h sub spl infin control of discrete time uncertain systems this paper considers h sub spl infin control problems involving discrete time uncertain linear systems the uncertainty is supposed to belong to convex bounded domains and no additional assumptions are made as for instance matching conditions two h sub spl infin guaranteed cost control problems are solved the first one concerns the determination of a state feedback gain if one exists in such way the h sub spl infin norm of a certain transfer function remains bounded by a prespecified h sub spl infin level for all possible models the second one includes this bound as an additional variable to be minimized to achieve the smallest feasible limiting bound the results follow from the simple geometry of those problems which are shown to be convex in the particular parametric space under consideration an example illustrates the theory

analysis and design of fuzzy control system abstract a continuous time fuzzy control system which is composed of a fuzzy model and a fuzzy controller is proposed under certain conditions the proposed fuzzy control system can be regarded as a fuzzy pid control system the stability analysis of the fuzzy control system is given a sufficient condition to guarantee the stability of the proposed fuzzy control system is proposed in terms of lyapunov s method the results can be applied to the design of a fuzzy pid control system the design procedure can also be applied to the controller design with a non fuzzy model examples are given to illustrate the design of the proposed fuzzy control system

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

chaotic functions with zero topological entropy on caracterise la classe m c i i des applications chaotiques en ce sens on montre que m contient certaines appliquations qui ont a la fois une entropie topologique nulle et des attracteurs infinis on montre que le complement de m consiste en applications qui ont seulement des trajectoires approchables par des cycles

continuous takagi sugeno s models reduction of the number of lmi conditions in various fuzzy control design technics fuzzy models of the takagi sugeno type enable representation of a wide class of nonlinear models conditions about their stabilization can be derived systematically usually these conditions are written as linear matrix inequality lmi problems in this paper we use a collection of properties concerning matrices to extend the area of solutions involving the feedback control laws we will work out with continuous fuzzy models and supply results about the stabilization the regulator problem and also hinfin control solutions based on a reduced number of decision variables implying a reduced number of lmi conditions are also proposed we show that a good tradeoff can been obtained

a piecewise approximation approach to nonlinear systems stability and region of attraction this paper discusses piecewise bilinear models and recurrent fuzzy systems as particular classes of dynamic fuzzy systems which can be dealt with in the same framework due to their structural similarity as universal approximators they are capable of representing any continuous nonlinear system dynamics with arbitrary accuracy by means of a rule base first basic definitions of both systems are revisited here and unifying canonical forms are given then a stability criterion is derived for the system classes which is based on approximating piecewise quadratic lyapunov functions and formulated in terms of linear matrix inequalities the main contribution is the demonstration of the stability analysis and estimation of region of attraction by means of these models outperforming methods reported in the literature

a fuzzy neural multi model for nonlinear systems identification and control the paper proposed to apply a hierarchical fuzzy neural multi model and takagi sugeno t s rules with recurrent neural procedural consequent part for systems identification states estimation and adaptive control of complex nonlinear plants the parameters and states of the local recurrent neural network models are used for a local direct and indirect adaptive trajectory tracking control systems design the designed local control laws are coordinated by a fuzzy rule based control system the upper level defuzzyfication is performed by a recurrent neural network the applicability of the proposed intelligent control system is confirmed by simulation examples and by a dc motor identification and control experimental results two main cases of a reference and plant output fuzzyfication are considered a two membership functions without overlapping and a three membership functions with overlapping in both cases a good convergent results are obtained

robust h control of uncertain fuzzy systems under time varying sampling robust h sampled data control for uncertain fuzzy systems is discussed in many practical situations a system is modeled as a continuous time fuzzy system while the control input is the zero order hold which can be represented as a piecewise continuous delay here we take a delay system approach to the h sampled data control problem the closed loop system with a sampled data state feedback controller becomes a system with time varying delay first h performance conditions for the closed loop system are given in terms of linear matrix inequalities lmis such conditions are derived by using the leibniz newton formula and free weighting matrix method for fuzzy time delay systems under the assumption that sampling time is not greater than some prescribed number then a design method for a robust h sampled data state feedback controller for uncertain fuzzy systems is proposed numerical examples are given to illustrate our robust h sampled data state feedback control design

chaotic iterations of fuzzy sets sufficient conditions are developed for the chaotic behaviour of iterative schemes involving continuous mappings from the metric space en d of fuzzy subsets of rn into itself the application of these conditions is then illustrated by means of a simple example of a mapping from e1 d into itself

newton s method for solving a system of fuzzy nonlinear equations abstract in this paper we propose the numerical solution for a system of fuzzy nonlinear equations by newton s method the fuzzy quantities are presented in parametric form some numerical illustrations are given to show the efficiency of algorithm

fault diagnosis of dynamical systems using recurrent fuzzy systems with application to an electrohydraulic servo axis this paper presents a novel approach for fault isolation based on discrete time recurrent fuzzy systems dtrfs extending the well known static fuzzy systems for fault isolation the dtrfs additionally allows for the isolation of faults causing dynamic residuals and the isolation of multiple subsequently occurring faults due to the flexibility of the dtrfs multiplicative as well as additive faults can be handled the approach is applied to an electrohydraulic servo axis with a duplex valve system experimental results at the testbed underline the effectiveness and applicability of the approach and show the enhanced performance compared to static fuzzy systems and state automata

robust h sub spl infin disturbance attenuation for a class of uncertain discrete time fuzzy systems the paper is concerned with robust stabilization and h sub spl infin control of a class of uncertain discrete time fuzzy systems the class of uncertain systems is described by state space takagi sugeno ts fuzzy models with linear nominal parts and norm bounded parameter uncertainties in the state and output equations first a sufficient condition on robust stability of the fuzzy models is proposed then h sub spl infin disturbance attenuation performance of the fuzzy models is analyzed some sufficient conditions are derived on robust h sub spl infin disturbance attenuation in which both robust stability and a prescribed h sub spl infin performance are required to be achieved irrespective of the uncertainties a numerical example shows the use of the results on the stabilization and h sub spl infin disturbance attenuation of a class of discrete time nonlinear systems via fuzzy switch

holomorphic embeddings of planar domains into c 2 in the case p 1 the question remains open given an open riemann surface e does there exist a proper holomorphic embedding of e into c2 trying to answer this question it is natural to begin with planar domains i e open connected subsets of c very few results are known and even in the simplest cases the construction of such an embedding is not easy kasahara and nishino kn st used a technique involving the fatou bieberbach map from c 2 to c 2 to prove that the unit disc can be properly holomorphically embedded into c 2 their method can be used to prove that for each m e w there is an m connected domain in c which can be properly holomorphically embedded into c 2 laufer la showed that every annulus can be properly holomorphically embedded into c 2 alexander ai used elliptic modular functions to construct such an embedding of the punctured disc into c 2 which after a slight modification becomes a proper holomorphic embedding of the unit disc into c 2

stabilizing controller design for uncertain nonlinear systems using fuzzy models a lyapunov based stabilizing control design method for uncertain nonlinear dynamical systems using fuzzy models is proposed the controller is constructed using a design model of the dynamical process to be controlled the design model is obtained from the truth model using a fuzzy modeling approach the truth model represents a detailed description of the process dynamics the truth model is used in a simulation experiment to evaluate the performance of the controller design a method for generating local models that constitute the design model is proposed sufficient conditions for stability and stabilizability of fuzzy models using fuzzy state feedback controllers are given the results obtained are illustrated with a numerical example involving a four dimensional nonlinear model of a stick balancer

analysis and design of fuzzy control systems using dynamic fuzzy global models a method for analysis and design of a fuzzy controller is developed for a class of fuzzy discrete time systems the method is based on a dynamical fuzzy state space model it is shown that the closed loop fuzzy system can be represented by a dynamical interval system and thus the methods of stability analysis in uncertain linear system theory can be used to analyse the global stability of the closed loop fuzzy system some examples are given to illustrate the application of the method

fuzzy feedback system analysis using transition matrices an analytical characterization of fuzzy feedback systems based on transition matrices is carried out in this paper the analysis faces both systems which use linear operators sum and product and those based on the max min operators we focus on the asymptotic trend of the system when the external input is held constant such study becomes a matrix convergence problem by means of the transition matrices that define the system behavior for the non linear case a sufficient condition of convergence of the system that in particular avoids oscillations is demonstrated

h fuzzy adaptive tracking control design for nonlinear systems with output delays abstract in this study we develop fuzzy adaptive tracking control via two layer fuzzy observers variable structure systems vss and h control algorithm for nonlinear systems with plant uncertainties output delays and external disturbances the takagi sugeno fuzzy dynamic model with adaptation capability is used to approximate the nonlinear system when the system states are not available the states estimated from two layer fuzzy observers combined with vss are used to develop the fuzzy adaptive controller in the first layer the output delays are partitioned into m 1 equal time intervals to construct the same number of fuzzy observers the output delayed states in each time interval are used as the premise variables in the if then rules the second layer of the fuzzy observers uses output delayed error states as its linguistic variables and it is defuzzified from the first layer next we develop a fuzzy adaptive controller to overcome the nonlinearities output delayed states and external disturbances such that h tracking performance is achieved the lyapunov criterion and linear matrix inequalities are used to derive the controller in the present study our previous method is extended to handle a class of uncertain nonlinear systems with output delays and external disturbances which is achieved using robust vss and h control techniques a magnetic levitation system and inverted pendulum system are used as simulation examples to illustrate the validity and confirm the performance of our proposed scheme

fuzzy control of model car this paper discusses fuzzy control of a model car fuzzy control rules are derived by modelling an expert s driving actions experiments are performed using a model car with a sensing unit and a micro computer

regularity and chaos in recurrent fuzzy systems abstract in this paper we shall present a mathematical definition of recurrent fuzzy systems and begin to systematically investigate the underlying theory involved unlike static fuzzy systems recurrent fuzzy systems are equipped with time delayed feedback of their output and allow representing knowledge based dynamic processes that may be stated in the form of if then rules we study their relationship to automata and show that they have an automaton like behavior when appropriately designed in other cases recurrent fuzzy system may exhibit chaotic behavior we present sufficient conditions for the occurrence of chaos in recurrent fuzzy systems that can easily be checked solely on the basis of the qualitative linguistically formulated models we also discuss the extent to which state graphs may be used for describing the behaviors of recurrent fuzzy systems

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

fast inference using transition matrices an extension to nonlinear operators fast inference using transition matrices fitms was recently presented as a new fast algorithm for performing inferences in fuzzy systems however this algorithm only applies to the standard additive model sam using the sum product inference composition in this paper we show how this methodology carries over to more general mamdani fuzzy systems i e those using t norms and t conorms that satisfy a requirement of distributivity in addition fitm as originally described requires inputs to be fuzzy sets we here extend this methodology to handle crisp inputs as well

stable adaptive fuzzy control of nonlinear systems a direct adaptive fuzzy controller that does not require an accurate mathematical model of the system under control is capable of incorporating fuzzy if then control rules directly into the controllers and guarantees the global stability of the resulting closed loop system in the sense that all signals involved are uniformly bounded is developed the specific formula for the bounds is provided so that controller designers can determine the bounds based on their requirements the direct adaptive fuzzy controller is used to regulate an unstable system to the origin and to control the duffing chaotic system to track a trajectory the simulation results show that the controller worked without using any fuzzy control rules and that after fuzzy control rules were incorporated the adaptation speed became much faster it is shown explicitly how the supervisory control forces the state to remain within the constraint set and how the adaptive fuzzy controller learns to regain control

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

matrix modeling of hierarchical fuzzy systems a matrix procedure to obtain a hierarchical decomposition of a multiple input single output miso fuzzy system is proposed it is based on the fast inference using transition matrices fitm framework recently described the resulting hierarchical system is totally equivalent to the original one in terms of input output relation a study of the rule reduction capability of this system is carried out additionally this paper describes a rule base definition procedure of each of the systems resulting within the hierarchy this procedure is based on closed form analytical expressions and it does not need any manual interaction

design of observer based h_ infty control for fuzzy time delay systems this paper addresses the problem of observer based hinfin control for nonlinear systems with time varying delay represented by takagi sugeno t s fuzzy model it presents a single step linear matrix inequality lmi method for the fuzzy control design which overcomes the drawback of the two step lmi approach often encountered in the literature the derivation relies mainly on a proposed matrix decoupling technique using which a resultant matrix inequality can be equivalently converted to strict lmis when restricted to delay free fuzzy systems the present results improve or reduce to existing ones illustrative examples show the effectiveness and merits of the present results

fuzzy regulators and fuzzy observers relaxed stability conditions and lmi based designs this paper presents new relaxed stability conditions and lmi linear matrix inequality based designs for both continuous and discrete fuzzy control systems they are applied to design problems of fuzzy regulators and fuzzy observers first takagi and sugeno s fuzzy models and some stability results are recalled to design fuzzy regulators and fuzzy observers nonlinear systems are represented by takagi sugeno s ts fuzzy models the concept of parallel distributed compensation is employed to design fuzzy regulators and fuzzy observers from the ts fuzzy models new stability conditions are obtained by relaxing the stability conditions derived in previous papers lmi based design procedures for fuzzy regulators and fuzzy observers are constructed using the parallel distributed compensation and the relaxed stability conditions other lmi s with respect to decay rate and constraints on control input and output are also derived and utilized in the design procedures design examples for nonlinear systems demonstrate the utility of the relaxed stability conditions and the lmi based design procedures

a limit theorem in some dynamic fuzzy systems abstract in this paper using a fuzzy relation we define a dynamic fuzzy system with a compact state space by introducing a contraction property we study the limit of a sequence of fuzzy states and obtain a theorem for the existence and uniqueness of the solution of a fuzzy relational equation as an application we deal with a dynamic fuzzy system with a terminal fuzzy gain and give some characterizations for the fuzzy expected gain a numerical example is given to comprehend our idea in this paper

mixed h sub 2 h sub spl infin fuzzy output feedback control design for nonlinear dynamic systems an lmi approach this study introduces a mixed h sub 2 h sub spl infin fuzzy output feedback control design method for nonlinear systems with guaranteed control performance first the takagi sugeno fuzzy model is employed to approximate a nonlinear system next based on the fuzzy model a fuzzy observer based mixed h sub 2 h sub spl infin controller is developed to achieve the suboptimal h sub 2 control performance with a desired h sub spl infin disturbance rejection constraint a robust stabilization technique is also proposed to override the effect of approximation error in the fuzzy approximation procedure by the proposed decoupling technique and two stage procedure the outcome of the fuzzy observer based mixed h sub 2 h sub spl infin control problem is parametrized in terms of the two eigenvalue problems evps one for observer and the other for controller the evps can be solved very efficiently using the linear matrix inequality lmi optimization techniques a simulation example is given to illustrate the design procedures and performances of the proposed method

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

self reference and chaos in fuzzy logic investigates a range of phenomena from dynamical systems or chaos theory which appear in a simple fuzzy logic with the introduction of self reference within that logic self referential sentences exhibit properties of fixed point attractors fixed point repellers and full chaos on the

robust load frequency control for uncertain nonlinear power systems a fuzzy logic approach a new robust load frequency control lfc methodology is proposed for controlling uncertain nonlinear power systems critical nonlinearity in the power system the valve position limit on the governor and the parametric uncertainty are concerned the takagi sugeno fuzzy model of the power system under consideration is first constructed to design the robust fuzzy model based lfc sufficient conditions for the robust asymptotic convergence of the frequency deviation are then provided in terms of linear matrix inequalities boundedness of the other system variables is also studied to ensure justifiable grounds for use of the proposed lfc method simulation results convincingly validate the effectiveness of the novel lfc design scheme and the theoretical discussions which give a positive answer to the quality control of the electric energy

equilibria of continuous time recurrent fuzzy systems abstract unlike static fuzzy systems recurrent fuzzy systems allow representing knowledge based dynamic processes that can be stated in the form of if then rules making it possible to model systems that can only be described qualitatively further possible applications exist in the case where the dynamics of a system are quantitatively known but only in certain mesh points the interpolating character of the fuzzy system between the dynamics of the mesh points yields a complete dynamic model based on discrete time recurrent fuzzy systems this article presents first steps towards the theory of continuous time recurrent fuzzy systems and provides criteria for the investigation of the dynamics of this class of systems

stability and control of fuzzy dynamic systems via cell state transitions in fuzzy hypercubes the objective of this paper is to provide fuzzy control designers with a generalized design tool for stable fuzzy logic controllers in an optimal sense given multiple sets of data disturbed by vagueness uncertainty we generate the implicative rules that guarantee stability and robustness of closed loop fuzzy dynamic systems first the mathematical basis of fuzzy hypercubes and fuzzy dynamic systems is rigorously studied by considering the membership conditions for perfect recall and the evidential combination for reliable reasoning second the author suggests the cell state transition method which utilizes hsu s cell to cell mapping concept as a result a generic and implementable design methodology for obtaining a fuzzy feedback gain k a fuzzy hypercube is provided and illustrated with simple examples the designed rules or membership functions in k form the cell state transitions that lead an initial state to the goal state globally the cell state transition approach provides flexibility in choosing different controller rule bases depending on optimal strategies

parameter identification of recurrent fuzzy systems with fuzzy finite state automata representation this paper presents the identification of nonlinear dynamical systems by recurrent fuzzy system rfs models two types of rfs models are discussed the takagi sugeno kang tsk type and the linguistic or mamdani type both models are equivalent and the latter model may be represented by a fuzzy finite state automaton ffa an identification procedure is proposed based on a standard general purpose genetic algorithm ga first the tsk rule parameters are estimated and in a second step the tsk model is converted into an equivalent linguistic model the parameter identification is evaluated in some benchmark problems for nonlinear system identification described in literature the results show that rfs models achieve good numerical performance while keeping the interpretability of the actual system dynamics

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

robustness design of nonlinear dynamic systems via fuzzy linear control this study introduces a fuzzy linear control design method for nonlinear systems with optimal h sup spl infin robustness performance first the takagi and sugeno fuzzy linear model 1985 is employed to approximate a nonlinear system next based on the fuzzy linear model a fuzzy controller is developed to stabilize the nonlinear system and at the same time the effect of external disturbance on control performance is attenuated to a minimum level thus based on the fuzzy linear model h sup spl infin performance design can be achieved in nonlinear control systems in the proposed fuzzy linear control method the fuzzy linear model provides rough control to approximate the nonlinear control system while the h sup spl infin scheme provides precise control to achieve the optimal robustness performance linear matrix inequality lmi techniques are employed to solve this robust fuzzy control problem in the case that state variables are unavailable a fuzzy observer based h sup spl infin control is also proposed to achieve a robust optimization design for nonlinear systems a simulation example is given to illustrate the performance of the proposed design method

multiple scattering of waves in random media a transfer matrix approach transfer matrices address multiple scattering of waves in dense media by relating properties of a thick slice of medium to the corresponding properties of a slice thin enough for multiple scattering to be absent hence scattering properties can easily be calculated we present a new method for deriving a whole hierarchy of transfer matrices which can be applied to studying statistics of waves in random media under conditions of extreme multiple scattering the new method based on matrix power series expansions confirms early results and carries them forward into new areas allowing us to study density of states fluctuations and transport phenomena

newton s method for solving fuzzy nonlinear equations in this paper we propose the numerical solution for a fuzzy nonlinear equation by newton s method the fuzzy quantities are presented in parametric form some numerical illustrations are given to show the efficiency of algorithms

maximal fluctuations a new phenomenon in disordered systems abstract rigorous results for 1d systems combined with more intuitive results for higher dimensions indicate that there is a universal theorem on fluctuations in the transmission coefficient of disordered systems recognising that the transmission coefficient for waves traversing a disordered system can be no greater than unity and no less than zero the theorem states that in each channel either t 2 1 or t 2 0 with the probability set by the conductance this is the most extreme excursion of the distribution possible hence the name maximal fluctuations the effect is distinct from the universal fluctuations which refer to the sensitivity of t to changes in the medium

analysis and design of fuzzy control systems using dynamic fuzzy state space models a discrete time fuzzy control system which is composed of a dynamic fuzzy model and a fuzzy state feedback controller is proposed stability of the fuzzy control system is discussed and two sufficient conditions to guarantee the stability of the system are given in terms of uncertain linear system theory an algorithm is developed to check the stability condition the controller design method is divided into two procedures one is to get the state feedback matrix by linear system theory in every local rule map the other is to determine conditions of global stability by using a nonlinear analysis method two examples are used to show the design method

characterization of the cal l _2 induced norm for linear systems with jumps with applications to sampled data systems this paper considers a continuous time linear system with finite jumps at discrete instants of time an iterative method to compute the cal l 2 induced norm of a linear system with jumps is presented each iteration requires solving an algebraic riccati equation it is also shown that a linear feedback interconnection of a continuous time finite dimensional linear time invariant fdlti plant and a discrete time finite dimensional linear shift invariant fdlsi controller can be represented as a linear system with jumps this leads to an iterative method to compute the cal l 2 induced norm of a sampled data system

stability analysis and systematic design of fuzzy control systems abstract a method of the stability analysis and systematic design of fuzzy control systems is presented in this paper the fuzzy control system is formulated by a set of local takagi sugeno fuzzy models t s fuzzy model with aggregation the controller is designed by state feedback for each local model separately it is shown that under some conditions the controller designed can guarantee the global stability of the closed loop fuzzy system the stability of the whole closed loop fuzzy system is also proved via the piecewise lyapunov function the simulation results for the fuzzy control of a nonlinear system the ball and beam system bb system show that this method is effective

a fuzzy relational equation in dynamic fuzzy systems for a dynamic fuzzy system the fundamental method is to analyze its recursive relation of the fuzzy states it is similar in that the bellman equation is an important tool in the dynamic programming here we will consider the existence and the uniqueness of solution of a fuzzy relational equation two examples which satisfies our conditions are given to illustrate the results

delay dependent lmi conditions for stability and stabilization of t s fuzzy systems with bounded time delay this paper studies the stability and stabilization problems for time delay nonlinear systems through takagi sugeno t s fuzzy model approach the time delays are assumed to be bounded but perhaps non smooth delay dependent conditions are presented in terms of lmis illustrative examples are given to show the effectiveness and merits of the present results

bloch waves in periodic multi layered acoustic waveguides the band spectrum and associated floquet bloch eigensolutions arising in acoustic and electromagnetic waveguides which have periodic structure along the guide while remaining of finite width are found homogeneous dirichlet or neumann conditions along the guide walls or an alternation of them are taken importantly in some cases a total stop band at zero frequency is identified providing space for low frequency localized modes geometric defects in the structured waveguide also create these modes numerical and asymptotic techniques identify dispersion curves and trapped modes some cases demonstrate maxima and minima of the spectral edges within the brillouin zone and also allow for ultraslow light or sound imaging applications using anomalous dispersion to generate subwavelength resolution are possible and are demonstrated

an interpolation theorem for proper holomorphic embeddings given a stein manifold x of dimension n 1 a discrete sequence a j subset x and a discrete sequence b j subset mathbb c m where m ge n left frac 3n 2 right 1 there exists a proper holomorphic embedding f colon x hookrightarrow mathbb c m satisfying f a j b j for every j 1 2

universality classes and fluctuations in disordered systems the medium we apply this result to trace t tl m where tl is the amplitude transmission matrix the eigenfunctions of tl t define a set of channels through which the current flows and the eigenvalues are the corresponding transmission coefficients we prove that these coefficients are either o 0 or 1 as l increases more channels are shut down this is the maximal fluctuation theorem fluctuations cannot be greater than this we expect that our classification scheme will prove of further value in proving theorems about limiting distributions we show by numerical simulations that our theorem holds good for a wide variety of systems in one two and three dimensions disordered media scatter waves incident upon them and induce in the scattered wavefield a degree of disorder which is far more extreme than the physical disorder of the medium itself the fluctuations are brought about by multiple scattering of the wavefield and its ability to interfere constructively or destructively with itself the most extreme instances are found in the absence of absorption when multiple scattering can have free rein as a specific example we consider the system shown in figure 1 in which waves are incident on a slab of disordered material of finite thickness in one direction but effectively infinite in the other directions we shall assume that the slab is statistically homogeneous the waves can be either transmitted through or reflected from the slab statistics in the transmission coefficient pose particular challenges as the thickness l of the slab is increased fluctuations in the transmission coefficient far from settling down to some average value become more extreme the question is what can we say about the limiting scattering properties of a thick slab of material as far as we are aware this question has only been addressed for special cases the results we derive here apply in very general circumstances

an approach to h control of fuzzy dynamic systems this paper presents an approach to h control of a class of continuous time nonlinear systems which can be represented by a fuzzy dynamic model a suitable piecewise differentiable quadratic lyapunov function is used to establish asymptotic stability and h performance of the closed loop fuzzy control system a constructive algorithm is developed to obtain the h feedback control law which involves solving a set of suitable algebraic riccati equations an example is given to illustrate the application of the method

analysis and design for a class of complex control systems part i fuzzy modelling and identification this paper is the first of two dealing with the analysis and design of a class of complex control systems this part deals with fuzzy modelling and identification the second paper is concerned with fuzzy controller design we believe that these two papers show a way to analyze and design complex control systems using a combination of fuzzy logic and modern control theory the complex systems studied in these two papers can be represented by a fuzzy aggregation of a set of local linear models the identification can be divided into two procedures the first procedure is the identification of the membership functions including the determination of the number of fuzzy rules and the estimation of the parameters in the membership functions the second is the identification of the local linear models including the determination of the structure and the parameters of the local rule maps and the global rule interpolation two examples are used to demonstrate the application of the modelling method

robust stabilization of uncertain linear systems quadratic stabilizability and h sup infinity control theory the problem of robustly stabilizing a linear uncertain system is considered with emphasis on the interplay between the time domain results on the quadratic stabilization of uncertain systems and the frequency domain results on h sup infinity optimization a complete solution to a certain quadratic stabilization problem in which uncertainty enters both the state and the input matrices of the system is given relations between these robust stabilization problems and h sup infinity control theory are explored it is also shown that in a number of cases if a robust stabilization problem can be solved via lyapunov methods then it can be also be solved via h sup infinity control theory based methods

qualitative modeling of dynamical systems employing continuous time recurrent fuzzy systems continuous time recurrent fuzzy systems ctrfs allow the representation of knowledge based dynamic processes that can be stated in the form of if then rules in this article we show how a ctrfs can not only be modeled by linguistically given knowledge but also by measured data furthermore a unified approach for both structure and parameter identification of continuous time recurrent fuzzy systems will be presented resulting in a linguistically interpretable model of the considered dynamic process the capability of the approach is shown by modeling of a biotechnological process

h sub infinity control and filtering for sampled data systems h sub infinity control and filtering problems for sampled data systems are studied necessary and sufficient conditions are obtained for the existence of controllers and filters that satisfy a specified h sub infinity performance bound when these conditions hold explicit formulas for a controller and a filter satisfying the h sub infinity performance bound are also given

embedding some riemann surfaces into mathbb c 2 with interpolation we prove that several types of open riemann surfaces including the finitely connected planar domains embed properly into mathbb c 2 such that the values on any given discrete sequence can be arbitrarily prescribed

an approach to h control of a class of nonlinear systems this paper considers robust h control of a class of nonlinear systems that can be represented by a heterogeneous model a new controller design method using both state feedback is proposed based on quadratic stability theory a number of necessary and sufficient conditions are derived for quadratic stabilizability with disturbance attenuation of the control system concerned an example is also given to demonstrate the performance of the proposed controller design methods

proper holomorphic embeddings of finitely and some infinitely connected subsets of into we show that any finitely connected domain open image in new window can be properly embedded into open image in new window for some sequences open image in new window can also be properly embedded into open image in new window

fast inference in sam fuzzy systems using transition matrices fast inference using transition matrices fitm is a new fast algorithm for performing inferences in fuzzy systems it is based on the assumption that fuzzy inputs can be expressed as a linear composition of the fuzzy sets used in the rule base this representation let us interpret a fuzzy set as a vector so we can just work with the coordinates of it instead of working with the whole set the inference is made using transition matrices the key of the method is the fact that a lot of operations can be precomputed offline to obtain the transition matrices so actual inferences are reduced to a few online matrix additions and multiplications the algorithm is designed for the standard additive model using the sum product inference composition

equilibria of recurrent fuzzy systems unlike static fuzzy systems recurrent fuzzy systems are equipped with feedback loops and thus exhibit dynamic behaviors the dynamics of a recurrent fuzzy system is largely determined by its rule base the dynamic behavior of a significant subclass of recurrent fuzzy systems may be immediately deduced from their rule base without need for analyzing their mathematical description their equilibrium points may be readily identified and their stability behaviors investigated based on their rule base the investigations involved lead to convergence theorems and other statements that preclude chaotic dynamics