing rank and positive semidefiniteness conditions of the p matrix a real symmetric matrix determined by the integrity basis the choice of the basic set of g invariant homogeneous polynomials forming an integrity basis is not unique so it is not unique the mathematical description of the orbit space too if g is an irreducible finite reflection group saito et al commun algebra 8 373 1980 characterized some special basic sets of g invariant homogeneous polynomials that they called flat they also found explicitly the flat basic sets of invariant homogeneous polynomials of all the irreducible finite reflection g

robustness design of time delay fuzzy systems using fuzzy lyapunov method abstract in this study we address a fuzzy lyapunov method for the stability analysis of time delay fuzzy systems subject to external disturbances a takagi sugeno t s fuzzy model and parallel distributed compensation pdc scheme are first employed to design a nonlinear fuzzy controller for the stabilization of time delay fuzzy systems according to the controlled system the h criterion is derived based on the fuzzy lyapunov method which is defined in terms of fuzzy blending quadratic lyapunov functions based on the stability criterion the time delay fuzzy systems are guaranteed to be stable the control problem can then be reformulated as a linear matrix inequality lmi problem a simulation is provided to explore the feasibility of the proposed fuzzy controller design method

fuzzy dynamical system approach for a dual parameter hybrid order robust control design abstract robust control for uncertain dynamical systems is considered the uncertainty is assumed to be bounded and the fuzzy set theory is adopted to describe the bound a new dual parameter hybrid order robust control design is then proposed in two steps first a class of robust controls is designed taking the advantage of the flexibility in choosing the order and a design parameter the controls are deterministic and are not if then fuzzy rules based deterministic performance including uniform boundedness and uniform ultimate boundedness for the controlled systems is guaranteed second a fuzzy set theoretic based performance index consisting of average and steady state system performance and control cost is proposed a constrained optimization problem is formulated with the intension of minimizing the performance index the objective of the optimization problem is to search for the optimal choice of dual parameters that minimizes the performance index we show that the solution to the optimization problem always exists as a result the resulting control design achieves two concurrent goals guaranteeing deterministic performance as well as minimizing the performance index the theory is illustrated by an unmanned aerial vehicle uav system control design

a theorem on orbit structures strata of compact linear lie groups we present a comprehensive constructive proof of a theorem characterizing the tangent space to a stratum orbit structure of the euclidean space rn seat of an orthogonal representation of a compact group g the characterization is made in terms of gradients of a complete set integrity basis of g invariant polynomials in a recent paper m abud and g sartori phys lett b 104 147 1981 the theorem which may be considered a generalization of a theorem by michel c r acad sci ser a 272 433 1971 has been shown to be effective in the determination of the equations of the strata and in the determination of natural extrema of g invariant functions

uniqueness theorem for integral equations and its application abstract this paper is devoted to answering a question asked recently by y li regarding geometrically interesting integral equations the main result is to give a necessary and sufficient condition on the parameters so that the integral equation with parameters to be discussed in this paper have regular solutions in the case such condition is satisfied we will write down the exact solution as its application of our method we should show that the non existence theory of the solutions of prescribed scalar curvature equation on s n can be generalized to that of prescribed branson paneitz q curvature equations on s n

a new computational approach to stability analysis and synthesis of linguistic fuzzy control system in this paper stability analysis and synthesis of the type ii singleton type linguistic fuzzy control system are addressed first stability theorems are given for both continuous time case and discrete time case and they are recast in the formulation of bilinear matrix inequalities bmis continuous and discrete iterative linear matrix inequality methods are presented to obtain the feasible solution for the stability conditions represented as the bmi the interesting feature of this paper is that the suggested method can be applied not only to the stability analysis but also to the controller synthesis when it is applied to the synthesis of the type ii fuzzy logic controller the resulting one can theoretically guarantee the stability of the closed loop system finally the effectiveness of the suggested method is illustrated via computer simulation

orbit spaces of reflection groups with 2 3 and 4 basic polynomial invariants functions which are covariant or invariant under the transformations of a compact linear group can be expressed advantageously in terms of functions defined in the orbit space of the group i e as functions of a finite set of basic invariant polynomials the equalities and inequalities defining the orbit spaces of all finite coregular real linear groups most of which are crystallographic groups with at most four independent basic invariants are determined for each group g acting in the euclidean space the results are obtained through the computation of a metric matrix which is defined only in terms of the scalar products between the gradients of a set of basic polynomial invariants of g the semi positivity conditions are known to determine all the equalities and inequalities defining the orbit space of g as a semi algebraic variety in the space spanned by the variables in a recent paper the matrices for have been determined in an alternative way as solutions of a universal differential equation the present paper yields a partial but significant check on the correctness and completeness of these solutions our results can be easily exploited in many physical contexts where the study of covariant or invariant functions is important for instance in the determination of patterns of spontaneous symmetry breaking in the analysis of phase spaces and structural phase transitions landau s theory in covariant bifurcation theory in crystal field theory and in most areas of solid state theory where use is made of symmetry adapted functions

the critical dimension for a fourth order elliptic problem with singular nonlinearity we study the regularity of the extremal solution of the semilinear biharmonic equation delta 2 u frac lambda 1 u 2 which models a simple micro electromechanical system mems device on a ball b subset mathbb r n under dirichlet boundary conditions u partial nu u 0 on partial b we complete here the results of lin and yang 14 regarding the identification of a pull in voltage 0 such that a stable classical solution u with 0 our main result asserts that the extremal solution u lambda is regular rm sup b u lambda 1 provided n leqq 8 while u lambda is singular rm sup b u lambda 1 for n geqq 9 in which case 1 c 0 x 4 3 leqq u lambda x leqq 1 x 4 3 on the unit ball where c 0 left frac lambda overline lambda right frac 1 3 and bar lambda frac 8 9 left n frac 2 3 right left n frac 8 3 right

infinitely many solutions for fourth order elliptic equations with general potentials abstract this paper is concerned with the following fourth order elliptic equations 2 u u v x u f x u in r n u h 2 r n where u r n r under general assumption on potential v x and f x u is indefinite sign and sublinear as u we establish the existence of infinitely many solutions by using the genus properties in critical point theory recent results from the literature are extended

multiple quenching solutions of a fourth order parabolic pde with a singular nonlinearity modeling a mems capacitor finite time singularity formation in a fourth order nonlinear parabolic partial differential equation pde is analyzed the pde is a variant of a ubiquitous model found in the field of microelectromechanical systems mems and is studied on a one dimensional 1d strip and the unit disc the solution itself remains continuous at the point of singularity while its higher derivatives diverge a phenomenon known as quenching for certain parameter regimes it is shown numerically that the singularity will form at multiple isolated points in the 1d strip case and along a ring of points in the radially symmetric two dimensional case the location of these touchdown points is accurately predicted by means of asymptotic expansions the solution itself is shown to converge to a stable self similar profile at the singularity point analytical calculations are verified by use of adaptive numerical methods which take advantage of symmetries exhibited by the underlying pde to accurately resolve solutions very close t

on polyharmonic regularizations of k hessian equations variational methods abstract this work is devoted to the study of the boundary value problem 1 u 1 k s k u f x r n u n u n 2 u n 1 u 0 x where the k hessian s k u is the k th elementary symmetric polynomial of eigenvalues of the hessian matrix and the datum f obeys suitable summability properties we prove the existence of at least two solutions of which at least one is isolated strictly by means of variational methods we look for the optimal values of n that allow the construction of such an existence and multiplicity theory and also investigate how a weaker definition of the nonlinearity permits improving these results