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

a sharper bonferroni procedure for multiple tests of significance summary a simple procedure for multiple tests of significance based on individual p values is derived this simple procedure is sharper than holm s 1979 sequentially rejective procedure both procedures contrast the ordered p values with the same set of critical values holm s procedure rejects an hypothesis only if its p value and each of the smaller p values are less than their corresponding critical values the new procedure rejects all hypotheses with smaller or equal p values to that of any one found less than its critical value

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

a flexible strategy for testing subgroups and overall population subgroup analyses in addition to the total study population analysis are common in clinical trials however it is well recognized that findings from subgroup analyses do not provide confirmatory evidence for subgroup treatment effects without placing a priori criteria for ensuring that their findings are scientifically sound in this paper we address some of the common pitfalls of subgroup analyses subgroups analyses inherently have low power for detecting treatment effects we investigate the power interplay for a subgroup analysis and that for the total study population and list factors that impact the power of a subgroup analysis then we introduce a flexible statistical strategy for testing a pre specified sequence of hypotheses for both the overall and a subgroup the proposed method strongly controls the familywise type i error rate and enjoys higher power than other traditional methods this testing strategy allows testing for a subgroup once a pre specified degree of consistency in the efficacy findings between the subgroup and the overall study population is met in addition it accounts for the dependency between test statistics for the subgroup and the overall study population we discuss the power performance of this new method and provide significance levels for subgroup analysis finally we illustrate its application through retrospective analysis of data from three published clinical trials

total positivity properties of absolute value multinormal variables with applications to confidence interval estimates and related probabilistic inequalities total positivity properties of multivariate densities are useful in deducing positive dependence of random vector components and related probability inequalities in this paper we determine necessary and sufficient conditions for total positivity of absolute value multinormal variables the results are applied to obtain positive dependence and associated inequalities for the multinormal and related distributions e g the multivariate t and wishart distributions inequalities of this type yield bounds for multivariate confidence set probabilities

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

an improved bonferroni procedure for multiple tests of significance summary a modification of the bonferroni procedure for testing multiple hypotheses is presented the method based on the ordered p values of the individual tests is less conservative than the classical bonferroni procedure but is still simple to apply a simulation study shows that the probability of a type i error of the procedure does not exceed the nominal significance level a for a variety of multivariate normal and multivariate gamma test statistics for independent tests the procedure has type i error probability equal to a the method appears particularly advantageous over the classical bonferroni procedure when several highly correlated test statistics are involved

the simes method for multiple hypothesis testing with positively dependent test statistics abstract the simes method for testing intersection of more than two hypotheses is known to control the probability of type i error only when the underlying test statistics are independent although this method is more powerful than the classical bonferroni method it is not known whether it is conservative when the test statistics are dependent this article proves that for multivariate distributions exhibiting a type of positive dependence that arise in many multiple hypothesis testing situations the simes method indeed controls the probability of type i error this extends some results established very recently in the special case of two hypotheses

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

a stagewise rejective multiple test procedure based on a modified bonferroni test summary simes 1986 has proposed a modified bonferroni procedure for the test of an overall hypothesis which is the combination of n individual hypotheses in contrast to the classical bonferroni procedure it is not obvious how statements about individual hypotheses are to be made for this procedure in the present paper a multiple test procedure allowing statements on individual hypotheses is proposed it is based on the principle of closed test procedures marcus peritz gabriel 1976 and controls the multiple level a

some probability inequalities for ordered rm mtp sb 2 random variables a proof of the simes conjecture some new probability inequalities involving the ordered components of an mtp 2 random vector are derived which provide an analytical proof of an important conjecture in the field of multiple hypothesis testing this conjecture has been mostly validated so far using simulation

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

testing each hypothesis marginally at alpha while still controlling fwer how and when this paper proposes a multiple testing procedure that allows one to reject each individual hypothesis at a prespecified level while still controlling the familywise error rate at in the strong sense typically rejecting a hypothesis when its marginal p value is in a multiple hypothesis testing setting will lead to an inflation of familywise error rate however this inflation can be avoided if a particular consistency criterion is prespecified and incorporated in the testing algorithm the criterion is equivalent to requiring that all p values be smaller than or equal to a particular threshold in the one sided hypothesis testing setting extensions to the two sided hypothesis testing setting and extensions to situations where the criterion can be chosen per user s preference are also presented copyright 2012 john wiley sons ltd

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

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

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

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

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

validity of the hochberg procedure revisited for clinical trial applications there is much interest in using the hochberg procedure hp for statistical tests on primary endpoints of confirmatory clinical trials the procedure is simple to use and enjoys more power than the bonferroni and the holm procedures however the hp is not assumption free like the other two procedures it controls the familywise type i error rate when test statistics used for statistical tests are independent or if dependent satisfy a conditionally independent formulation otherwise its properties for dependent tests at present are not fully understood consequently its use for confirmatory trials especially for their primary endpoints remains worrisome confirmatory trials are typically designed with 1 2 primary endpoints therefore a question was raised at the food and drug administration as to whether the hp is a valid test for the simple case of performing treatment to control comparisons on two primary endpoints when their test statistics are not independent confirmatory trials for statistical tests normally use simple test statistics such as the normal z student s t and chi square the literature does include some work on the hp for dependent cases covering these test statistics but concerns remain regarding its use for confirmatory trials for which endpoint tests are mostly of the dependent kind the purpose of this paper is therefore to revisit this procedure and provide sufficient details for better understanding of its performance for dependent cases related to the aforementioned question published 2015 this article is a u s government work and is in the public domain in the usa

direct solvers performance on h adapted grids we analyse the performance of direct solvers when applied to a system of linear equations arising from an h adapted c 0 finite element space theoretical estimates are derived for typical h refinement patterns arising as a result of a point edge or face singularity as well as boundary layers they are based on the elimination trees constructed specifically for the considered grids theoretical estimates are compared with experiments performed with mumps using the nested dissection algorithm for construction of the elimination tree from metis library the numerical experiments provide the same performance for the cases where our trees are identical with those constructed by the nested dissection algorithm and worse performance for some cases where our trees are different we also present numerical experiments for the cases with mixed singularities where how to construct optimal elimination trees is unknown in all analysed cases the use of h adaptive grids significantly reduces the cost of the direct solver algorithm per unknown as compared to uniform grids the theoretical estimates predict and the experimental data confirm that the computational complexity is linear for various refinement patterns in most cases the cost of the direct solver per unknown is lower when employing anisotropic refinements as opposed to isotropic ones

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

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

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

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

is the simes improved bonferroni procedure conservative summary simes 1986 proposed a modified bonferroni procedure for conducting multiple tests of significance he proved that when the n test statistics are independent his procedure has exact size a already hommel 1983 had considered a similar procedure and shown that it need not be conservative he gave an attainable upper bound for its anticonservativeness here we show that for one sided tests based on positively correlated bivariate normal test statistics the procedure is conservative and for negatively correlated such variables it is anticonservative two sided tests based on bivariate normal variables are always conservative some numerical values are given which show that for all practical purposes the nominal a value can be used

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

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

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