on consistency and ranking of alternatives in fuzzy ahp abstract in fuzzy ahp where pairwise comparisons are described by membership values the treatment of consistency has largely been sketchy this paper proposes a fuzzy consistency definition with consideration of a tolerance deviation essentially the fuzzy ratios of relative importance allowing certain tolerance deviation are formulated as constraints on the membership values of the local priorities the fuzzy local and global weights are determined via the extension principle the alternatives are ranked on the basis of the global weights by application of a maximum minimum set ranking method our analysis uses only the data which are considered as consistent the proposed approach is computationally efficient as it consists of solving only linear programs an example is included for illustrative purpose

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

design of an adaptive fuzzy model based controller for chaotic dynamics in lorenz systems with uncertainty this paper presents the control methodology for uncertain chaotic dynamics of lorenz systems an adaptive fuzzy control afc scheme based on well known takagi sugeno t s fuzzy models for the mimo plants is constructed the developed control law and adaptive law guarantee the boundedness of all signals in the closed loop system in addition the chaotic state tracks the state of the stable reference model srm asymptotically with time for any bounded reference input signal the proposed control is applied to control of an uncertain lorenz system such as stabilization synchronization and chaotic model following control cmfc

how to make a decision the analytic hierarchy process abstract this paper serves as an introduction to the analytic hierarchy process a multicriteria decision making approach in which factors are arranged in a hierarchic structure the principles and the philosophy of the theory are summarized giving general background information of the type of measurement utilized its properties and applications

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

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

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

the generalized richardson extrapolation process grep 1 and computation of derivatives of limits of sequences with applications to the d 1 transformation abstract let sm be an infinite sequence whose limit or antilimit s can be approximated very efficiently by applying a suitable extrapolation method e0 to sm assume that the sm and hence also s are differentiable functions of some parameter d d s being the limit or antilimit of d d sm and that we need to approximate d d s a direct way of achieving this would be by applying again a suitable extrapolation method e1 to the sequence d d sm and this approach has often been used efficiently in various problems of practical importance unfortunately as has been observed at least in some important cases when d d sm and sm have essentially different asymptotic behaviors as m the approximations to d d s produced by this approach despite the fact that they are good do not converge as quickly as those obtained for s and this is puzzling in a recent paper a sidi extrapolation methods and derivatives of limits of sequences math comp 69 2000 305 323 we gave a rigorous mathematical explanation of this phenomenon for the cases in which e0 is the richardson extrapolation process and e1 is a generalization of it and we showed that the phenomenon has nothing to do with numerics following that we proposed a very effective procedure to overcome this problem that amounts to first applying the extrapolation method e0 to sm and then differentiating the resulting approximations to s as a practical means of implementing this procedure we also proposed the direct differentiation of the recursion relations of the extrapolation method e0 used in approximating s we additionally provided a thorough convergence and stability analysis in conjunction with the richardson extrapolation process from which we deduced that the new procedure for d d s has practically the same convergence properties as e0 for s finally we presented an application to the computation of integrals with algebraic logarithmic endpoint singularities via the romberg integration in this paper we continue this research by treating sidi s generalized richardson extrapolation process grep 1 in detail we then apply the new procedure to various infinite series of logarithmic type whether convergent or divergent in conjunction with the d 1 transformation of levin and sidi both the theory and the numerical results of this paper too indicate that this approach is the preferred one for computing derivatives of limits of infinite sequences and series

new convergence results on the generalized richardson extrapolation process grep 1 for logarithmic sequences let a t a t i 0 iti as t 0 where a t and t are known for 0 0 but a and the i are not known the generalized richardson extrapolation process grep 1 is used in obtaining good approximations to a the limit or antilimit of a t as t 0 the approximations an j to a obtained via grep 1 are defined by the linear systems a tl an j tl i 0n 1 itli l j j 1 j n where tl l 0 is a decreasing positive sequence with limit zero the study of grep 1 for slowly varying functions a t was begun in two recent papers by the author for such a t we have t t as t 0 with possibly complex and 0 1 2 in the present work we continue to study the convergence and stability of grep 1 as it is applied to such a t with different sets of collocation points tl that have been used in practical situations in particular we consider the cases in which i tl are arbitrary ii liml tl 1 tl 1 iii tl cl q as l for some c q 0 iv tl 1 tl 0 1 for all l v liml tl 1 tl 0 1 and vi tl 1 tl 0 1 for all l

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

robust stability of uncertain discrete time singular fuzzy systems this paper considers the problem of robust stability analysis of uncertain discrete time singular fuzzy systems described by a class of extended takagi sugeno fuzzy dynamic models with time varying norm bounded parameter uncertainties a sufficient condition ensuring a discrete singular fuzzy system to be regular causal and stable is proposed in terms of a set of linear matrix inequalities based on this a robust stability condition is obtained both of these conditions can be checked by using recently developed algorithms in solving lmis examples are provided to demonstrate the reduced conservatism and effectiveness of the proposed conditions

a multicriteria evaluation of methods for obtaining weights from ratio scale matrices abstract ratio scale matrices are commonly used as a vehicle to distinguish among competing alternatives or conflicting criteria the issue of extracting weights out of such matrices has attracted increasing attention in recent years and resulted in the development of several scaling methods this paper presents an attempt to evaluate some of the more known techniques in this area the evaluation procedure includes random generation of a large number of representative matrices which are used to evaluate the various scaling methods according to the specified criteria the performance of the different techniques is analyzed with respect to the proposed criteria and conclusions are drawn

two new classes of nonlinear transformations for accelerating the convergence of infinite integrals and series two new classes of nonlinear transformations the d transformation to accelerate the convergence of infinite integrals and the d transformation to accelerate the convergence of infinite series are presented in the course of the development of these transformations two interesting asymptotic expansions one for infinite integrals and the other for infinite series are derived the transformations d and d can easily be applied to infinite integrals 0f t dt whose integrands f t satisfy linear differential equations of the form f t s m k 1p k t f k t and to infinite series s r 1f r w terms f r satisfy a linear difference equation of the form f r s m k 1p k r d kf r such that in both cases the p k have asymptotic expansions in inverse powers of their arguments in order to be able to apply these transformations successfully one need not know explicitly the differential equation that the integrand satisfies or the difference equation that the terms of the series satisfy mere knowledge of the existence of such a differential or difference equation and its order m is enough this broadens the areas to which these methods can be applied the connection between the d and d transformations with some known transformations in shown the use and the remarkable efficiency of the d and d transformations are demonstrated through several numerical examples the computational aspects of these transformations are described in detail

incorporating the uncertainty of decision judgements in the analytic hierarchy process abstract the uncertainty in the relative weights of a pairwise comparison matrix in the analytic hierarchy process ahp is caused by the uncertainty in our decision judgements and in many cases can not be avoided in this paper it is explicitly shown how such uncertainties can be incorporated within the framework of ahp and how the resulting uncertainties in the relative priorities of the decision alternatives can be computed the required algorithm and the computational procedures are also developed and illustrated with examples uncertainty is introduced as a fundamental concept independent of the concept of consistency with a view to extend the ahp as a decision analysis procedure

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

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

asymptotic analysis of a generalized richardson extrapolation process on linear sequences in this work we give a detailed convergence and stability analysis for the author s generalized richardson extrapolation process grep m as this is being applied to linearly convergent or divergent infinite sequences a n where a n a m k 1 n k i 0 ki n k i as n k 1 being distinct the quantity we would like to compute is a whether it is the limit or antilimit of a n such sequences arise for example as partial sums of power series and of fourier series of functions that have algebraic and or logarithmic branch singularities specifically we define the grep m approximation a n m j to a with n n 1 n m and 0 via the linear systems a l a n m j m k 1 l k n i 0 1 ki l k 1 j l j m k 1 n k where ki are additional unknowns we study the convergence and stability properties of a n m j as j we show in particular that a n m j a m k 1 o j k j k 2nk as j when compared with a j a m k 1 o j k j k as j this result shows that grep m is a true convergence acceleration method for the sequences considered in addition we show that grep m is stable for the case being studied and we also quantify its stability properties the results of this work are the first ones pertaining to grep m with m 1

asymptotically necessary and sufficient conditions for takagisugeno models using generalized non quadratic parameter dependent controller design results in this paper generalize recent approaches on non quadratic controller design for takagisugeno models based on a matrix transformation conditions thus obtained depend on a single parameter which allows an efficient search of feasible solutions via linear matrix inequalities moreover they include and outperform former advances such as polya s approaches on the same framework some examples are included to illustrate the proposed generalization

robust stabilizing controller design for takagi sugeno fuzzy descriptor systems under state constraints and actuator saturation abstract the aim of this paper is to present a new framework for designing robust controllers for uncertain nonlinear systems described by takagi sugeno fuzzy descriptor systems and subject to input and state constraints for this a novel structure of modified parallel distributed compensation control laws is proposed the controller parameters can be obtained through the numerical resolution of an optimization problem with linear matrix inequality constraints derived from lyapunov s stability theory and the choice of an original lyapunov function this ensures the stabilization of the closed loop system and the respect of the state and input constraints regionally the technique is illustrated through three numerical examples

nonfragile control with guaranteed cost of t s fuzzy singular systems based on parallel distributed compensation this paper investigates the nonfragile guaranteed cost control problem for a class of uncertain nonlinear singular state delayed systems that is described by takagi sugeno models the upper bound of state delay is assumed to be available a linear quadratic cost function is specified as the performance index of the closed loop system attention is focused on the fuzzy state feedback controller design via parallel distributed compensation scheme which not only guarantees the regular impulse free and asymptotically stable of the closed loop fuzzy singular delay system but also provides an optimized upper bound of the guaranteed cost function for the possibility of feedback gain variation and all admissible uncertainties all derived sufficient conditions are given in terms of linear matrix inequalities some numerical examples are provided to illustrate the effectiveness of the proposed design scheme

a new methodology for sensitivity and stability analysis of analytic network models abstract in this paper we develop a methodology to study the sensitivity and the stability of models built using the analytic network process we study two types of stability core and solution stability the former deals with finding the region of the perturbation space in which the initial solution i e the alternative that is ranked first obtained from the anp model remains most preferred the latter deals with finding the regions of the perturbation space in which the solutions that were not initially most preferred i e alternatives that were not ranked first become most preferred i e they are ranked first the methodology consists of three stages generation of the perturbation space finding the boundaries of the regions in the perturbation space in which the different alternatives are ranked first and finding the stability regions

further convergence and stability results for the generalized richardson extrapolation process grep 1 with an application to the d 1 transformation for infinite intergals abstract let a t a t i 0 iti as t 0 where a t and t are known for 0 0 but a and the i are not known the generalized richardson extrapolation process grep 1 is used in obtaining good approximations to a the limit or antilimit of a t as t 0 the convergence and stability properties of grep 1 for the case in which t t as t 0 0 1 2 have been studied to a large extent in a recent work by the author in the present work we continue this study for the case in which is complex when the set of extrapolation points is t i t 0 i i 0 1 with 0 1 we give a complete convergence and stability analysis under very weak assumptions on t we show that this analysis applies to the levin sidi d 1 transformation that is a grep 1 as this transformation is used for computing both convergent and divergent infinite range integrals of functions f x that essentially satisfy f x x 1 as x with as above in case of divergence we show that the d 1 transformation produces approximations to the associated hadamard finite parts we append numerical examples that demonstrate the theory

convergence analysis for a generalized richardson extrapolation process with an application to the d 1 transformation on convergent and divergent logarithmic sequences in an earlier work by the author the generalized richardson extrapolation process grep was introduced and some of its convergence and stability properties were discussed in a more recent work by the author a special case of grep which we now call grep 1 was considered and its properties were reviewed with emphasis on oscillatory sequences in the first part of the present work we give a detailed convergence and stability analysis of grep 1 as it applies to a large class of logarithmic sequences both convergent and divergent in particular we prove several theorems concerning the columns and the diagonals of the corresponding extrapolation table these theorems are very realistic in the sense that they explain the remarkable efficiency of grep 1 in a very precise manner in the second part we apply this analysis to the levin sidi d 1 transformation as the latter is used with a new strategy to accelerate the convergence of infinite series that converge logarithmically or to sum the divergent extensions of such series this is made possible by the observation that when the proper analogy is drawn the d 1 transformation is in fact a grep 1 we append numerical examples that demonstrate the theory

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

an algorithm for a special case of a generalization of the richardson extrapolation process a special case of a generalization of the richardson extrapolation process is considered and its complete solution is given in closed form using this an algorithm for implementing the extrapolation is devised it is shown that this algorithm needs a very small amount of arithmetic operations and very little storage convergence and stability properties for some cases are also considered

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

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

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

transitive calibration of the ahp verbal scale abstract one of the strengths of the analytic hierarchy process ahp is that it allows decision makers to specify their preferences using a verbal scale yet as is well known a strict reliance on the corresponding saaty 1 9 numeric scale can induce some inconsistency hence we argue that in certain situations it may be appropriate to calibrate the verbal scale the result of this calibration is a geometric scale based on a single parameter we present some limited evidence that this geometric scale marginally outperforms the saaty 1 9 scale moreover we suggest that this calibration can be used to do a simple sensitivity analysis in cases where judgements are uncertain

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

approaches to quadratic stability conditions and h sub spl infin control designs for t s fuzzy systems in this paper the problems of quadratic stability conditions and h sub spl infin control designs for takagi sugeno t s fuzzy systems have been studied first a new quadratic stability condition which is more simple than that in a previous paper has been proposed second two new sufficient conditions in the terms of linear matrix inequalities lmis which guarantee the existence of the state feedback h sub spl infin control for the t s fuzzy systems have been proposed the conditions are not only simple but also consider the interactions among the fuzzy subsystems finally based on the lmis the h sub spl infin controller designing methods for the t s fuzzy systems have been given

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

an extended multistep shanks transformation and convergence acceleration algorithm with their convergence and stability analysis the molecule solution of an extended discrete lotka volterra equation is constructed from which a new sequence transformation is proposed a convergence acceleration algorithm for implementing this sequence transformation is found it is shown that our new sequence transformation accelerates some kinds of linearly convergent sequences and factorially convergent sequences with good numerical stability some numerical examples are also presented

eigenvector and logarithmic least squares abstract the eigenvector method deals with two questions simultaneously closeness and order together they belong to the field topology of order the metric idea of closeness is inadequate to judge what is a good approximation to data involving order relations there is usually a condition which relates order in the derived scale to order in the data this is precisely the kind of condition captured by the eigenvector but not by the logarithmic least squares estimate

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 rational approach to handling fuzzy perceptions in route choice abstract the purpose of this paper is to develop a heuristic way for handling fuzzy perceptions in explaining route choice behavior from behavioral point of view a hybrid model where route choice decision making is described in a hierarchy uses concepts from fuzzy logic and the analytical hierarchy process ahp is proposed for making possible a more proper description of route choice behavior in transportation systems teodorovic and kikuchi s transportation route choice model using fuzzy inference technique paper presented at the first international symposium on uncertainty modeling and analysis fuzzy reasoning probabilistic models and risk management university of college park maryland 1990 p 140 fuzzy if then rules are adopted to represent a typical driver s psychology for capturing essential preferences pairwise among alternatives that a driver may consider the ahp is then incorporated in this model to capture the imaginary psychological process that represent underlying observable behavior to estimate drivers preference allotment among the alternatives this new procedure is applied in a real world sample based on stated values of subjects findings show that this method provides intuitively and statistically promising results

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

relaxed lmi based stability conditions for takagi sugeno fuzzy control systems using regional membership function shape dependent analysis approach this paper presents relaxed stability conditions for takagi sugeno t s fuzzy model based control systems it is assumed that the stability conditions are represented by some inequalities in the form of a p dimensional fuzzy summation to investigate the system stability the inequalities are expanded to n dimensional fuzzy summation n ges p the boundary and regional informations of membership functions are then utilized for relaxation of stability analysis results two analysis approaches are proposed in this paper the first approach is called the global membership function shape dependent approach in which the lower and upper bounds of the membership functions and its products from 2 to n in the full operating domain are considered in the stability analysis the second approach is named as the regional membership function shape dependent approach in which the operating region is partitioned to subregions and the boundary information of membership functions on each operating subregion is employed to facilitate the stability analysis in both approaches by the help of the boundary and or regional information of the membership functions some inequality constraints in the form of multidimensional fuzzy summation containing some slack matrices are constructed stability conditions in the form of linear matrix inequalities lmis are derived numerical examples are given to demonstrate the effectiveness of the proposed stability conditions

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

controller design for discrete time descriptor models a systematic lmi approach this paper provides a systematic way to generalize the controller design for discrete time nonlinear descriptor models the controller synthesis is done using a takagi sugeno representation of the descriptor models and linear matrix inequalities we propose approaches to exploit the discrete time nature of the problem by using delayed lyapunov functions which allow delayed controller gains in addition the well known finsler s lemma is used to avoid the explicit substitution of the closed loop dynamics examples are provided to show the effectiveness of the proposed results

admissibility analysis and control synthesis for t s fuzzy descriptor systems the problem of admissibility analysis and control synthesis for takagi sugeno fuzzy descriptor systems is investigated first based on nonquadratic fuzzy lyapunov function and fully using the information of fuzzy membership functions a new relaxed sufficient condition ensuring a fuzzy descriptor system to be admissible regular impulse free and stable is proposed in which it is not necessary to require every fuzzy subsystem to be stable second the other sufficient condition for the admissibility is obtained without the information of time derivatives of fuzzy membership functions following the analysis both parallel and nonparallel distributed compensation controllers are designed linear matrix inequalities conditions are given to construct the controllers finally some examples are provided to illustrate the main results in this paper less conservative than some earlier related results

reciprocal distributions in the analytic hierarchy process abstract the paper analyses a special kind of probability distributions used to capture the existing uncertainty for the judgements in the analytic hierarchy process ahp these distributions called reciprocal satisfy the reciprocity axiom of the ahp methodology first we define and characterise the reciprocal distributions and present some results and properties associated with them we then study the relationship between the reciprocal and symmetrical random variables and the distribution of the priorities vector considering the eigenvector method egv in the consistent case and the row geometric mean method rgm as priorization methods and assuming that the judgements follow reciprocal distributions we prove that the elements of the priorities vector are distributed according to reciprocal random variables the knowledge of these distributions will allow us to obtain the probability of two interesting events in practical selection problems the probability that a given alternative would be ranked in the first position and the probability of a given ranking preference structure for the whole set of alternatives in particular we find the analytic expressions for these probabilities when a reciprocal random variable such as the lognormal is used

interval estimation of priorities in the ahp this paper extends and modifies the analytic hierarchy process ahp and the synthetic hierarchy method shm of priority estimation to accommodate random data in the pairwise comparison matrices it employs a cauchy distribution to describe the pairwise comparison of alternatives in saaty matrices and shows how to modify these matrices in order to handle random data the use of random data yields saaty matrices that are not reciprocally symmetrical several variants of the ahp are then modified i to accommodate reciprocally asymmetric matrices and ii to allow each priority estimate to be expressed on an interval of possible values rather than as a single discrete point the merits of interval estimation are illustrated by an example

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

mean square admissibility for stochastic ts fuzzy singular systems based on extended quadratic lyapunov function approach the mean square admissibility problem of stochastic ts fuzzy singular systems via an extended quadratic lyapunov function is investigated in this paper comparing with the existing quadratic lyapunov function method the extended quadratic lyapunov function method can relax stabilization conditions firstly the sufficient condition is given for the mean square admissibility of stochastic ts fuzzy singular systems based on an extended quadratic lyapunov function approach secondly two sufficient conditions for mean square admissibility of closed loop systems via the parallel distributed compensation pdc fuzzy controller and non parallel distributed compensation non pdc fuzzy controller are proposed furthermore through the extended quadratic lyapunov function method and non pdc fuzzy controller the less conservative mean square admissibility conditions on solving fuzzy controllers are derived in terms of linear matrix inequalities lmis finally some simulation examples are given to show the effectiveness and merits of the proposed fuzzy controller design methodology

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

convex stability analysis of nonlinear singular systems via linear matrix inequalities stability analysis of nonlinear singular systems arising from differential algebraic equations is addressed in this paper exploiting the fact that it belongs to the class of positvstellensatz problems by means of the direct lyapunov method and a variety of convex descriptor forms sufficient conditions in terms of linear matrix inequalities are developed issues concerning proper initialization and simulation are also considered illustrative examples are provided

a thurstonian view of the analytic hierarchy process abstract the application of deterministic decision models in situations characterized by noise and uncertainty is likely to produce results of questionable value in this paper some very simple probabilistic models are developed and substituted for the deterministic scales used in the analytic hierarchy process ahp it is shown that the use of these probabilistic models can extend the domain of ahp to situations such as consensual or group decision making that possess significant amounts of uncertainty in addition explicit measures of the variation present in the evaluation of decision alternatives and attributes are obtained

delay dependent stability and h control for a class of fuzzy descriptor systems with time delay this paper addresses issues of stability analysis and h control for a class of fuzzy time delay descriptor systems described by an extended takagi sugeno t s fuzzy model a delay dependent stability criterion is first presented and a h control synthesis approach is then developed both the stability criterion and the h controller synthesis are based on the solutions of linear matrix inequalities lmis finally two examples are given to illustrate the effectiveness of the approaches proposed in this paper

observer design for takagi sugeno descriptor models this paper considers observer design for nonlinear descriptor systems we propose approaches based on takagi sugeno ts models an extended estimation vector is used in order to keep the descriptor structure of the observer the design conditions are expressed as linear matrix inequalities the proposed observer structure via an intermediate variable as estimated variable is able to recover the previous observer results for ts descriptors moreover through a direct extension via so called finsler s lemma relaxed conditions are obtained numerical examples show the effectiveness of the proposed approaches

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

sliding mode control of singular stochastic markov jump systems an investigation has been made into the sliding mode control smc problem for singular stochastic markov systems ssmss in this paper by using replacement of matrix variables a new mean square admissibility criterion of ssmss is proposed first based on this admissibility criterion the desired state feedback controller is designed to guarantee the closed loop system to be mean square admissible then the obtained results given in the form of strict linear matrix inequalities are applied to solve smc problem of ssmss in order to illustrate the workability and applicability of the theoretic results developed numerical examples are provided

stability analysis of discrete singular fuzzy systems abstract this work mainly develops a discrete singular fuzzy model and discusses its stability the standard discrete t s model is generalized into the so called discrete singular takagi sugeno dst s model which can represent a larger class of nonlinear systems and the stability criteria of this system are then investigated these criteria are described by non strict linear matrix inequalities and we thus involve the projection method for ensuring stability based on some derived projection operators a projection algorithm is proposed for solving a feasible solution an illustrating example demonstrates the validity and effectiveness of the proposed method

capturing group preferences in a multicriteria decision abstract this paper examines the extent to which methods used for analyzing judgments from a group of decision makers result in preference rankings which are consistent with the group member s subjective beliefs about their preferences in a laboratory group decision setting the analytic hierarchy process a newly developed probabilistic extension to the ahp and two pairwise voting methods are used to develop separate preference rankings based on input from the group members the probabilistic version of the ahp in its first independent test is found to provide more insight into the group decision while requiring fewer a priori assumptions a commonly used and easily implemented pairwise voting procedure is found to be significantly inferior to the other methods in its ability to capture the group s preference rankings this underscores the importance of using appropriate decision models for developing a full understanding of group preferences

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 descriptor systems and nonlinear model following control this paper defines a fuzzy descriptor system by extending the ordinary takagi sugeno t s fuzzy model several kinds of stability conditions for the fuzzy descriptor system are derived and represented in terms of linear matrix inequalities lmis we illustrate an example of defining the fuzzy descriptor system instead of the ordinary t s fuzzy model an lmi design approach is employed to find stable feedback gains and a common lyapunov function in addition this paper presents a nonlinear model following control for the fuzzy descriptor system a new parallel distributed compensation the so called twin parallel distributed compensations tpdc to realize the nonlinear model following control is proposed we present a design technique based on the tpdc the proposed method is a unified approach to nonlinear model following control it contains the regulation and servo control problems as special cases

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

sos based stability analysis of polynomial fuzzy model based control systems via polynomial membership functions this paper presents stability analysis of polynomial fuzzy model based fmb control systems using the sum of squares sos approach recently stability analysis of the polynomial fuzzy control systems which is a generalized form of the well known takagi sugeno t s fmb control systems has been reported in the form of sos based stability conditions lack of information on the relations between membership functions and premise variables in the existing stability analysis approaches causes conservatism of their results in this paper to derive relaxed stability conditions for polynomial fmb control systems membership functions which are approximated with polynomials and carrying relations between membership functions and premise variables are brought into the stability analysis considering a polynomial fmb control system and based on the lyapunov stability theory stability conditions in the form of fuzzy summations are derived where each term contains product of membership functions of the polynomial fuzzy model and polynomial fuzzy controller each product term is approximated by a polynomial in order to obtain better approximation the operating domain of membership functions is partitioned to subregions then sos based stability conditions for all subregions are derived unlike some published stability analysis approaches the proposed one can be employed for stability analysis of polynomial fuzzy control systems under imperfect premise matching of which the fuzzy model and fuzzy controller do not share the same membership functions the solution of the sos based stability conditions can be found numerically using sostools which is a free third party matlab toolbox numerical examples are given to illustrate the effectiveness of the proposed stability conditions