optimization of type 2 fuzzy systems based on bio inspired methods a concise review a review of the optimization methods used in the design of type 2 fuzzy systems which are relatively novel models of imprecision has been considered in this work the fundamental focus of the work has been based on the basic reasons of the need for optimizing type 2 fuzzy systems for different areas of application recently bio inspired methods have emerged as powerful optimization algorithms for solving complex problems in the case of designing type 2 fuzzy systems for particular applications the use of bio inspired optimization methods have helped in the complex task of finding the appropriate parameter values and structure of the fuzzy systems in this review we consider the application of genetic algorithms particle swarm optimization and ant colony optimization as three different paradigms that help in the design of optimal type 2 fuzzy systems we also provide a comparison of the different optimization methods for the case of designing type 2 fuzzy systems

stability analysis and synthesis of nonlinear time delay systems via linear takagi sugeno fuzzy models abstract this paper concerns with the stability analysis and synthesis of nonlinear retarded systems via linear takagi sugeno ts fuzzy model approach first the ts fuzzy models with time delay are present and the stability conditions are derived using lyapunov razumikhin functional approach then a stabilization approach for nonlinear retarded systems through fuzzy state feedback and fuzzy observer based controller is proposed it shows that the analysis results provide an efficient technique for the design of fuzzy controllers sufficient conditions for the existence of fuzzy state feedback gain and fuzzy observer gain of the time delay systems are derived through the numerical solution of a set of coupled linear matrix inequalities

exponential stability of impulsive systems with application to uncertain sampled data systems we establish exponential stability of nonlinear time varying impulsive systems by employing lyapunov functions with discontinuity at the impulse times our stability conditions have the property that when specialized to linear impulsive systems the stability tests can be formulated as linear matrix inequalities lmis then we consider lti uncertain sampled data systems in which there are two sources of uncertainty the values of the process parameters can be unknown while satisfying a polytopic condition and the sampling intervals can be uncertain and variable we model such systems as linear impulsive systems and we apply our theorem to the analysis and state feedback stabilization we find a positive constant which determines an upper bound on the sampling intervals for which the stability of the closed loop is guaranteed the control design lmis also provide controller gains that can be used to stabilize the process we also consider sampled data systems with constant sampling intervals and provide results that are less conservative than the ones obtained for variable sampling intervals

a fuzzy lyapunov krasovskii functional approach to sampled data output feedback stabilization of polynomial fuzzy systems this paper presents an output feedback exponential stabilization condition of sampled data polynomial fuzzy control systems under variable sampling rates compared with previous work the proposed method is less conservative because of the newly developed time dependent fuzzy lyapunov krasovskii functional that is based on the conventional fuzzy lyapunov function moreover the controller is allowed to contain polynomial gain matrices thereby improving the control performance and design flexibility this is realized by assuming the difference between the continuous and discrete time state vectors as time varying norm bounded uncertainties which are manipulated using a robust control technique a new sufficient condition is introduced to cast the stability condition containing the integral term as the sum of square conditions finally the effectiveness of the proposed method is validated by simulations

new robust stability conditions and design of robust stabilizing controllers for takagi sugeno fuzzy time delay systems in this paper we consider robust stability and stabilization of uncertain takagi sugeno fuzzy time delay systems where uncertainties come into the state and input matrices some stability conditions and robust stability conditions for fuzzy time delay systems have already been obtained in the literature however those conditions are rather conservative and do not guarantee the stability of a wide class of fuzzy systems this is true in case of designing stabilizing controllers for fuzzy time delay systems and it thus leads to a conservative fuzzy controller design as well we first consider rather relaxed robust stability conditions of uncertain fuzzy systems to this end we introduce an auxiliary system to the original fuzzy time delay system to obtain generalized delay dependent stability conditions such an auxiliary system has some arbitrary matrices that generalize not only the system representation but also delay dependent stability conditions conditions we obtain here are delay dependent conditions that depend on the upper bound of time delay and are given in terms of linear matrix inequalities lmis then we compare our delay dependent stability conditions with other conditions in the literature and show that our conditions guarantee the stability of a wider class of systems than others next we consider the robust stabilization problem with memoryless and delayed state feedback controllers based on our generalized robust stability conditions we obtain delay dependent sufficient conditions for the closed loop system to be robustly stable and give a design method of robustly stabilizing controllers finally we give three examples that illustrate our results

asymptotics beats monte carlo the case of correlated local vol baskets we consider a basket of options with both positive and negative weights in the case where each asset has a smile i e evolves according to its own local volatility and the driving brownian motions are correlated in the case of positive weights the model has been considered in a previous work by avellaneda boyer olson busca and friz we derive highly accurate analytic formulas for the prices and the implied volatilities of such baskets the relative errors are of order 10 4 or better for t 10 3 for t 2 and 10 2 for t 10 years the computational time required to implement these formulas is under two seconds even in the case of a basket on 100 assets the combination of accuracy and speed makes these formulas potentially attractive both for calibration and for pricing in comparison simulation based techniques are prohibitively slow in achieving a comparable degree of accuracy thus the present work opens up a new paradigm in which asymptotics may arguably be used for pricing as well as for calibration 2014 wiley periodicals inc

finite time resilient reliable sampled data control for fuzzy systems with randomly occurring uncertainties abstract this paper deals with the problem of finite time passivity based h resilient reliable state feedback sampled data control for takagi sugeno fuzzy systems with randomly occurring uncertainties and gain variations where the randomly occurring characteristics are designed by stochastic variables satisfying the bernoulli distribution the main objective of this paper is to design a resilient reliable sampled data controller such that the resulting closed loop system is finite time bounded and satisfies finite time mixed h and passive performance index based on the constructed lyapunov krasovskii functional and wirtinger integral inequality some delay dependent sufficient conditions are derived for achieving the required result of the considered systems moreover the derived finite time stability conditions are established in the form of linear matrix inequalities lmis which can be solved by matlab lmi toolbox finally two numerical examples are presented to demonstrate the applicability of the proposed control design technique

interval type 2 fuzzy sampled data control of time delay systems abstract the problem of interval type 2 it2 fuzzy sampled data stabilization is addressed for nonlinear continuous time systems with time varying delay and parameter uncertainties the input delay approach together with free weighting and slack matrices is utilized to enforce the stability analysis and a sufficient condition is formulated based on the condition an it2 fuzzy sampled data controller is developed such that the closed loop system is asymptotically stable illustrative examples are used to manifest the merits of this design

an improved input delay approach to stabilization of fuzzy systems under variable sampling in this paper we investigate the problem of stabilization for sampled data fuzzy systems under variable sampling a novel lyapunov krasovskii functional lkf is defined to capture the characteristic of sampled data systems and an improved input delay approach is proposed by the use of an appropriate enlargement scheme new stability and stabilization criteria are obtained in terms of linear matrix inequalities lmis compared with the existing results the newly obtained ones contain less conservatism some illustrative examples are given to show the effectiveness of the proposed method and the significant improvement on the existing results

robust sampled data stabilization of uncertain fuzzy systems via input delay approach this paper is concerned with robust sampled data stabilization for uncertain fuzzy systems the system is modeled as a continuous time fuzzy system while the control input is a zero order sampled data signal when a zero order control input is considered the closed loop system can be seen as an input delay system hence an input delay system approach is introduced for sampled data control design sufficient stability conditions for the closed loop system are given in terms of linear matrix inequalities lmis under the assumption that sampling interval is not greater than some prescribed number stability conditions for fuzzy time delay systems are given by using jensen s inequality which simplifies conditions with less matrix variables a design method of robust sampled data state feedback controller for uncertain fuzzy systems is then proposed numerical examples are given to illustrate our robust sampled data state feedback control design and to show the effectiveness over other existing results

multilevel monte carlo path simulation we show that multigrid ideas can be used to reduce the computational complexity of estimating an expected value arising from a stochastic differential equation using monte carlo path simulations in the simplest case of a lipschitz payoff and a euler discretisation the computational cost to achieve an accuracy of o e is reduced from o e 3 to o e 2 log e 2 the analysis is supported by numerical results showing significant computational savings

an approximation formula for basket option prices under local stochastic volatility with jumps this paper develops a new approximation formula for pricing basket options in a local stochastic volatility model with jumps in particular the model admits local volatility functions and jump components in not only the underlying asset price processes but also the volatility processes to the best of our knowledge the proposed formula is the first one which achieves an analytical approximation for the basket option prices under this type of the models moreover in numerical experiments we provide approximate prices for basket options on the wti futures and brent futures based on the parameters through calibration to the plain vanilla option prices and confirm the validity of our approximation formula

support function machine for set based classification with application to water quality evaluation in some applications measurement errors and multiple repeated measurements often lead to a set based classification task where objects are represented with a set of samples and the traditional support vector machines svms do not work in these settings to deal with this problem we construct a new classifier called support function machine sfm in this work first sets in d dimensional euclidean space r d are mapped into an infinite dimensional banach space c s whose elements are functions via support functions and then set based classification in r d is converted into function based classification in c s second we define the hyperplane via the riesz representation theorem in banach space and discuss the hausdorff distance of hyperpalnes and maximum margin principle mmp in c s based on mmp we construct an optimal problem and discuss some of its properties thereafter we establish an sfm to solve set based classification experiments about water quality evaluation and set valued data classifications show the superiority of sfm

new approach to delay dependent stability analysis and stabilization for continuous time fuzzy systems with time varying delay this paper is concerned with delay dependent stability analysis and stabilization problems for continuous time takagi and sugeno t s fuzzy systems with a time varying delay a new method for the delay dependent stability analysis and stabilization is suggested which is less conservative than other existing ones first based on a fuzzy lyapunov krasovskii functional lkf a delay dependent stability criterion is derived for the open loop fuzzy systems in the derivation process some free fuzzy weighting matrices are introduced to express the relationships among the terms of the system equation and among the terms in the leibniz newton formula then a delay dependent stabilization condition based on the so called parallel distributed compensation pdc scheme is worked out for the closed loop fuzzy systems the proposed stability criterion and stabilization condition are represented in terms of linear matrix inequalities lmis and compared with the existing ones via two examples finally application to control of a truck trailer is also given to illustrate the effectiveness of the proposed design method

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

on certain schlomilch type series abstract by using a form of the poisson summation formula together with a generalization due to srivastava and exton of the discontinuous integral of weber and schafheitlin and the heretofore not readily available cosine transform of the hypergeometric function 1 f 2 b 2 t 2 b 0 several new schlomilch and fourier type series are evaluated by specialization of the latter series numerous results appearing in the literature are obtained in a unified way

new results on h filtering for fuzzy systems with interval time varying delays this paper investigates the problem of h filtering for continuous takagi sugeno t s fuzzy systems with an interval time varying delay in the state based on the delay partitioning idea a new approach is proposed for solving this problem which can achieve much less conservative feasibility conditions the attention is focused on the design of an h filter via the parallel distributed compensation scheme such that the filter error system is asymptotically stable and the h attenuation level from disturbance to estimation error is below a prescribed scalar the constructed lyapunov krasovskii functional by applying the delay partitioning method can potentially guarantee the obtained delay dependent conditions to be less conservative than those in the literature the obtained results are formulated in the form of linear matrix inequalities lmis which can be readily solved via standard numerical software finally an example is illustrated to show the reduction in conservatism of the proposed filter design method

robust sampled data control with random missing data scenario the problem of robust sampled data control for uncertain dynamic systems in the presence of missing data has been investigated by using stochastic variables with a bernoulli distributed white sequence to model missing data along with time varying norm bounded uncertainties and the input delay approach for sampled data systems two models for the considered sampled data control system are proposed as the consecutive missing data scenario moreover when data are missing the control signals are held as the last received data sufficient conditions for the existence of desired robust sampled data controllers are presented in the form of a linear matrix inequality a numerical example is given to illustrate the validity of the proposed methods and to compare the results between the two proposed models of the sampled data control system

on sampled data fuzzy control design approach for t s model based fuzzy systems by using discretization approach in this paper a sampled data fuzzy control design approach for takagi sugeno t s model based fuzzy systems is proposed firstly the t s model based fuzzy systems are approximated by t s fuzzy model based discrete systems with parameter uncertainties then a sufficient condition on the existence of a sampled data fuzzy controller for the fuzzy systems is formulated in the form of linear matrix inequalities which are proposed in some symmetrical form so the proposed fuzzy control design approach will be less conservative and some problems in the existing literature can be solved finally a simulation example is discussed to show the effectiveness of the obtained fuzzy control design approach in this paper

on error estimates for asymptotic expansions with malliavin weights application to stochastic volatility model this paper proposes a unified method for precise estimates of the error bounds in asymptotic expansions of an option price and its greeks sensitivities under a stochastic volatility model more generally we also derive an error estimate for an asymptotic expansion around a general partially elliptic diffusion and a more general wiener functional which is applicable to various important valuation and risk management tasks in the financial business such as the ones for multidimensional diffusion and nondiffusion models in particular we take the malliavin calculus approach and estimate the error bounds for the malliavin weights of both the coefficient and the residual terms in the expansions by effectively applying the properties of kusuoka stroock functions introduced by kusuoka kusuoka s 2003 malliavin calculus revisited j math sci univ tokyo 10 261 277 functions moreover a numerical experiment under the heston type model confirms the effectiveness of our method

finite dimensional guaranteed cost sampled data fuzzy control for a class of nonlinear distributed parameter systems in this paper a finite dimensional guaranteed cost sampled data fuzzy control gcsdfc problem is addressed for a class of nonlinear parabolic partial differential equation pde systems initially applying the galerkin s method to the pde system a nonlinear ordinary differential equation ode system is derived the resulting nonlinear ode system can accurately describe the dominant dynamics of the pde system which is subsequently expressed by the takagi sugeno t s fuzzy model then a guaranteed cost sampled data fuzzy controller is developed to stabilize exponentially the closed loop slow fuzzy system while providing an upper bound for the quadratic cost function a novel time dependent functional is constructed to derive the condition for the existence of the proposed controller which is presented by bilinear matrix inequalities bmis moreover a suboptimal gcsdfc problem to minimize the cost bound can be formulated as a bmi optimization problem a local optimization algorithm that views the bmi as a double linear matrix inequality lmi is given to solve this bmi optimization problem in which a latin hypercube sampling lhs method is proposed to find an initially feasible solution for starting the algorithm furthermore it is shown that the proposed controller can ensure the exponential stability of the closed loop pde system finally simulation results on the fisher equation and the temperature profile of a catalytic rod show that the proposed design strategy is effective

a general control variate method for multi dimensional sdes an application to multi asset options under local stochastic volatility with jumps models in finance abstract this paper presents a new control variate method for general multi dimensional stochastic differential equations sdes including jumps in order to reduce the variance of monte carlo method our control variate method is based on an asymptotic expansion technique and does not require an explicit characteristic function of sdes this is an extension of previous researches using asymptotic expansions to obtain the control variates for such general models moreover in our control variate method the regression estimators can be chosen for each number of jump times with a stratified sampling and improve the efficiency of the variance reduction this paper also provides the asymptotic bias and variance of our method in terms of its terminal time and a small noise parameter used in an asymptotic expansion method for an application of our method we evaluate multi asset options whose payoffs are expressed as linear functions of the underlying asset price processes in general local stochastic volatility with jumps models and show a calculation scheme of control variates for greeks in numerical experiments we apply the new control variate method to pricing basket spread and average options and delta of basket options under a zabr type local stochastic volatility model with jumps and confirm that our method works very well

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

robust stability and stabilizing controller design of fuzzy systems with discrete and distributed delays in this paper we consider delay dependent stability conditions of takagi sugeno fuzzy systems with discrete and distributed delays although many kinds of stability conditions for fuzzy systems with discrete delays have already been obtained almost no stability condition for fuzzy systems with distributed delays has appeared in the literature this is also true in case of the robust stability for uncertain fuzzy systems with distributed delays here we employ a generalized lyapunov functional to obtain delay dependent stability conditions of fuzzy systems with discrete and distributed delays we introduce some free weighting matrices to such a lyapunov functional in order to reduce the conservatism in stability conditions these techniques lead to generalized and less conservative stability conditions we also consider the robust stability of fuzzy time delay systems with uncertain parameters applying the same techniques made on the stability conditions we obtain delay dependent sufficient conditions for the robust stability of uncertain fuzzy systems with discrete and distributed delays moreover we consider the state feedback stabilization based on stability and robust stability conditions we obtain conditions for the state feedback controller to stabilize the fuzzy time delay systems finally we give two examples to illustrate our results delay dependent stability conditions obtained here are shown to guarantee a wide stability region

h control for sampled data nonlinear systems described by takagi sugeno fuzzy systems in this paper we consider the design problem of output feedback h controllers for sampled data fuzzy systems we first transfer them into equivalent jump fuzzy systems we establish the so called bounded real lemma for jump fuzzy systems and give a design method of suboptimal output feedback h controllers in terms of two riccati inequalities with jumps we then apply the main results to the sampled data fuzzy systems and obtain a design method of suboptimal output feedback h controllers we give a numerical example and construct a suboptimal output feedback h controller

technical communique improved delay dependent stability criteria for systems with a delay varying in a range this paper provides improved delay dependent stability criteria for systems with a delay varying in a range the criteria improve over some previous ones in that they have fewer matrix variables yet less conservatism which is established theoretically an example is given to show the advantages of the proposed results

some remarks on the use of time varying delay to model sample and hold circuits this note revises the so called input delay approach to the control of sampled data systems with nonuniform sampling in which the sample and hold circuit is embedded into an analog system with a time varying input delay it is shown that the conservatism in calculating the maximal admissible sampling period is reduced by about 57 if the time varying delay embedding step is omitted

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

new results on delay dependent robust stability criteria of uncertain fuzzy systems with state and input delays this paper focuses on the delay dependent stability analysis and stabilization for uncertain t s fuzzy control systems with state and input delays the key features of the approach include the introduction of uncorrelated augmented matrix items into the lyapunov functional and the use of a tighter bounding technology in fact these techniques lead to more general and less conservative stability conditions that guarantee a wide stability region our delay dependent stability conditions thus obtained are given in terms of linear matrix inequalities lmis finally some examples are included to show that the proposed criteria improve the existing results significantly

local stabilization of discrete time t s fuzzy systems with magnitude and energy bounded disturbances recently the local stability and local stabilization problems have been investigated by several authors for nonlinear systems described by takagi sugeno t s fuzzy systems in this paper we study the local stabilization problem for discrete time t s fuzzy systems with magnitude and energy bounded disturbances the control design problem is cast as a linear matrix inequality lmi optimization the state feedback controller is designed in such a way that if the initial state is within a certain domain then the state trajectories under bounded disturbances will not escape the fuzzy modelling region of the state space finally examples are given to demonstrate the validity of the proposed method

sliding mode fuzzy control for takagi sugeno fuzzy systems with bilinear consequent part subject to multiple constraints this paper investigated the multiple performance constrained sliding mode fuzzy control problem for continuous time stochastic nonlinear systems with multiplicative noises the stochastic nonlinear systems considered in this paper are represented by takagi sugeno t s fuzzy models with a bilinear consequent part to simultaneously satisfy stability passivity and variance constraints sufficient conditions are derived in terms of linear matrix inequalities based on lyapunov theory by solving the corresponding sufficient conditions a parallel distributed compensation based fuzzy controller is obtained to ensure the stability of the closed loop nonlinear systems subject to variance and passivity performance constraints the main contribution of this paper is a sliding mode fuzzy controller developed such that the considered multiple performance constraints can be satisfied for the t s fuzzy systems with a bilinear consequent part finally a numerical example for controlling a ship steering system is provided to demonstrate the validity and effectiveness of the proposed sliding mode fuzzy control method

improved delay dependent robust stabilization conditions of uncertain t s fuzzy systems with time varying delay this paper aims to develop simplified yet improved delay dependent robust control for uncertain t s fuzzy systems with time varying delay this is achieved through constructing new lyapunov krasovskii functionals and improving jensen s inequality unlike existing work in this area the approach developed in this paper employs neither free weighing matrices nor model transformations as a result simplified yet improved stability conditions are obtained for t s fuzzy systems with norm bounded type uncertainties for controller synthesis of the fuzzy systems the stabilization problem with memoryless state feedback control is solved via utilizing a cone complementarity minimization algorithm numerical examples are given to demonstrate the effectiveness of the proposed approach

a class of bessel summations these quantities have a host of useful properties which are concisely summarized in 3 in particular l s x is an entire function except for the trivial character x n 1 for which l s 1 c s has a simple pole at s 1 we shal express s x as a power series indicate various sets of parameters for which it can be summed in closed form and give some examples the mellin transform of s x is 2

cubature on wiener space it is well known that there is a mathematical equivalence between solving parabolic partial differential equations pdes and the integration of certain functionals on wiener space monte carlo simulation of stochastic differential equations sdes is a naive approach based on this underlying principle in finite dimensions it is well known that cubature can be a very effective approach to integration we discuss the appropriate extension of this idea to wiener space in the process we develop high order numerical schemes valid for high dimensional sdes and semi elliptic pdes

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 parallel plate fed slot antenna loaded by a dielectric semicylinder moment method oriented singular integral equation techniques are used for the exact analysis of parallel plate fed slot antennas loaded by a dielectric semicylinder both for tm and for te incident mode excitations high order acceleration techniques are developed that help recast all matrix elements into rapidly converging series this in conjunction with the small matrix sizes required enables one to obtain extremely accurate results with low computational cost

improved delay dependent stability criteria for time delay systems this note provides an improved asymptotic stability condition for time delay systems in terms of a strict linear matrix inequality unlike previous methods the mathematical development avoids bounding certain cross terms which often leads to conservatism when time varying norm bounded uncertainties appear in a delay system an improved robust delay dependent stability condition is also given examples are provided to demonstrate the reduced conservatism of the proposed conditions

fuzzy guaranteed cost control for nonlinear systems with time varying delay this paper focuses on the problem of guaranteed cost control for takagi sugeno t s fuzzy systems with time varying delayed state a linear quadratic cost function is considered as a performance index of the closed loop fuzzy system then the guaranteed cost control of the closed loop fuzzy system is discussed and the sufficient conditions are provided for the construction of a guaranteed cost controller via state feedback and observer based output feedback when these conditions which are given in terms of the feasibility of linear matrix inequalities lmis are satisfied the designed state feedback controller and observer based controller gain matrices can be obtained via a convex optimization problem two illustrative examples are provided to demonstrate the effectiveness of the approaches proposed in this paper

stabilization of nonlinear systems under variable sampling a fuzzy control approach this paper investigates the problem of stabilization for a takagi sugeno t s fuzzy system with nonuniform uncertain sampling the sampling is not required to be periodic and the only assumption is that the distance between any two consecutive sampling instants is less than a given bound by using the input delay approach the t s fuzzy system with variable uncertain sampling is transformed into a continuous time t s fuzzy system with a delay in the state though the resulting closed loop state delayed t s fuzzy system takes a standard form the existing results on delay t s fuzzy systems cannot be used for our purpose due to their restrictive assumptions on the derivative of state delay a new condition guaranteeing asymptotic stability of the closed loop sampled data system is derived by a lyapunov approach plus the free weighting matrix technique based on this stability condition two procedures for designing state feedback control laws are given one casts the controller design into a convex optimization by introducing some over design and the other utilizes the cone complementarity linearization idea to cast the controller design into a sequential minimization problem subject to linear matrix inequality constraints which can be readily solved using standard numerical software an illustrative example is provided to show the applicability and effectiveness of the proposed controller design methodology

guaranteed cost control of t s fuzzy systems with state and input delays this paper focuses on the problem of guaranteed cost control for t s fuzzy systems with state and input delays stability and stabilization conditions are first proposed which are delay dependent for state delay and delay independent for input delay further the guaranteed cost problem is addressed all the results are presented in terms of linear matrix inequalities lmis some examples are used to illustrate the effectiveness and feasibility of the approaches proposed in this paper

sampled data robust h control for t s fuzzy systems with time delay and uncertainties abstract this paper investigates sampled data robust h control for t s fuzzy systems with time delay and uncertainties by introducing the free weighting matrices to deal with the integral items and converting the coupling time varying matrix inequalities into a group of decoupling matrix inequalities an innovative delay dependent stabilization criterion is first presented then a sampled data h controller is designed to stabilize the t s fuzzy system to achieve the prescribed disturbance attenuation level which is dependent on both the size of state delay and upper bound of allowable sampling period since 1 the sawtooth structure of delay is fully considered 2 neither model transformation nor bounding techniques are employed in deriving the delay dependent results and 3 none of the integral items are arbitrarily ignored and magnified the less conservative results can be expected a practical application example is given to demonstrate the effectiveness of the proposed methods

on equivalence and efficiency of certain stability criteria for time delay systems in recent years there have been a number of new delay dependent stability criteria based on linear matrix inequalities published in the literature this note aims to theoretically establish the equivalence of seven of these stability criteria moreover the efficiency of these stability criteria is assessed based on the number of unknowns in the linear matrix inequalities

parameterized linear matrix inequality techniques in fuzzy control system design this paper proposes different parameterized linear matrix inequality plmi characterizations for fuzzy control systems these plmi characterizations are in turn relaxed into pure lmi programs which provides tractable and effective techniques for the design of suboptimal fuzzy control systems the advantages of the proposed methods over earlier ones are then discussed and illustrated through numerical examples and simulations

mean square stabilization for sampled data t s fuzzy systems with random packet dropout this paper investigates the problem of mean square stabilization for sampled data takagi sugeno t s fuzzy networked control systems with random packet dropouts the packet dropout process is modeled as a discrete time markovian chain with complete or incomplete accessible transition probability matrix based on the lyapunov function approach sufficient conditions are derived for the mean square stability the corresponding sampled data fuzzy controller design algorithm formulated in terms of linear matrix inequalities is also given based upon the stability conditions the numerical examples and simulations are provided to illustrate the usefulness of the developed theory

robust h_ infty control for uncertain takagi sugeno fuzzy systems with interval time varying delay this paper is concerned with the problem of robust hinfin control for a class of uncertain time delay fuzzy systems the time delay is assumed to be a time varying continuous function belonging to a given interval which means that the lower and upper bounds for the time varying delay are available no restriction on the derivative of the time varying delay is needed which allows the time delay to be a fast time varying function the takagi sugeno t s uncertain fuzzy model with interval time varying delay is adopted based on the lyapunov krasovskii functional approach some delay dependent conditions for the existence of robust hinfin controller are formulated in the form of linear matrix inequalities lmis when these lmis are feasible an hinfin controller is presented a numerical example is given to demonstrate the effectiveness of the proposed method

design of polynomial fuzzy observer controller with membership functions using unmeasurable premise variables for nonlinear systems in this paper the stability of polynomial fuzzy model based pfmb observer control system is investigated via lyapunov stability theory the polynomial fuzzy observer with unmeasurable premise variables is designed to estimate the system states then the estimated system states are used for the state feedback control of nonlinear systems although the consideration of the polynomial fuzzy model and unmeasurable premise variables enhances the applicability of the fuzzy model based fmb control strategy it leads to non convex stability conditions therefore the refined completing square approach is proposed to derive convex stability conditions in the form of sum of squares sos with less manually designed parameters in addition the membership functions of the polynomial observer controller are optimized by the improved gradient descent method which outperforms the widely applied parallel distributed compensation pdc approach according to a general performance index simulation examples are provided to verify the proposed design and optimization scheme

technical communique delay range dependent stability for systems with time varying delay this paper is concerned with the stability analysis for systems with time varying delay in a range an appropriate type of lyapunov functionals is proposed to investigate the delay range dependent stability problem the present results may improve the existing ones due to a method to estimate the upper bound of the derivative of lyapunov functional without ignoring some useful terms and the introduction of additional terms into the proposed lyapunov functional which take into account the range of delay numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method

output feedback lmi tracking control conditions with h criterion for uncertain and disturbed t s models this work concerns the tracking problem of uncertain takagi sugeno t s continuous fuzzy model with external disturbances the objective is to get a model reference based output feedback tracking control law the control scheme is based on a pdc structure a fuzzy observer and a h performance to attenuate the external disturbances the stability of the whole closed loop model is investigated using the well known quadratic lyapunov function the key point of the proposed approaches is to achieve conditions under a lmi linear matrix inequalities formulation in the case of an uncertain and disturbed t s fuzzy model this formulation facilitates obtaining solutions through interior point optimization methods for some nonlinear output tracking control problems finally a simulation is provided on the well known inverted pendulum testbed to show the efficiency of the proposed approach

robust tracking controller design for non gaussian singular uncertainty stochastic distribution systems abstract in this paper the robust tracking control problem for uncertain singular stochastic distribution control sdc systems is considered a new control target where the distribution tracking error at each time instant satisfies a certain upper bound beyond a limited time is proposed this control target is different from the tracking control in the output sdc systems which makes the output probability density function pdf track a desired pdf as close as possible then an instant performance index instead of the infinite integration index is adopted and the upper bound of this index is taken as the stability condition of a lyapunov function to obtain a robust tracking controller via an augmentation control and linear matrix inequality lmi simulations are also included to show the effectiveness of the proposed algorithm and encouraging results have been obtained

robust stability and stabilization for uncertain takagi sugeno fuzzy time delay systems in this paper we consider robust stability and stabilization of uncertain takagi sugeno fuzzy time delay systems where uncertainties come into the state and input matrices some stability conditions and robust stability conditions for fuzzy time delay systems have already been obtained in the literature however those conditions are rather conservative and do not guarantee the stability and robust stability for a wide class of fuzzy systems this is true in case of designing stabilizing controllers for fuzzy time delay systems we first consider robust stability conditions of uncertain fuzzy systems conditions we obtain here are delay dependent conditions that depend on the upper bound of time delay and are given in linear matrix inequalities lmis an appropriate selection of lyapunov krasovskii function and introduction of free weighting matrices generalize robust stability conditions next we consider the stabilization problem with memoryless and delayed feedback controllers based on our generalized robust stability conditions we obtain delay dependent sufficient conditions for the closed loop system to be robustly stable and give a design method of robustly stabilizing controllers finally we give two examples that illustrate our results we compare our conditions with other stability conditions and show our conditions are rather generalized

separability of set valued data sets and existence of support hyperplanes in the support function machine abstract the support function machine sfm has been shown to be effective in separating set valued data sets however in sfm the separability of set valued data and the existence of support hyperplanes which can provide useful guidance for improving algorithms for use in applications have not been discussed in theory therefore in this paper we firstly discuss the problem of whether the linearly separable set valued data in r d are still linearly separable after being mapped into the infinite dimensional banach space c s by support functions secondly we discuss the problem of whether the linearly inseparable set valued data in r d are linearly separable after being mapped into c s if not in which situations are they linearly separable thirdly we discuss the existence of support hyperplanes in sfm finally two experiments with set valued data sets are provided to verify the reasoning in the above discussions and the correctness of their conclusions

two numerical solutions for the parallel plate fed slot antenna an integrodifferential equation for the electric field in the aperture of a parallel plate waveguide fed slot antenna is numerically solved using galerkin s method with a basis of edge condition weighted chebyshev polynomials and pulse expansion with point matching efficient algorithms are obtained for the elements of the reduced matrix equations for both moment methods the numerical convergence of the techniques is demonstrated by the resultant aperture field distributions and input reflection coefficients for the case of dominant transverse electromagnetic mode excitation

an observer based approach to controlling time delay chaotic systems via takagi sugeno fuzzy model this study presents a fuzzy model based control criterion for time delay chaotic systems with uncertainty the takagi sugeno t s fuzzy model is adopted for representing a chaotic system possessing a time delay a unified approach for designing a fuzzy observer which integrates parallel distributed compensation with an adaptive updating method is first discussed an observer based fuzzy control scheme is then developed to deal with stabilization and tracking problems based on lyapunov stability analysis sufficient conditions that ensure robust control performance of time delay chaotic systems are derived these conditions are represented in terms of linear matrix inequalities and adaptive updating laws finally the proposed approach is validated through numerical synchronization stabilization and model tracking control simulations

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

an auxiliary system discretization approach to takagi sugeno fuzzy models abstract this paper proposes a new procedure for discretizing nonlinear systems described by takagi sugeno fuzzy models the discretization procedure consists of obtaining a linear auxiliary system that approximates the takagi sugeno model over a sampling instant by discretizing this auxiliary system a norm bounded uncertain linear discrete time system is found which is capable of representing the fuzzy model this auxiliary system as well as the norm bounded uncertainty is found by solving an optimization problem with linear matrix inequality lmi constraints to illustrate the discretization procedure a constant state observer is synthesized based on simple lmi conditions and then applied to a real nonlinear chua s circuit additionally a state feedback controller based on our discretization approach is synthesized and we obtain larger maximum sampling periods than other tested strategies from the literature

delay dependent stability analysis and controller synthesis for markovian jump systems with state and input delays this paper focuses on the problem of delay dependent robust stochastic stability analysis and controller synthesis for markovian jump systems with state and input delays it is assumed that the delays are constant and unknown but their upper bounds are known by constructing a new lyapunov krasovskii functional and introducing some appropriate slack matrices new delay dependent stochastic stability and stabilization conditions are proposed by means of linear matrix inequalities lmis an important feature of the results proposed here is that all the robust stability and stabilization conditions are dependent on the upper bound of the delays memoryless state feedback controllers are designed such that the closed loop system is robustly stochastically stable some numerical examples are provided to illustrate the effectiveness of the proposed method

a triangulation approach to asymptotically exact conditions for fuzzy summations many takagi sugeno t s fuzzy control synthesis problems in the literature are expressed as the problem of finding decision variables in a double convex sum fuzzy summation of positive definite matrices matricespsila coefficients in the summation take values in the standard simplex this paper presents a triangulation approach to the problem of generating simplicial partitions of the standard simplex in order to set up a family of sufficient conditions and in parallel another family of necessary ones for fuzzy summations the conditions proposed in this paper are asymptotically exact as the size of the involved simplices decreases its conservativeness vanishes for a sufficiently fine partition sufficiently dense mesh of vertex points the set of conditions is in the form of linear matrix inequalities lmis for which efficient software is available