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

the zeros of derivatives of entire functions and the polya wiman conjecture an entire function f x which assumes only real values on the real axis is said to be a real entire function thus if f is a real entire function then its maclaurin coefficients are all real and consequently the zeros of f are symmetrically located with respect to the real axis one of the intuitive principles underlying the theory of distribution of zeros of successive derivatives of real entire functions was formulated by polya p4 in his celebrated survey article entitled on the zeros of the derivatives of a function and its analytic character in this work p4 p 181 polya states the real axis seems to exert an influence on the complex zeros of f n z it seems to attract these zeros when the order is less than 2 and it seems to repel them when the order is greater than 2 indeed the first confirmation of this principle was made by alander a2 see also p6lya p2 who in 1930 showed that the polya wiman conjecture is true if the order of f x is less than 2 3 in wil and wi2 wiman established the validity of this conjecture for functions f x of order at most 1 while in 1937 polya p3 proved it for functions of order less than 4 3 a general survey of these results and related conjectures may be found in p2 and p4 for more recent surveys of this and related areas of research see boas b2 and prather pr it seems that no progress has been made on the p6lya wiman conjecture since the publication of polya s 4 3 theorem in 1937 our proof of the conjecture is self contained and does not rely on the results cited above in section 2 we will 1 introduce some definitions and notations 2 state some of the properties of functions in the laguerre p6lya class and 3 prove the polya wiman conjecture theorem 3 in the proof of theorem 3 we

collocation software for boundary value differential algebraic equations we describe the methods and implementation of a general purpose code coldae this code can solve boundary value problems for nonlinear systems of semi explicit differential algebraic equations daes of index at most 2 fully implicit index 1 boundary value dae problems can be handled as well the code coldae is an extension of the package colnew colsys for solving boundary value odes the implemented method is piecewise polynomial collocation at gaussian points extended as needed by the projection method of ascher petzold for general semi explicit index 2 problems as well as for fully implicit index 1 problems we define a em selective projected collocation method and demonstrate its use the mesh selection procedure of colsys is modified for the case of index 2 constraints we also discuss shooting for initial guesses the power and generality of the code are demonstrated by examples

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

nonlinear mixed h 2 h control for robust tracking design of robotic systems a mixed h 2 h control design is proposed in this study for tracking of rigid 2 robotic systems under parameter perturbations and external disturbances the design objective is that under a prescribed disturbance attenuation level h attenuation constraint the optimal least square error h 2 optimal tracking 2 must be achieved additionally an explicit and global solution to this nonlinear time varying mixed h 2 h control problem is presented by combining nonlinear minimax nash game theory and lq optimal control techniques moreover by virtue of the skew symmetric property of robotic systems and adequate choice of state variable transformation only two linear algebraic instead of nonlinear timevarying riccati like equations are required to construct the proposed mixed h 2 h tracking control law furthermore these two linear algebraic equations 2 can be solved with a very simple method so that a closed form nonlinear mixed h 2 h tracking controller can be constructed finally extensive

collocation methods for index 1 daes with a singularity of the first kind we study the convergence behavior of collocation schemes applied to approximate solutions of bvps in linear index 1 daes which exhibit a critical point at the left boundary such a critical point of the dae causes a singularity within the inherent ode system we focus our attention on the case when the inherent ode system is singular with a singularity of the first kind apply polynomial collocation to the original dae system and consider different choices of the collocation points such as equidistant gaussian or radau points we show that for a well posed boundary value problem for daes having a sufficiently smooth solution the global error of the collocation scheme converges with the order o h s where s is the number of collocation points superconvergence cannot be expected in general due to the singularity not even for the differential components of the solution the theoretical results are illustrated by numerical experiments

on the stability of fuzzy systems studies the global asymptotic stability of a class of fuzzy systems it demonstrates the equivalence of stability properties of fuzzy systems and linear time invariant lti switching systems a necessary and sufficient condition for the stability of such systems are given and it is shown that under the sufficient condition a common lyapunov function exists for the lti subsystems a particular case when the system matrices can be simultaneously transformed to normal matrices is shown to correspond to the existence of a common quadratic lyapunov function a constructive procedure to check the possibility of simultaneous transformation to normal matrices is provided

a nash game approach to mixed h sub 2 h sub spl infin control the established theory of nonzero sum games is used to solve a mixed h sub 2 h sub spl infin control problem our idea is to use the two pay off functions associated with a two player nash game to represent the h sub 2 and h sub spl infin criteria separately we treat the state feedback problem and we find necessary and sufficient conditions for the existence of a solution both the finite and infinite time problems are considered in the infinite horizon case we present a full stability analysis the resulting controller is a constant state feedback law characterized by the solution to a pair of cross coupled riccati equations which may be solved using a standard numerical integration procedure we begin our development by considering strategy sets containing linear controllers only at the end of the paper we broaden the strategy sets to include a class of nonlinear controls it turns out that this extension has no effect on the necessary and sufficient conditions for the existence of a solution or on the nature of the controllers

novel stability criteria for t s fuzzy systems in this paper novel stability conditions for takagi sugeno t s fuzzy systems are presented the so called nonquadratic membership dependent lyapunov function is first proposed which is formulated in a higher order form of both the system states and the normalized membership functions than existing techniques in the literature then new membership dependent stability conditions are developed by the new lyapunov function approach it is shown that the conservativeness of the obtained criteria can be further reduced as the degree of the lyapunov function increases two numerical examples are given to demonstrate the effectiveness and less conservativeness of the obtained theoretical results

lqg control with an h sup infinity performance bound a riccati equation approach an lqg linear quadratic gaussian control design problem involving a constraint on h sup infinity disturbance attenuation is considered the h sup infinity performance constraint is embedded within the optimization process by replacing the covariance lyapunov equation by a riccati equation whose solution leads to an upper bound on l sub 2 performance in contrast to the pair of separated riccati equations of standard lqg theory the h sup infinity constrained gains are given by a coupled system of three modified riccati equations the coupling illustrates the breakdown of the separation principle for the h sup infinity constrained problem both full and reduced order design problems are considered with an h sup infinity attenuation constraint involving both state and control variables an algorithm is developed for the full order design problem and illustrative numerical results are given

disturbance observer based robust mixed h2 h fuzzy tracking control for hypersonic vehicles this paper introduces a disturbance observer do based mixed h2 h robust fuzzy tracking control design for the longitudinal dynamics of a generic hypersonic vehicle hv with modeled and unmodeled disturbances a takagisugeno ts fuzzy model is firstly employed to approximate the nonlinear dynamics of hv subsequently based on the fuzzy model a do is constructed to estimate the modeled disturbance next by integrating the hv dynamics the tracking error integral and the disturbance estimation error dynamics an augmented system is established for the control design then a do based mixed h2 h robust fuzzy control design is developed to ensure the asymptotic stability as well as the mixed h2 h control performance of the augmented system the proposed control scheme includes a fuzzy tracking controller with state feedback plus the tracking error integral a robust nonlinear compensator for eliminating the matched part of the compound disturbance consisting of the unmodeled disturbance and fuzzy modeling error and a do based compensator for the modeled disturbance cancellation the outcome of the do based mixed h2 h robust fuzzy control problem is formulated in terms of linear matrix inequalities lmis furthermore by utilizing the existing lmi optimization technique a suboptimal controller is obtained in the sense of minimizing an upper bound of h2 performance finally simulation results on an hv demonstrate the effectiveness of the proposed design method

mixed h 2 h autopilot design of bank to turn missiles using fuzzy basis function networks this paper presents a novel mixed h2 h autopilot design for bank to turn missiles based on sliding control theory the proposed autopilot utilizes a fuzzy basis function network to approximate the unknown nonlinear functions of bank to turn missile dynamics enabling a mixed h2 h controller with weight updating laws to be applied to attenuate the effects of approximation errors and external disturbances moreover the mixed h2 h autopilot design can minimize h2 performance criteria under a desired h disturbance rejection constraint unlike general mixed h2 h control problems the proposed h2 h autopilot with self tuning fuzzy basis function network can avoid solving coupled riccati equations by adequately selecting diagonal weighting matrices in the h2 performance criterion and h constraint therefore the proposed h2 h control approach can be implemented efficiently computer simulation results are presented to illustrate the effectiveness of the proposed mixed h2 h autopilot for btt missiles

multiobjective output feedback control via lmi optimization this paper presents an overview of a linear matrix inequality lmi approach to the multiobjective synthesis of linear output feedback controllers the design objectives can be a mix of h sub spl infin performance h sub 2 performance passivity asymptotic disturbance rejection time domain constraints and constraints on the closed loop pole location in addition these objectives can be specified on different channels of the closed loop system when all objectives are formulated in terms of a common lyapunov function controller design amounts to solving a system of linear matrix inequalities the validity of this approach is illustrated by a realistic design example

convergence of collocation schemes for boundary value problems in nonlinear index 1 daes with a singular point we analyze the convergence behavior of collocation schemes ap plied to approximate solutions of bvps in nonlinear index 1 daes which exhibit a critical point at the left boundary such a critical point of the dae causes a singularity in the inherent nonlinear ode system in particular we focus on the case when the inherent ode system is singular with a singularity of the rst kind and apply polynomial collocation to the original dae system we show that for a certain class of well posed boundary value problems in daes having a sufficiently smooth solution the global error of the collocation scheme converges uniformly with the so called stage order due to the sin gularity superconvergence at the mesh points does not hold in general the theoretical results are supported by numerical experiments

analysis of a new error estimate for collocation methods applied to singular boundary value problems we discuss an a posteriori error estimate for the numerical solution of boundary value problems for nonlinear systems of ordinary differential equations with a singularity of the first kind the estimate for the global error of an approximation obtained by collocation with piecewise polynomial functions is based on the defect correction principle we prove that for collocation methods which are not superconvergent the error estimate is asymptotically correct as an essential prerequisite we derive convergence results for collocation methods applied to nonlinear singular problems

a fuzzy logic based approach to qualitative modeling this paper discusses a general approach to quali tative modeling based on fuzzy logic the method of qualitative modeling is divided into two parts fuzzy modeling and linguistic approximation it proposes to use a fuzzy clustering method fuzzy c means method to identify the structure of a fuzzy model to clarify the advantages of the proposed method it also shows some examples of modeling among them a model of a dynamical process and a model of a human operator s control action

the convergence of shooting methods for singular boundary value problems we investigate the convergence properties of single and multiple shooting when applied to singular boundary value problems particular attention is paid to the well posedness of the process it is shown that boundary value problems can be solved efficiently when a high order integrator for the associated singular initial value problems is available moreover convergence results for a perturbed newton iteration are discussed

newton cotes integration for approximating stieltjes generalized euler constants in the laurent expansion s a 1 s 1 k 0 1 k k a k s 1 k 0 1 we also conjecture that limk k 1 2 k k 0 a special case of a more general conjecture relating the values of k a and k a for 0 0 we conjecture that for nonintegral r r is precisely 1 r times the r th weyl fractional derivative at s 1 of the entire function s 1 s 1 1 we also conjecture that g now defined for all real arguments r 0 is smooth our numerical method uses newton cotes integration formulae for very high degree interpolating polynomials it differs in implementation from but compares in error bounding to euler maclaurin summation based methods

robust h control of multiple time delay uncertain nonlinear system using fuzzy model and adaptive neural network in this paper a robust control method which combines fuzzy model based control with adaptive neural network control is presented for a class of uncertain nonlinear system with multiple time delay the fuzzy t s model with multiple time delay is adopted for the approximate modeling of the nonlinear system with some unknown uncertainties and fuzzy model based h control law is designed by means of lmi method a full adaptive rbf neural network is added to the fuzzy h control in order to guarantee the robust stability of the controlled system the effect of the unknown uncertainties and the error caused by fuzzy modeling can be overcome by adaptive tuning of the weights centers and widths of the rbf neural network on line and no constraint or matching conditions are required the stability of the designed closed loop system is thus proved the proposed method is applied to a multiple time delay nonlinear chaotic system and the simulation results show that the proposed method cannot only stabilize the chaos systems but has strong robustness against uncertainties and external disturbance

an approach to fuzzy control of nonlinear systems stability and design issues presents a design methodology for stabilization of a class of nonlinear systems first the authors represent a nonlinear plant with a takagi sugeno fuzzy model then a model based fuzzy controller design utilizing the concept of the so called parallel distributed compensation is employed the main idea of the controller design is to derive each control rule so as to compensate each rule of a fuzzy system the design procedure is conceptually simple and natural moreover the stability analysis and control design problems can be reduced to linear matrix inequality lmi problems therefore they can be solved efficiently in practice by convex programming techniques for lmis the design methodology is illustrated by application to the problem of balancing and swing up of an inverted pendulum on a cart

on the number of nonreal zeros of real entire functions and the fourier polya conjecture this paper is concerned with a general theorem on the number of nonreal zeros of transcendental functions j fourier formulated the theorem in his work analyse des equations determineesin 1831 but he did not give a proof roughly speaking the theorem states that if a real entire function f x can be expressed as a product of linear factors then we can count the nonreal zeros of f x by observing the behavior of the derivatives of f x on the real axis alone as we shall see in the sequel this theorem completely justifies his former argument by which he tried to prove that the function j0 2 x has only real zeros it seems that no complete proof of the theorem is known and no general theorem has been published that justifies the argument later in 1930 g polya published a paper entitled some problems connected with fourier s work on transcendental equations p3 in this paper polya conjectured two hypothetical theorems that are closely related to fourier s unproved theorem in fact he conjectured three but he proved that two of them are equivalent to each other the first hypothetical theorem is a modernized formulation of the theorem and it justifies fourier s argument completely the second conjecture was proved in 1990 but it is impossible to justify the argument using the conjecture alone in the present paper we prove polya s formulation of the theorem his first conjecture as well as its extensions give a very simple and direct proof of the second conjecture mentioned above and exhibit some applications of the results in particular we completely justify fourier s argument by our general theorems acknowledgments professor fefferman has encouraged and helped us to publish this paper the authors truly thank him for this the authors also thank professor csordas for his kind interest in the results and his valuable suggestions on the proof of the polya wiman conjecture 1 historical introduction in this section we briefly explain our results as well as their background a real entire function is an entire function that assumes only real values on the real axis fourier s unproven theorem asserts that we can know the number of nonreal zeros of such real entire functions by counting their critical points which are defined as follows let f x be a real analytic function defined in an open

disturbance attenuation and h sub infinity control via measurement feedback in nonlinear systems a solution to the problem of disturbance attenuation via measurement feedback with internal stability is presented for an affine nonlinear system it is shown that the concept of disturbance attenuation in the sense of truncated l sub 2 norms can be given an interpretation in terms of the response to periodic inputs in the sense of rms amplitude even in the nonlinear setup in the case of state feedback a family of controllers is also provided the proofs of all these results are simple and provide deeper insight even in the analysis of the corresponding linear control problem

multiobjective investment policy for a nonlinear stochastic financial system a fuzzy approach the financial market always suffers from continuous and discontinuous jump changes and can be regarded as a nonlinear stochastic jump diffusion system most investors expect their investment policies to be not only higher benefits but also lower risk as a multiobjective optimization problem mop in this study a multiobjective h 2 h infty fuzzy investment is proposed for nonlinear stochastic jump diffusion financial systems to achieve the desired target with minimum investment cost and risk in pareto optimal sense simultaneously the takagi sugeno t s fuzzy model is used to approximate the nonlinear stochastic jump diffusion financial system to simplify the multiobjective h 2 h infty investment policy design procedure by the help of the t s fuzzy model the multiobjective h 2 h infty fuzzy investment policy problem of nonlinear stochastic financial system can be transformed to a linear matrix inequality constrained lmi constrained mop to avoid solving the annoying hamilton jacobi inequalities because the lmi constrained mop is not easy to directly calculate its pareto optimal solutions an indirect method is proposed to solve this mop for the multiobjective h 2 h infty fuzzy investment policy design of nonlinear stochastic jump diffusion financial systems an lmi constrained multiobjective evolution algorithm lmi constrained moea is also developed to efficiently solve the pareto optimal solutions of the lmi constrained mop for the multiobjective h 2 h infty fuzzy investment policy design of nonlinear stochastic jump diffusion financial systems when the pareto optimal regulation solutions are solved by the proposed lmi constrained moea investors can select one investment policy to achieve their desired target with minimum investment cost and risk according to his her own preference

h sub spl infin output feedback control of discrete time fuzzy systems with application to chaos control this paper presents an observer based h sub spl infin output feedback synthesis method for discrete time fuzzy dynamic systems based on a piecewise lyapunov function the basic idea of the approach is to design an observer based piecewise linear output feedback control law to guarantee the global stability with h sub spl infin performance of the resulting closed loop fuzzy control systems it is shown that the controller parameters can be obtained by solving a set of linear matrix inequalities lmis that are numerically feasible with commercially available software application to control chaotic systems is given to illustrate the effectiveness and advantages of the proposed method

lmi based fuzzy chaotic synchronization and communications addresses synthesis approaches for signal synchronization and secure communications of chaotic systems by using fuzzy system design methods based on linear matrix inequalities lmis by introducing a fuzzy modeling methodology many well known continuous and discrete chaotic systems can be exactly represented by takagi sugeno t s fuzzy models with only one premise variable following the general form of fuzzy chaotic models the structure of the response system is first proposed then according to the applications of synchronization to the fuzzy models that have common bias terms or the same premise variable of drive and response systems the driving signals are developed with four different types fuzzy character crisp and predictive driving signals synthesizing from the observer and controller points of view all types of drive response systems achieve asymptotic synchronization for chaotic communications the asymptotical recovering of messages is ensured by the same framework it is found that many well known chaotic systems can achieve their applications on asymptotical synchronization and recovering messages in secure communication by using either one type of driving signals or all several numerical simulations are shown with expected satisfactory performance

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

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

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

the application of runge kutta schemes to singular initial value problems a theory for explicit runge kutta schemes applied to the initial value problem for a first order system of differential equations with a singularity of the first kind is developed it is shown that in general the order of convergence is at most two but that the usual order up to a logarithmic term can be obtained for level three and four schemes applied to specific problems 1 introduction in this paper we examine the application of explicit runge kutta schemes to the numerical solution of the problem

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

differentiation evens out zero spacings if f is a polynomial with all of its roots on the real line then the roots of the derivative f are more evenly spaced than the roots of f the same holds for a real entire function of order 1 with all its zeros on a line in particular we show that if f is entire of order 1 and has sufficient regularity in its zero spacing then under repeated differentiation the function approaches after normalization the cosine function we also study polynomials with all their zeros on a circle and we find a close analogy between the two situations this sheds light on the spacing between zeros of the riemann zeta function and its connection to random matrix polynomials

mixed spl hscr sub 2 and spl hscr sub spl infin performance objectives ii optimal control this paper considers the analysis and synthesis of control systems subject to two types of disturbance signals white signals and signals with bounded power the resulting control problem involves minimizing a mixed spl hscr sub 2 and spl hscr sub spl infin norm of the system it is shown that the controller shares a separation property similar to those of pure spl hscr sub 2 or spl hscr sub spl infin controllers necessary conditions and sufficient conditions are obtained for the existence of a solution to the mixed problem explicit state space formulas are also given for the optimal controller

new approaches to relaxed quadratic stability condition of fuzzy control systems this paper deals with the quadratic stability conditions of fuzzy control systems that relax the existing conditions reported in the previous literatures two new conditions are proposed and shown to be useful in analyzing and designing fuzzy control systems the first one employs the s procedure to utilize information regarding the premise parts of the fuzzy systems the next one enlarges the class of fuzzy control systems whose stability is ensured by representing the interactions among the fuzzy subsystems in a single matrix and solving it by linear matrix inequality the relationships between the suggested stability conditions and the conventional well known stability conditions reported in the previous literatures are also discussed and it is shown in a rigorous manner that the second condition of this paper includes the conventional conditions finally some examples and simulation results are presented to illustrate the effectiveness of the stability conditions

fuzzy control theory a nonlinear case abstract sources of nonlinearity in a fuzzy controller include the fuzzification algorithm used for the controller inputs fuzzy control rules type of fuzzy logic used for evaluating the fuzzy control rules and the defuzzification algorithm used for the controller output we analyze the performance of a simple fuzzy controller with linear and nonlinear defuzzification algorithms we prove theoretically that such a fuzzy controller the smallest possible with two inputs error and rate change of error and a nonlinear defuzzification algorithm is equivalent to a nonfuzzy nonlinear proportional integral pi controller with proportional gain and integral gain changing with error and rate change of error about a setpoint furthermore this fuzzy controller is precisely equivalent to a conventional linear pi controller if a linear defuzzification algorithm is employed computer simulation showed that the performance of the fuzzy controller was almost the same as that of the pi controller when first order and second order linear processes were used furthermore the fuzzy controller was significantly better when a first order with a time delay model was used more importantly the simulated result illustrated that the fuzzy controller was stable when a nonlinear process model was controlled but the pi controller was unstable

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

control synthesis of t s fuzzy systems based on a new control scheme this paper studies the control synthesis problem of takagi sugeno t s fuzzy systems by splitting the premise variable spaces and using the properties of fuzzy sets a new control scheme is proposed based on a new class of fuzzy lyapunov functions and a convex condition for designing fuzzy controllers is given where the new fuzzy lyapunov functions and fuzzy controllers are constructed based on the split subspaces in particular some existing fuzzy lyapunov functions and control schemes are special cases of the new lyapunov function and control scheme respectively numerical examples are given to illustrate the effectiveness of the proposed method

static output feedback mathscr h _ bm infty control of continuous time t s fuzzy affine systems via piecewise lyapunov functions this paper investigates the problem of robust h output feedback control for a class of continuous time takagi sugeno t s fuzzy affine dynamic systems with parametric uncertainties and input constraints the objective is to design a suitable constrained piecewise affine static output feedback controller guaranteeing the asymptotic stability of the resulting closed loop fuzzy control system with a prescribed h disturbance attenuation level based on a smooth piecewise quadratic lyapunov function combined with s procedure and some matrix inequality convexification techniques some new results are developed for static output feedback controller synthesis of the underlying continuous time t s fuzzy affine systems it is shown that the controller gains can be obtained by solving a set of linear matrix inequalities lmis finally three examples are provided to illustrate the effectiveness of the proposed methods

asymptotic estimation of ξ 2n 1 2 on a conjecture of farmer and rhoades we verify a very recent conjecture of farmer and rhoades on the asymptotic rate of growth of the derivatives of the riemann xi function at s 1 2 we give two separate proofs of this result with the more general method not restricted to s 1 2 we briefly describe other approaches to our results give a heuristic argument and mention supporting numerical evidence

convergent lmi relaxations for quadratic stabilizability and mathscr h _ infty control of takagi sugeno fuzzy systems this paper investigates the quadratic stabilizability of takagi sugeno t s fuzzy systems by means of parallel distributed state feedback compensators using finsler s lemma a new design condition assuring the existence of such a controller is formulated as a parameter dependent linear matrix inequality lmi with extra matrix variables and parameters in the unit simplex algebraic properties of the system parameters and recent results of positive polynomials are used to construct lmi relaxations that differently from most relaxations in the literature provide certificates of convergence to solve the control design problem due to the degrees of freedom obtained with the extra variables the conditions presented in this paper are an improvement over earlier results based only on polya s theorem and can be viewed as an alternative to the use of techniques based on the relaxation of quadratic forms an extension to cope with guaranteed h infin attenuation levels is also given with proof of asymptotic convergence to the global optimal controller under quadratic stability the efficiency of the proposed approach in terms of precision and computational effort is demonstrated by means of numerical comparisons with other methods from the literature

observer based adaptive fuzzy control for siso nonlinear systems abstract the observer based indirect and direct adaptive fuzzy controllers are developed for a class of siso uncertain nonlinear systems the proposed approaches do not need the availability of the state variables by designing the state observer the adaptive fuzzy systems which are used to model the unknown functions can be constructed using the state estimations thus a new hybrid adaptive fuzzy control method is proposed by combining the above adaptive fuzzy system with the h control technique based on lyapunov stability theorem the proposed adaptive fuzzy control system can guarantee the stability of the whole closed loop systems and obtain good tracking performance as well the proposed methods are applied to an inverted pendulum system and a chaotic system and achieve satisfactory simulation results

universal oscillations of high derivatives differentiation generates oscillations for the n th derivative f n t of a function f t that is analytic in a strip including the real t axis the oscillations occupy a t interval that gets larger as n increases the oscillations are studied in detail using integral representations and large n asymptotics for functions with singularities poles or branch points in the complex t plane the oscillations of high derivatives are determined by the singularities for entire functions the oscillations originate in complex saddle points in a wide class of cases the oscillations are contained in a gaussian envelope in the t interval where f n t is largest with the envelope including about graphic 1 oscillations examples of the universal oscillations are given for f t with a simple pole competing branch points a single saddle competing pole and saddle and where the zeros are confined to half the real axis 1 embed inline graphic 1 gif

differential algebraic equations with properly stated leading terms in this paper we study differential algebraic equations daes of the form a g t d g t b g t 0 with in some sense well matched matrix functions a g t and d g t d g g t as they arise e g in circuit simulation we characterize index 1 daes in this context after analyzing those index 1 equations themselves we apply runge kutta methods and bdfs provide stability inequalities and show convergence the cases of the image space of d g t or the nullspace of a g t remaining constant are pointed out to be essentially favourable for the qualitative behaviour of the approximations on long intervals hence when modelling with daes one should try for those constant subspaces relations to quasilinear daes in standard formulation e g t g g t 0 are considered too

theory of the fuzzy controller abstract we first introduce notation in an attempt to standardize the description of a basic fuzzy controller if r 1 r 2 r n are the real number inputs to the fuzzy controller and is its defuzzified output then f r 1 r n for some function f by the theory of the fuzzy controller we mean in this paper the study of the structure of f for elementary fuzzy controllers using this standardized notation we first survey the known results on the theory of the fuzzy controller and then discuss important future research topics in this area

mixed h sub 2 h sub infinity control a convex optimization approach the problem of finding an internally stabilizing controller that minimizes a mixed h sub 2 h sub infinity performance measure subject to an inequality constraint on the h sub infinity norm of another closed loop transfer function is considered this problem can be interpreted and motivated as a problem of optimal nominal performance subject to a robust stability constraint both the state feedback and output feedback problems are considered it is shown that in the state feedback case one can come arbitrarily close to the optimal even over full information controllers mixed h sub 2 h sub infinity performance measure using constant gain state feedback moreover the state feedback problem can be converted into a convex optimization problem over a bounded subset of n n and n q where n and q are respectively the state and input dimensions real matrices using the central h sub infinity estimator it is shown that the output feedback problem can be reduced to a state feedback problem in this case the dimension of the resulting controller does not exceed the dimension of the generalized plant

secure communications of chaotic systems with robust performance via fuzzy observer based design this paper presents a systematic design methodology for fuzzy observer based secure communications of chaotic systems with guaranteed robust performance the takagi sugeno fuzzy models are given to exactly represent chaotic systems then the general fuzzy model of many well known chaotic systems is constructed with only one premise variable in fuzzy rules and the same premise variable in the system output based on this general model the fuzzy observer of chaotic system is given and leads the stability condition of a linear matrix inequality problem when taking the fuzzy observer based design to applications on secure communications the robust performance is presented by simultaneously considering the effects of parameter mismatch and external disturbances then the error of the recovered message is stated in an h sup spl infin criterion in addition if the communication system is free of external disturbances the asymptotic recovering of the message is obtained in the same framework the main results also hold for applications on chaotic synchronization numerical simulations illustrate that this proposed scheme yields robust performance

symmetric collocation methods for linear differential algebraic boundary value problems we present symmetric collocation methods for linear differential algebraic boundary value problems without restrictions on the index or the structure of the differential algebraic equation in particular we do not require a separation into differential and algebraic solution components instead we use the splitting into differential and algebraic equations which arises naturally by index reduction techniques and apply gaus type for the differential part and lobatto type for the algebraic part collocation schemes to obtain a symmetric method which guarantees consistent approximations at the mesh points under standard assumptions we show solvability and stability of the discrete problem and determine its order of convergence moreover we show superconvergence when using the combination of gaus and lobatto schemes and discuss the application of interpolation to reduce the number of function evaluations finally we present some numerical comparisons to show the reliability and efficiency of the new methods

static output feedback fuzzy controller for chen s chaotic system with uncertainties static output feedback stabilization of chen s chaotic system with uncertainties is studied from a fuzzy control approach an uncertain takagi sugeno ts fuzzy model for the uncertain chen s chaotic system is first constructed then the uncertain ts fuzzy model is represented as a set of uncertain linear systems and a controller design algorithm is proposed specifically a switching static output feedback fuzzy model based controller is designed by solving some linear matrix inequalities lmi which are derived from the developed local representations simulation results have confirmed the effectiveness and feasibility of the proposed modeling and control methods

stability conditions for lmi based fuzzy control from viewpoint of membership functions in this paper we investigate the stability conditions for linear matrix inequality lmi based fuzzy control design especially we focus on the dependence of the stability upon membership functions in general the membership functions in the rule bases of takagi sugeno t s fuzzy model and controllers are the same and restricted between 0 and 1 in contrast to this setting we obtain some new results when different membership functions are considered and their values lying outside the interval of 0 1 are allowed applying lyapunov equation and a convex hull of fuzzy subsystems we first establish a relationship between the stable interval characteristic polynomial and a set of feasible lmis then kharitonov s theorem gives an insight for the solvability of stabilization problems using lmi based design and this leads that the membership functions have an influence on stability on the other hand the lmi condition leads to the well known results for lmi based fuzzy control design we further indicate that the different lmi conditions arise due to the same or different membership functions and find their own applications on adaptive fuzzy control finally if the unit interval constraint is removed an lmi condition for global stability is obtained

asymptotically correct error estimation for collocation methods applied to singular boundary value problems we discuss an a posteriori error estimate for collocation methods applied to boundary value problems in ordinary differential equations with a singularity of the first kind as an extension of previous results we show the asymptotical correctness of our error estimate for the most general class of singular problems where the coefficient matrix is allowed to have eigenvalues with positive real parts this requires a new representation of the global error for the numerical solution obtained by piecewise polynomial collocation when applied to our problem class

landau siegel zeros and zeros of the derivative of the riemann zeta function abstract we show that if the derivative of the riemann zeta function has sufficiently many zeros close to the critical line then the zeta function has many closely spaced zeros this gives a condition on the zeros of the derivative of the zeta function which implies a lower bound of the class numbers of imaginary quadratic fields

analytical and numerical treatment of a singular initial value problem in avalanche modeling we discuss a leading edge model used in the computation of the run out length of dry flowing avalanches the model has the form of a singular initial value problem for a scalar ordinary differential equation describing the avalanche dynamics existence uniqueness and smoothness properties of the analytical solution are shown we also prove the existence of a unique root of the solution moreover we present a fortran 90 code for the numerical computation of the run out length the code is based on a solver for singular initial value problems which is an implementation of the acceleration technique known as iterated defect correction based on the implicit euler method

localized periodic patterns for the non symmetric generalized swift hohenberg equation abstract a new asymptotic multiple scale expansion is used to derive envelope equations for localized spatially periodic patterns in the context of the generalized swift hohenberg equation an analysis of this envelope equation results in parametric conditions for localized patterns furthermore it yields corrections for wave number selection which are an order of magnitude larger for asymmetric nonlinearities than for the symmetric case the analytical results are compared with numerical computations which demonstrate that the condition for localized patterns coincides with vanishing hamiltonian and lagrangian for periodic solutions one striking feature of the choice of scaling parameters is that the derived condition for localized patterns agrees with the numerical results for a significant range of parameters which are an o 1 distance from the bifurcation thus providing a novel approach for studying these localized patterns

crystallization of random trigonometric polynomials we give a precise measure of the rate at which repeated differentiation of a random trigonometric polynomial causes the roots of the function to approach equal spacing this can be viewed as a toy model of crystallization in one dimension in particular we determine the asymptotics of the distribution of the roots around the crystalline configuration and find that the distribution is not gaussian

a stability approach to fuzzy control design for nonlinear systems abstract by the application of fuzzy set theory a method for feedback control of nonlinear systems based on the principle of sliding mode control is developed called fuzzy sliding mode control the control method provides a simple way to achieve asymptotic stability of the systems other attractive features of the method include a minimal realization of the fuzzy controller and robustness against model uncertainties and external disturbances in addition the method is capable of handling the chattering problem inherent to sliding mode control simply and effectively a simulation study of an inverted pendulum system is presented to demonstrate these features of the method also it is indicated that the method is easy to use for practicing control engineers

on the zeros of the derivatives of real entire functions and wiman s conjecture let f be an entire function of finite order real on the real axis and possessing only real zeros a classical problem proposed by g p6lya 9 10 and a wiman 1 is to determine from the hadamard canonical representation of the function the number of nonreal zeros of the higher derivatives of f in this paper we shall prove the following conjecture of wiman which has been open since 1915

density profile equation with p laplacian analysis and numerical simulation analytical properties of a nonlinear singular second order boundary value problem in ordinary differential equations posed on an unbounded domain for the density profile of the formation of microscopic bubbles in a nonhomogeneous fluid are discussed especially sufficient conditions for the existence and uniqueness of solutions are derived two approximation methods are presented for the numerical solution of the problem one of them utilizes the open domain matlab code bvpsuite the results of numerical simulations are presented and discussed

piecewise quadratic stability of fuzzy systems presents an approach to stability analysis of fuzzy systems the analysis is based on lyapunov functions that are continuous and piecewise quadratic the approach exploits the gain scheduling nature of fuzzy systems and results in stability conditions that can be verified via convex optimization over linear matrix inequalities examples demonstrate the many improvements over analysis based on a single quadratic lyapunov function special attention is given to the computational aspects of the approach and several methods to improve the computational efficiency are described

parabolic monge ampere methods for blow up problems in several spatial dimensions this paper constructs and analyses an adaptive moving mesh scheme for the numerical simulation of singular pdes in one or more spatial dimensions the scheme is based on computing a legendre transformation from a regular to a spatially non uniform mesh via the solution of a relaxed form of the monge ampere equation the method is shown to preserve the inherent scaling properties of the pde and to identify natural computational coordinates numerical examples are presented in one and two dimensions which demonstrate the effectiveness of this approach

relaxed stability conditions for continuous time t s fuzzy control systems via augmented multi indexed matrix approach this paper is concerned with the problem of developing an advanced strategy to reduce the conservatism in stability analysis and control synthesis of continuous time takagi sugeno t s fuzzy systems a novel augmented multi indexed matrix approach is proposed to implement new right hand side slack variables technique for the homogenous polynomial setting combining with the finsler lemma with homogenous matrix lagrange multipliers convergent linear matrix inequality lmi relaxations for stability analysis are proposed by using the generalization of the polya theorem for the case of positive polynomials with matrix valued coefficients a new type of state feedback controller namely the homogeneous polynomially nonquadratic control law hpnqcl is developed to conceive less conservative stabilization conditions the obtained stability and stabilization conditions are further relaxed by using the proposed right hand side slack variables technique moreover the advantages over the existing control schemes are certificated in theory three numerical examples are also provided to illustrate the effectiveness of the proposed methods