analysis of the fuzzy controllability property and stabilization for a class of t s fuzzy models in this paper the controllability property for a class of takagi sugeno t s fuzzy models is analyzed while a fully nonlinear stabilizer is designed in a practical way it is shown that global fuzzy stabilizers can be constructed in a nonconservative way by means of a relatively simple approach the existence of such controllers depends on the fuzzy controllability conditions which are derived in a straightforward way the main advantage of the proposed approach is that the convergence of the closed loop system can be imposed arbitrarily some examples are given in order to illustrate the validity of the method finally the proposed controller is applied on an underactuated system known as pendubot and the results are compared with an stabilizer designed on the basis of lmis

fault detection for uncertain fuzzy systems an lmi approach this paper studies the problem of designing a robust fault detection system for uncertain takagi sugeno fuzzy models the worst case fault sensitivity measure is formulated in terms of linear matrix inequalities the existence of a robust fault detection system that guarantees i the l2 gain from a fault signal to a residual signal greater than a prescribed value and ii the l2 gain from an exogenous input to a residual signal less than a prescribed value is given in terms of the solvability of linear matrix inequalities numerical examples are used to illustrate the effectiveness of the proposed design techniques

an equivariant analogue of glauberman s zj theorem we will prove an analogue of glauberman s zj theorem 4 and 6 theorem 8 2 1 p 279 that can be used to study finite groups that admit a coprime group of automorphisms this analogue is unusual in that no hypothesis of p stability is required used in conjunction with the bender method it may make it possible to prove very general results about finite groups that admit a coprime group of automorphisms the reader is referred to 7 and 8 for a fuller discussion of the bender method glauberman s zj theorem and p stability before stating the main result of this paper we introduce some notation if r and g are groups then we say that r acts coprimely on g if r acts as a group of automorphisms on g if r and g have coprime orders and if at least one of r or g is soluble suppose that r acts coprimely on g and that p is a prime define

fuzzy filter design for ito stochastic systems with application to sensor fault detection the paper deals with the robust fault detection problem for takagi sugeno t s fuzzy ito stochastic systems our aim is to develop a robust fault detection approach to the t s fuzzy systems with brownian motion by using a general observer based fault detection filter as a residual generator the robust fault detection is formulated as a filtering problem attention is focused on the design of both the fuzzy rule independent and the fuzzy rule dependent fault detection filters guaranteeing a prescribed noise attenuation level in an hinfin sense sufficient conditions are proposed to guarantee the mean square asymptotic stability with an hinfin performance for the fault detection system the corresponding solvability conditions for the desired fuzzy rule independent and fuzzy rule dependent fault detection filters are also established finally a numerical example is provided to illustrate the effectiveness of the proposed theory

solution of a non convex optimization arising in pi pid control design as shown by astrom et al automatica 34 5 1998 585 the problem of designing a stabilizing pi controller based on minimizing integral of error associated with step load disturbance while subjecting to constraints on maximum sensitivity and or complementary sensitivity amounts to that of finding the maximum allowable integral gain the latter problem is a non convex optimization problem whose true solution cannot be obtained with a guarantee by a gradient based search algorithm in this paper we present a novel and effective approach to solve such a non convex optimization problem our approach is based on regarding an equality constraint set on controller gain parameters as a two dimensional value set in the complex plane and using the notion of principal points to characterize its boundary with this treatment we are able to derive analytical expressions for describing the boundary of an equality constraint set in the controller gain plane these expressions allow one to trace the boundaries of equality constraint sets using an existing path following algorithm hence by constructing the boundary of the feasible domain in the controller gain space the maximum allowable integral gain can be obtained in addition to having the ability to obtain global optimal solution our approach can handle sensitivity and complementary sensitivity constraints simultaneously without using an iterative procedure

model construction rule reduction and robust compensation for generalized form of takagi sugeno fuzzy systems this paper presents a systematic procedure of fuzzy control system design that consists of fuzzy model construction rule reduction and robust compensation for nonlinear systems the model construction part replaces the nonlinear dynamics of a system with a generalized form of takagi sugeno fuzzy systems which is newly developed by us the generalized form has a decomposed structure for each element of a sub i and b sub i matrices in consequent parts the key feature of this structure is that it is suitable for constructing if then rules and reducing the number of if then rules the rule reduction part provides a successive procedure to reduce the number of if then rules furthermore we convert the reduction error between reduced fuzzy models and a system to model uncertainties of reduced fuzzy models the robust compensation part achieves the decay rate controller design guaranteeing robust stability for the model uncertainties finally two examples demonstrate the utility of the systematic procedure developed

successive identification of a fuzzy model and its applications to prediction of a complex system abstract a successive identification method of a fuzzy model is suggested the identification mechanism consists of two levels one is the supervisor level and the other is the adjustment level the supervisor level determines a policy of parameter adjustment using a set of fuzzy adjustment rules the adjustment rules are derived from the fuzzy implications of a fuzzy model and are extended to fuzzy adjustment rules by using an extended concept of zadeh s contrast intensification the adjustment level executes the policy of parameter adjustment determined with the fuzzy adjustment rules the parameter adjustment consists of premise parameter adjustment and consequent parameter adjustment both of them are realized by the weighted recursive least square algorithm finally it is shown from two examples that the method is very useful for modeling complex systems

fuzzy rule based combination of linear and switching state feedback controllers this paper presents a fuzzy rule base combined controller which is a fuzzy rule based combination of linear and switching state feedback controllers for nonlinear systems subject to parameter uncertainties the switching state feedback controller is employed to drive the system states toward the origin when the system state approaches the origin the linear state feedback controller will gradually replace the switching state feedback controller the smooth transition between the linear and switching state feedback controllers is governed by the fuzzy rules by using the fuzzy rule based combination technique the proposed fuzzy rule base combined controller integrates the advantages of both the linear and switching state feedback controllers but eliminates their disadvantages as a result the proposed fuzzy controller provides good performance during the transient period and the chattering effect is removed when the system state approaches the origin stability conditions will be derived to guarantee the system stability furthermore a saturation function is employed to replace the switching component to alleviate the chattering during the transient period by using the proposed fuzzy rule based combination technique the steady state error introduced by the saturation function can be eliminated application examples will be given to show the merits of the proposed approach

decomposition property of fuzzy systems and its applications this paper presents the decomposition property of fuzzy systems using a simple constructive decomposition procedure that is by properly dividing the input space into sub input spaces a general fuzzy system is decomposed into several sub fuzzy systems which are the simplest fuzzy systems in the sub input spaces based on the decomposition property of fuzzy systems the analysis of fuzzy systems can be divided into two steps first analyze the properties of the simplest fuzzy systems and then use the decomposition property to extend the results to general fuzzy systems using this idea two applications of the decomposition property are given the first is the application to the representation capability analysis of fuzzy systems the second is the application to the analysis of a class of nonlinear control systems then based on the piecewise affine fuzzy system model the existence condition and the design of a stable control for a class of single input single output siso nonlinear systems are presented

h output feedback control of fuzzy system models under sampled measurements this paper studies the problem of control for a class of fuzzy system models by using a linear output controller the system under consideration is described by a continuous time fuzzy system model under sampled output measurements the premise variables of the fuzzy system model are assumed unmeasurable we develop a technique for designing an output feedback control law which globally stabilises this class of fuzzy system models a design algorithm for constructing the linear output controller is given a numerical simulation example is given to show the potential of the proposed techniques

nonsolvable signalizer functors on finite groups recently gorenstein and lyons obtained the first nonsolvable signalizer functor theorems 9 they pinpointed certain unbalancing problems this paper grew from an attempt to manage such problems theorem a is the result theorem b and corollary c give some measure of the practical scope of theorem a suppose p is a prime a is an elementary abelian p subgroup of a finite group g and 8 is an a signalizer functor on g the unbalancing difficulties referred to above occur only if there are certain nonidentity subgroups x of g such that c a is solvable using methods of glauberman s lemma 2 11 and theorem 4 51 we are able to reduce the problem either the unbalancing problems vanish or o c a is solvable the latter case is treated in 131 the rest of the work is treated here this work pivots on theorems 5 16 and 6 5 results which closely resemble 5 lemma 2 11 and theorem 4 5 1

nonfragile h_ infty filtering of continuous time fuzzy systems this paper is concerned with the problem of nonfragile h filtering for a class of continuous time fuzzy systems attention is focused on the design of a filter such that the filtering error system preserves a prescribed h performance where the filter to be designed is assumed to have gain variations by using the quadratic lyapunov function approach and adding slack matrix variables sufficient conditions for designing the nonfragile h filter are proposed in terms of solutions to a set of linear matrix inequalities lmis finally a simulation example will be given to show the efficiency of the proposed design methods

design of fuzzy pid controllers using modified triangular membership functions a design method for fuzzy proportional integral derivative pid controllers is investigated in this study based on conventional triangular membership functions used in fuzzy inference systems the modified triangular membership functions are proposed to improve a system s performance according to knowledge based reasonings the parameters of the considered controllers are tuned by means of genetic algorithms gas using a fitness function associated with the system s performance indices the merits of the proposed controllers are illustrated by considering a model of the induction motor control system and a higher order numerical model

the generalized tp model transformation for t s fuzzy model manipulation and generalized stability verification this paper integrates various ideas about the tensor product tp model transformation into one conceptual framework and formulates it in terms of the takagi sugeno t s fuzzy model manipulation and control design framework several new extensions of the tp model transformation are proposed such as the quasi and full compact and rank reduced higher order singular value decomposition based canonical form of t s fuzzy models and the bilinear multi pseudo convex partial tp model transformations all of these extensions together form the generalized tp model transformation which provides an effective tool to freely and readily manipulate the antecedent sets and rules of t s fuzzy models and also provides main fuzzy rule component analysis as well as a means for complexity and accuracy tradeoffs it is demonstrated in this paper that the proposed manipulation forms a new effective and necessary optimization step of t s fuzzy or polytopic models and linear matrix inequality based control design and can also decrease conservativeness identification techniques are typically constructed according to the available data and measurement set as well as the type of system to be identified as a result they may not always provide good representations for control design frameworks this paper demonstrates that the proposed tp model transformation is unique in that it bridges between various soft computing based identification techniques and t s fuzzy model based approaches finally this paper proposes the multi tp model transformation which is a tractable and nonheuristic framework to verify the stability of the result of fuzzy or various soft computing based control designs the multi tp model transformation could provide an answer to the frequently emerging criticisms regarding the lack of mathematical stability verification techniques in the soft computing based control design control examples are provided in this paper

design of fuzzy controllers for uncertain nonlinear systems using stability and robustness analyses this paper analyzes the stability and robustness of uncertain nonlinear systems and shows that the analysis results provide an efficient technique for the design of fuzzy controllers based on a fuzzy plant model describing an uncertain nonlinear plant this design involves the derivation of a stability criterion and a robust area in the uncertain parameter space in terms of some measures of the closed loop control system matrices an application example on balancing an inverted pendulum is given to illustrate the simple design methodology the stability and the robustness of the feedback system incorporated with the proposed fuzzy 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

fuzzy network model based fuzzy state controller design the performance of model based controller design relies heavily on the quality and suitability of the utilized process model this contribution proposes a fuzzy network based nonlinear controller design methodology fuzzy networks are a model approach combining high approximation quality with high interpretability the input output i o models commonly used for identification are transformed to fuzzy state space models transferring and adjusting methods from linear state space theory a control concept consisting of a fuzzy state controller and an adaptive set point filter for nonlinear dynamic processes is deduced the capability of the method is demonstrated for a hydraulic drive

brief probabilistic solutions to some np hard matrix problems during recent years it has been shown that a number of problems in matrix theory are np hard including robust nonsingularity robust stability robust positive semidefiniteness robust bounded norm state feedback stabilization with structural and norm constraints etc in this paper we use standard bounds on empirical probabilities as well as recent results from statistical learning theory on the vc dimension of families of sets defined by a finite number of polynomial inequalities to show that for each of the above problems as well as for still more general and more difficult problems there exists a polynomial time randomized algorithm that can provide a yes or no answer to arbitrarily small levels of accuracy and confidence

a general fuzzy scheme for nonlinear processes with stability analysis abstract in this paper we develop a general fuzzy control scheme for nonlinear processes assuming little knowledge about the dynamics of the controlled process the proposed scheme starts by probing the process at different points in its operating region to generate a fuzzy quantisation a simple local controller is then designed at each fuzzy locality a fuzzy inference mechanism then links up tje local controllers to form a global controller which can be further refined by the learning algorithm by employing a newly developed structure adaptive fuzzy modelling scheme the appropriate fuzzy rule base for the inference mechanism can be extracted stably and efficiently the conditions for the stability of the global controller are rigourously established simulation results are presented to illustrate the effectiveness of the scheme

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

on the upsilon invariant and satellite knots we study the effect of satellite operations on the upsilon invariant of ozsvath stipsicz szabo we obtain results concerning when a knot and its satellites are independent for example we show that the set d 2 i 1 i 1 infty is a basis for an infinite rank summand of the group of smooth concordance classes of topologically slice knots for d the positive clasped untwisted whitehead double of any knot with positive tau invariant e g the right handed trefoil we also prove that the image of the mazur satellite operator on the smooth knot concordance group contains an infinite rank subgroup of topologically slice knots

stability and the fuzzy controller abstract this paper corrects a part of the main result theorem 1 in buckley fuzzy sets and systems 77 1996 167 173

analysis and design of fuzzy reduced dimensional observer and fuzzy functional observer on the basis of the t s fuzzy model this paper discusses the following three problems the fuzzy reduced dimensional observer the general structure of the fuzzy observer the fuzzy functional observer for both the continuous and discrete case respectively the separation property that is the fuzzy controller and the fuzzy observer can be independently designed is also addressed the numerical simulation and the experiment on an inverted pendulum system are given to illustrate the soundness of these results

delay dependent stabilization for stochastic fuzzy systems with time delays this paper is concerned with the delay dependent stabilization problem for a class of time delay stochastic fuzzy systems the time delays are assumed to appear in both the state and the control input the purpose is the design of a state feedback fuzzy controller such that the resulting closed loop system is asymptotically stable in the mean square a delay dependent condition for the solvability of this problem is obtained in terms of relaxed linear matrix inequalities lmis by solving these lmis a desired controller can be obtained finally a numerical example is given to demonstrate the effectiveness of the present results

rcg r signalizers in finite groups abstract let r be a prime and suppose the r group r acts as a group of automorphisms on the r group g we study the rc g r invariant subgroups of g and how they influence the structure of g an application to the study of the automorphism group of a simple group is presented

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

a methodology to design stable nonlinear fuzzy control systems the stability of nonlinear systems has to be investigated without making linear approaches in order to do this there are several techniques based on lyapunov s second method for example krasovskii s method allows to prove the sufficient condition for the asymptotic stability of nonlinear systems this method requires the calculation of the jacobian matrix in this paper an equivalent mathematical closed loop model of a multivariable nonlinear control system based on fuzzy logic theory is developed later this model is used to compute the jacobian matrix of a closed loop fuzzy system next an algorithm to solve the jacobian matrix is proposed the algorithm uses a methodology based on the extension of the state vector the developed algorithm is completely general it is independent of the type of membership function that is chosen for building the fuzzy plant and controller models and it allows the compound of different membership functions in a same model we have developed a matlab s function that implements the improved algorithm together with a series of additional applications for its use the designed software provides complementary functions to facilitate the reading and writing of fuzzy systems as well as an interface that makes possible the use of all the developed functions from the matlab s environment which allows to complement and to extend the possibilities of the matlab s fuzzy logic toolbox an example with a fuzzy controller for a nonlinear system to illustrate the design procedure is presented the work developed in this paper can be useful for the analysis and synthesis of fuzzy control systems

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

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

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

stability analysis of control system having pd type of fuzzy controller stability of a control system having pd type of fuzzy controller a two input and single output controller is analyzed in this paper using yakubovich s method in this analysis the controller is treated as a two input and two output controller and the nonlinearity of the controller is characterized as the sector condition absolute stability conditions are derived for the control system as three conditions two are conditions for either one of control modes p or d is independently operating the third is the condition for two modes are simultaneously active the former two conditions are nothing but popov s conditions for two siso systems a new graphical method is proposed to solve the latter condition this method is explained illustratively using an example and the results obtained are compared numerically with those by other graphical methods as well as simulation results

a new proof of the solvable signalizer functor theorem abstract a new proof of glauberman s solvable signalizer functor theorem is presented the solvable signalizer functor theorem is one of the background results needed for the new proof of the classification of the finite simple groups in the gorenstein lyons solomon book series

stability analysis of the simplest takagi sugeno fuzzy control system using circle criterion in this paper we present two sufficient conditions in the frequency domain for the global stability analysis of the simplest takagi sugeno t s fuzzy control system based on the circle criterion and its graphical interpretation these conditions are significant in graphically designing the simplest t s fuzzy controller in the frequency domain four numerical examples are provided to demonstrate the efficiency of our two frequency domain based conditions furthermore this t s fuzzy controller and the linear proportional controllers are also compared it is concluded that the simplest t s fuzzy controller can outperform the linear proportional controllers in a noisy environment with external disturbances

a descriptor system approach to non fragile h control for uncertain fuzzy neutral systems in this paper the problem of non fragile h control for a class of uncertain takagi sugeno t s fuzzy neutral systems with linear fractional parametric uncertainties is considered the non fragile h control problem is to design a state feedback controller with parameter uncertainties such that the l 2 induced gain of the mapping from the exogenous input to the controlled output is less than some prescribed level based on lyapunov krasovskii functional the descriptor model transformation and lmi approach new sufficient conditions for solvability of this problem are obtained it is shown that by a novel controller design method the desired state feedback fuzzy controller can be constructed by solving a set of lmis and the minimum h disturbance attenuation level can be obtained via using the lmi algorithm mincx finally an illustrative numerical example is provided to demonstrate correctness and effectiveness of the theoretical results

a new approach to robust and non fragile h control for uncertain fuzzy systems this paper investigates the robust h control and non fragile control problems for takagi sugeno t s fuzzy systems with linear fractional parametric uncertainties the robust h control problem is to design a state feedback controller such that the robust stability and a prescribed h performance of the resulting closed loop system is ensured and the non fragile h control problem is to design a state feedback controller with parameter uncertainties based on the linear matrix inequality lmi approach new sufficient conditions for the solvability of the two problems are obtained it is shown that the desired state feedback fuzzy controller can be constructed by solving a set of lmis numerical examples are also provided to demonstrate the effectiveness of the proposed design method

analysis and design of an affine fuzzy system via bilinear matrix inequality a novel analysis and design method for affine fuzzy systems is proposed both continuous time and discrete time cases are considered the quadratic stability and stabilizability conditions of the affine fuzzy systems are derived and they are represented in the formulation of bilinear matrix inequalities bmis two diffeomorphic state transformations one is linear and the other is nonlinear are introduced to convert the plant into more tractable affine form the conversion makes the stability and stabilizability problems of the affine fuzzy systems convex and makes the problems solvable directly by the convex linear matrix inequality lmi technique the bias terms of the fuzzy controller are solved simultaneously together with the gains finally the applicability of the suggested method is demonstrated via an example and computer simulation

robust h fuzzy static output feedback control of t s fuzzy systems with parametric uncertainties this paper addresses robust h fuzzy static output feedback control problem for t s fuzzy systems with time varying norm bounded uncertainties sufficient conditions for synthesis of a fuzzy static output feedback controller for t s fuzzy systems are derived in terms of a set of linear matrix inequalities lmis in comparison with the existing literatures the proposed approach not only simplifies the design procedure but also achieves a better h performance three drawbacks existing in the previous papers such as coordinate transformation same output matrices and bmi problem have been eliminated the effectiveness of the proposed design method is demonstrated by an example for the control of a truck trailer system

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

a hall higman shult type theorem for arbitrary finite groups we shall extend a fixed point theorem of shult to arbitrary finite groups this will have applications to the study of group automorphisms

a fake compact contractible 4 manifold here we construct a fake smooth structure on a compact contractible 4 manifold w where w is a well known mazur manifold obtained by attaching in two handle to s x b along its boundary as in figure 1 here we use the conventions of 2 the results of this paper imply theorem 1 there is a smooth contractible 4 manifold v with dv d w such that v is homeomorphic but not diffeomorphic to w relative to the boundary let a be the loop in dw given by s x p c s x s d s x b as in figure 2 zeeman raised the question whether a is slice in w 12 i e if a bounds an imbedded smooth d in w even though it turned out that a is slice in another smooth contractible manifold with the same boundary 2 the original question has remained open let d w d w be the diffeomorphism obtained by first surgering s x b to b xs in the interior of w then surgering the other imbedded b x s back to s x b i e replacing the dots in figure 2 clearly this diffeomorphism extends to a self homotopy equivalence of w in fact by 9 extends to a homeomorphism f w w in 2 p 279 the question of whether extends to a diffeomorphism of w was posed if it did a would be slice in w since f a is clearly slice in w here we answer these questions negatively theorem 2 is not slice in w in particular f does not extend to a self diffeomorphism of w theorem 1 follows from theorem 2 as follows let f w w be a homeomorphism extending let v be the smooth structure on w obtained by pulling back the smooth structure of w by f this gives a diffeomorphism f v w extending on the boundary if g w v

an approach to the analysis of fuzzy systems this paper deals with a formal description of ill defined processes fuzzy systems by the use of fuzzy relational equations it is pointed out that fuzzy relational equations form a generalized version of the difference equations widely considered in control theory some equivalence between these two kinds of description is presented basic problems of fuzzy systems e g identification prediction sensitivity and stability are shown and numerical algorithms are given indices of each method are introduced especially the degree of fuzziness the sensitivity index which makes it possible to express the quality of each of them

universal fuzzy controllers for a class of nonlinear systems in this paper we address the issues of universal fuzzy controllers we first present a universal function approximation theorem based on a fuzzy dynamic model then we show the results of universal fuzzy controllers for a large class of nonlinear systems

lmi based design of stabilizing fuzzy controllers for nonlinear systems described by takagi sugeno fuzzy model abstract there have been several recent studies concerning the stability of fuzzy control systems and the synthesis of stabilizing fuzzy controllers this paper reports on a related study of the takagi sugeno ts fuzzy systems and it is shown that the controller synthesis problems for the nonlinear systems described by the ts fuzzy model can be reduced to convex problems involving linear matrix inequalities lmis after classifying the ts fuzzy systems into three families based on how diverse their input matrices are a unique controller synthesis procedure is given for each of the families a numerical example is presented to illustrate the synthesis procedures developed in this paper

group actions corks and exotic smoothings of mathbb r 4 r 4 we provide the first information on diffeotopy groups of exotic smoothings of mathbb r 4 for each of uncountably many smoothings there are uncountably many isotopy classes of self diffeomorphisms we realize these by various explicit group actions there are also actions at infinity by nonfinitely generated groups for which no nontrivial element extends over the whole manifold in contrast every diffeomorphism of the end of the universal mathbb r 4 extends our techniques apply to many other open 4 manifolds and are related to cork theory we show that under broad hypotheses cork twisting is equivalent up to blowups to twisting on an exotic mathbb r 4 and give applications

a decomposition theorem for h cobordant smooth simply connected compact 4 manifolds theorem let m and n be smooth h cobordant compact 1 connected 4 manifolds there exist decompositions m m0 m1 and n n0 n1 where m0 and n0 are smooth compact contractible 4 manifolds with boundary so that m1 and n1 are dieomorphic if m and n are closed then we may further arrange that m1 and n1 are 1 connected in fact if w is an h cobordism connecting m and n then w can be written w w0 i w1 where w0 m0 n0 is an often nontrivial h cobordism and w1 m1 n1 is smoothly the product h cobordism m1 i m1 f0 g m1 f1 g this theorem lies in the mainstream of combinatorial 4 manifold theory circa 1975 but oddly the result was overlooked it now ts into a rich context donaldson theory and raises new questions when compared with the known examples in 1988 akbulut a showed that a manifold x homotopy equivalent to a k3 surface could after blowing up a point be transformed into a rational surface q by cutting out and regluing a certain contractible mazur manifold by an involution of its boundary at the time a rather delicate argument of fintushel and stern relying on the observed presence of the homology sphere 2 3 7 x showed that certain donaldson invariants of x and its blow up x were nontrivial this distinguished x from the h cobordant manifold q in retrospect this was the rst nontrivial example of our theorem the result was a surprise the donaldson invariant which derives from the second homology had been localized on a contractible piece recently bizaca and gompf bg have shown that x is in fact dieomorphic to k3 allowing a more direct analysis of its donaldson invariant see e g qk or km they also nd an innite family of examples

h_ infty fuzzy control of nonlinear systems under unreliable communication links this paper investigates the problem of h infin fuzzy control of nonlinear systems under unreliable communication links the nonlinear plant is represented by a takagi sugeno t s fuzzy model and the control strategy takes the form of parallel distributed compensation the communication links existing between the plant and controller are assumed to be imperfect that is data packet dropouts occur intermittently which appear typically in a network environment and stochastic variables satisfying the bernoulli random binary distribution are utilized to model the unreliable communication links attention is focused on the design of h infin controllers such that the closed loop system is stochastically stable and preserves a guaranteed h infin performance two approaches are developed to solve this problem based on the quadratic lyapunov function and the basis dependent lyapunov function respectively several examples are provided to illustrate the usefulness and applicability of the developed theoretical results

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

robust synthesis of a pid controller by uncertain multimodel approach this paper presents an effective method to design a pid or pi controller for nonlinear systems where desirable robustness and performance properties must be maintained across a large range of operating conditions for this purpose an uncertain multimodel of the original nonlinear system is used the uncertainties affecting the system are treated as stochastic matrices based on this multimodel representation a robust pid controller can be designed in order to obtain acceptable performance for all operating conditions numerical examples show the practical applicability of the proposed method

instanton homology of seifert fibred homology three spheres for an oriented integral homology 3 sphere 2 a casson has introduced an integer invariant a 2 that is defined by using the space 2 of conjugacy classes of irreducible representations of 2 into su 2 see 1 this invariant a 2 can be computed from a surgery or heegard description of 2 and satisfies a 2 ju 2 mod 2 where i 2 is the kervaire milnor rochlin invariant of 2 this powerful new invariant was used to settle an outstanding problem in 3 manifold topology namely showing that if 2 is a homotopy 3 sphere then ju 2 o c taubes 17 utilizing gauge theoretic considerations has reinterpreted casson s invariant in terms of flat connections refining this approach a floer 13 has recently defined another invariant of 2 its instanton homology which takes the form of an abelian group 2 with a natural z8 grading that is an enhancement of a 2 in that

fuzzy modeling and control of multilayer incinerator abstract a method to design a fuzzy controller based on a fuzzy model is suggested the identification method of a fuzzy model is also discussed the suggested method is applied for the modelling and control of a multilayer incinerator the performance of the designed fuzzy controller is tested by computer simulation using the identified process model the results are satisfactory

obstructing pseudoconvex embeddings and contractible stein fillings for brieskorn spheres abstract a question in low dimensional symplectic topology asks whether every compact contractible 4 manifold admits the structure of a stein domain a related conjecture due to gompf asserts that no nontrivial brieskorn homology sphere admits a pseudoconvex embedding in c 2 with either orientation we give the first known example of a contractible boundary irreducible 4 manifold that admits no stein structure with either orientation though its boundary has stein fillings with both orientations we also verify gompf s conjecture with one orientation for a family of brieskorn spheres of which some are known to admit a smooth embedding in c 2 a byproduct of our example is the construction of a cork that does not admit a stein structure with either orientation

robust fuzzy h control for uncertain nonlinear systems via state feedback an lmi approach this paper presents a method for designing robust fuzzy h controllers which stabilize nonlinear systems and guarantee an induced l2 norm bound constraint on disturbance attenuation for all admissible uncertainties takagi and sugeno fuzzy models with uncertainties are used as the model for the uncertain nonlinear systems fuzzy control systems utilize the concept of the so called parallel distributed compensation pdc using a single quadratic lyapunov function the stability with decay rate and disturbance attenuation for takagi and sugeno fuzzy model with parameter uncertainties are discussed a sufficient condition for the presence of the robust fuzzy h controllers is then presented in terms of linear matrix inequalities lmis finally design examples of robust fuzzy h controllers for uncertain nonlinear systems are presented

further comment on optimal fuzzy controller design local concept approach stability analysis and optimality are important in any systems in the paper optimal fuzzy controller design local concept approach optimal fuzzy controller is design for takagi sugeno fuzzy model unfortunately it seems that some errors are happen and no simple correction can be done in this paper we show that some errors exit in the aforementioned paper with simple and clear examples

isotopy of surfaces in 4 manifolds after a single stabilization abstract any two homologous closed oriented surfaces of the same genus embedded in a smooth 4 manifold x with simply connected complement are shown to be smoothly isotopic in x s 2 s 2 if the surfaces are ordinary and in x s 2 s 2 if they are characteristic

robust fuzzy logic control of mechanical systems an approach for the design of fuzzy control laws for tracking control of a large class of mechanical systems is proposed the approach employs the framework of lyapunov s stability theory to formulate a class of control laws that guarantee convergence of the tracking errors to within specification limits in presence of bounded parameter uncertainties and input disturbances the proposed control laws possess a large number of parameters and functional relationships to be chosen by the designer according to a methodology developed in the paper the large number of design degrees of freedom makes the approach suitable for fuzzy logic implementation a number of fuzzy implementations of the proposed control methodology are provided all implementations guarantee tracking error convergence to within prespecified performance limits an extensive simulation study using a model of a two degree of freedom robot manipulator was conducted fuzzy and non fuzzy implementations of the proposed methodology were compared to control laws designed using other design methods simulation study results indicate a superiority of the proposed control methodology compared to other approaches the study also demonstrates better performance of the fuzzy control implementation compared to its non fuzzy counterpart

designing fuzzy controllers from a variable structures standpoint a procedure is presented for designing fuzzy controllers based upon variable structures techniques three such controllers are presented the fuzzy equivalents of sliding mode controllers saturating controllers and tanh controllers by using an approach based upon variables structures vss techniques the stability of each of these controllers is assured by using a sliding surface the order of the rule base is reduced to size r spl times m where r is the number of inputs and m is the number of fuzzification levels this combination makes the proposed design procedure able to generate simple controllers with guaranteed stability properties to illustrate the proposed design procedure fuzzy controllers are designed for a ball and beam system it is demonstrated that in spite of this system being a fourth order unstable system the proposed design procedure results in simple stable fuzzy controllers

fuzzy controllers as gain scheduling approximators abstract nonlinear systems can be linearized according to lyapunov s linearization method and then approximated by takagi sugeno ts fuzzy models the paper shows that the corresponding control strategy with ts controllers is closely related to traditional gain scheduling generally speaking gain scheduling deals with the connection of different linear controllers acting as a global nonlinear control law ts control defines a linear controller for each linearized region as well as smooth control transitions between those regions in this connection slowly varying operating conditions are assumed for the design of the linear controllers the lqr design method has been used which guarantees optimal control of a linearized system with respect to an integral criterion however since ts control is an approximation method solutions are bound to be suboptimal and stability is hence a concern the method is compared with a continuous change of control parameters based on the continuous on line lqr design for each point in state space additional control rule weights have been introduced to promote optimization the above method is illustrated by a simple one link manipulator arm

automorphisms of k groups i abstract this is the first in a sequence of papers that will develop the theory of automorphisms of nonsolvable finite groups the sequence will culminate in a new proof of mcbride s nonsolvable signalizer functor theorem which is one of the fundamental results required for the proof of the classification of the finite simple groups