design for self organizing fuzzy neural networks based on genetic algorithms a novel hybrid learning algorithm based on a genetic algorithm to design a growing fuzzy neural network named self organizing fuzzy neural network based on genetic algorithms sofnnga to implement takagi sugeno ts type fuzzy models is proposed in this paper a new adding method based on geometric growing criterion and the epsiv completeness of fuzzy rules is first used to generate the initial structure then a hybrid algorithm based on genetic algorithms backpropagation and recursive least squares estimation is used to adjust all parameters including the number of fuzzy rules this has two steps first the linear parameter matrix is adjusted and second the centers and widths of all membership functions are modified the ga is introduced to identify the least important neurons i e the least important fuzzy rules simulations are presented to illustrate the performance of the proposed algorithm

hamiltonian and super hamiltonian systems of a hierarchy of soliton equations abstract by considering an isospectral eigenvalue problem a hierarchy of soliton equations are derived two types of extensions are presented by enlarging the associated spectral problem with the aid of generalized trace identity and the super trace identity the hamiltonian and super hamiltonian structures for the integrable extensions are established

spectral and computational properties of band symmetric toeplitz matrices abstract we are investigating spectral properties of band symmetric toeplitz matrices bst matrices by giving a suitable representation of a bst matrix we achieve separation results and multiplicity conditions for the eigenvalues of a 7 r 5 diagonal bst matrix and also structural properties of the eigenvectors we give eigenvalue bounds for a 2k 1 diagonal bst matrix and also necessary and sufficient conditions for positive definiteness which are easy to check the same conditions apply in the case of block bst matrices either with full blocks or with bst blocks we exhibit fast computational methods for the evaluation of the determinant and the characteristic polynomial of a bst matrix either for sequential or for parallel computations two algorithms based on the bisection technique and newton s method are shown to be very fast for computing the eigenvalues of a 7 or 5 diagonal bst matrix

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

current algebra aks theorem and new super evolution equations the authors have deduced a new class of integrable super evolution equations by using a supersymmetric version of the aks adler kostant sym theorem in conjunction with the homogeneous space reduction technique of marshall 1988 and current algebra of samenov tian shansky 1983

nonlinear super integrable hamiltonian couplings based on a kind of new lie superalgebras we proposed a scheme for constructing nonlinear super integrable couplings super trace identity over the corresponding loop superalgebras is used to furnish the super hamiltonian structures for the resulting nonlinear super integrable couplings we illustrate the application of the scheme by means of an enlarged super ablowitz kaup newell segur akns matrix spectral problem and present a nonlinear super integrable hamiltonian couplings for the super akns hierarchy

output feedback robust h sup spl infin control of uncertain fuzzy dynamic systems with time varying delay this paper presents an output feedback robust h sup spl infin control problem for a class of uncertain fuzzy dynamic systems with time varying delayed state the takagi sugeno fuzzy model is employed to represent an uncertain nonlinear systems with time varying delayed state using a single quadratic lyapunov function the globally exponential stability and disturbance attenuation of the closed loop fuzzy control system are discussed sufficient conditions for the existence of robust h sup spl infin controllers are given in terms of matrix inequalities constructive algorithm for design of robust h sup spl infin controller is also developed the resulting controller is nonlinear and automatically tuned based on fuzzy operation

adaptive synchronization of uncertain chaotic systems based on t s fuzzy model this paper presents an adaptive approach for synchronization of takagi sugeno t s fuzzy chaotic systems t s fuzzy model can represent a general class of nonlinear system and we employ it for fuzzy modeling of the chaotic drive system since the output of the drive system is only available for synchronization the response system is designed based on fuzzy adaptive observer for uncertain parameters and parameter mismatch cases we analyze the stability of the overall fuzzy synchronization system by applying lyapunov stability theory and derive stability conditions by solving linear matrix inequalities lmis problem the adaptive law is derived to estimate the uncertain parameters or parameter mismatch numerical examples are given to demonstrate the validity of the proposed fuzzy adaptive synchronization approach

two integrable hamiltonian hierarchies in sl 2 r and so 3 r with three potentials by introducing two specific matrix spectral problems associated with sl 2 r and so 3 r matrix lie algebras we generate two integrable hamiltonian hierarchies with three potentials the computation and analysis on their hamiltonian structures by means of the trace identity show that the resulting hierarchies are liouville integrable namely that each hierarchy consists of commuting hamiltonian soliton equations

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 inversion algorithms of toeplitz plus hankel matrices the paper deals with the problems of fast inversion of matricesa t h wheret is toeplitz andh is hankel several algorithms are presented and compared among them algorithms working for arbitrary strongly nonsingular matricesa t h

diagonal pivoting for partially reconstructible cauchy like matrices with applications to toeplitz like linear equations and to boundary rational matrix interpolation problems abstract in an earlier paper we exploited the displacement structure of cauchy like matrices to derive for them a fast o n 2 implementation of gaussian elimination with partial pivoting one application is to the rapid and numerically accurate solution of linear systems with toeplitz like coefficient matrices based on the fact that the latter can be transformed into cauchy like matrices by using the fast fourier sine or cosine transform however symmetry is lost in the process and the algorithm given is not optimal for hermitian coefficient matrices in this paper we present a new fast o n 2 implementation of symmetric gaussian elimination with partial diagonal pivoting for hermitian cauchy like matrices and show how to transform hermitian toeplitz like matrices to hermitian cauchy like matrices obtaining algorithms that are twice as fast as those in the earlier work numerical experiments indicate that in order to obtain not only fast but also numerically accurate methods it is advantageous to explore the important case in which the corresponding displacement operators have nontrivial kernels this situation gives rise to what we call partially reconstructible matrices which are introduced and studied in the present paper we extend the transformation technique and the generalized schur algorithms i e fast displacement based implementations of gaussian elimination to partially reconstructible matrices we show by a variety of computed examples that the incorporation of diagonal pivoting methods leads to high accuracy we focused in this paper on the design of new numerically reliable algorithms for hermitian toeplitz like matrices however the proposed algorithms have other important applications in particular we briefly describe how they recursively solve a boundary interpolation problem for j unitary rational matrix functions

chaotic synchronization cryptosystems combined with rsa encryption algorithm abstract chaotic synchronization has suffered from demodulating information by hackers via the public channel different methods have been developed to hide the contents of a message using chaotic signals nevertheless many studies have shown that most of the existing methods are unreliable in the aspect of security according to the above in order to enhance the strength of the cryptosystem and provide greater security we carry out double encryption which combines chaotic synchronization with rsa algorithm in this study a design methodology for neural network nn based secure communications in multiple time delay chaotic mtdc systems is proposed to obtain double encryption via rsa algorithm and chaotic synchronization rsa algorithm is an asymmetric encryption and its strength is based on the tremendous difficulty of factorizing two large prime numbers accordingly it takes much more time to process rsa algorithm if the length of the key is much longer a shorter key is used to decrease the processing time of rsa algorithm in this work nevertheless it will result in a lower security of the cryptosystem in order to enhance the strength of the cryptosystem we carry out double encryption which combines chaotic synchronization with rsa algorithm moreover an iga is proposed in this study to effectively overcome the weakness of the traditional ga on the basis of the iga a fuzzy controller is synthesized to not only realize the exponential synchronization but also achieve optimal h performance by minimizing the disturbances attenuation level finally a numerical example with simulations is given to illustrate the effectiveness of our approach

an exact recursion for the composite nearest neighbor degeneracy for a 2 n lattice space a set theoretic argument is utilized to develop a recursion relation that yields exactly the composite nearest neighbor degeneracy for simple indistinguishable particles distributed on a 2 n lattice space the associated generating functions as well as the expectation of the resulting statistics are also treated

fast gaussian elimination with partial pivoting for matrices with displacement structure fast o n 2 implementation of gaussian elimination with partial pivoting is designed for matrices possessing cauchy like displacement structure we show how toeplitz like toeplitz plus hankel like and vandermonde like matrices can be transformed into cauchy like matrices by using discrete fourier cosine or sine transform matrices in particular this allows us to propose a new fast o n 2 toeplitz solver gko which incorporates partial pivoting a large set of numerical examples showed that gko demonstrated stable numerical behavior and can be recommended for solving linear systems especially with nonsymmetric indefinite and ill conditioned positive definite toeplitz matrices it is also useful for block toeplitz and mosaic toeplitz toeplitz block matrices the algorithms proposed in this paper suggest an attractive alternative to look ahead approaches where one has to jump over ill conditioned leading submatrices which in the worst case requires o n 3 operations

lie algebras and korteweg de vries equations abstract for each metrizable lie algebra g an infinite commuting hierarchy of bi hamiltonian integrable extensions of the korteweg de vries kdv hierarchy is found the classical kdv hierarchy itself corresponds to the case g 0 the construction is based on the hamiltonian formalism on the dual space to a certain one parameter family of differential lie algebras produced from g

robust stability analysis and fuzzy scheduling control for nonlinear systems subject to actuator saturation takagi sugeno ts fuzzy models can provide an effective representation of complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning applied to a set of linear input output submodels in this paper the ts fuzzy modeling approach is utilized to carry out the stability analysis and control design for nonlinear systems with actuator saturation the ts fuzzy representation of a nonlinear system subject to actuator saturation is presented in our ts fuzzy representation the modeling error is also captured by norm bounded uncertainties a set invariance condition for the system in the ts fuzzy representation is first established based on this set invariance condition the problem of estimating the domain of attraction of a ts fuzzy system under a constant state feedback law is formulated and solved as a linear matrix inequality lmi optimization problem by viewing the state feedback gain as an extra free parameter in the lmi optimization problem we arrive at a method for designing state feedback gain that maximizes the domain of attraction a fuzzy scheduling control design method is also introduced to further enlarge the domain of attraction an inverted pendulum is used to show the effectiveness of the proposed fuzzy controller

on the stability of solution methods for band toeplitz systems abstract this paper is concerned with the numerical stability of inversion algorithms for banded toeplitz systems we analyze the numerical behavior of one algorithm due to b w dickinson ieee trans acoust speech signal process 27 421 423 1979 and two algorithms due to a k jain ieee trans acoust speech signal process 26 121 126 1978 we show that none of the three algorithms is weakly stable when used to invert symmetric positive definite systems one of jain s algorithms is shown to be weakly stable when used to invert a symmetric banded toeplitz matrix with a well conditioned positive definite infinite extension we present a new algorithm which is weakly stable under a more general condition and can be modified to invert certain toeplitz like matrices

the trace identity a powerful tool for constructing the hamiltonian structure of integrable systems a new approach to hamiltonian structures of integrable systems is proposed by making use of a trace identity for a variety of isospectral problems that can be unified to one model x u it is shown that both the related hierarchy of evolution equations and the hamiltonian structure can be obtained from the same solution of the equation vx u v

tensor rank and border rank of band toeplitz matrices let mathcal b n h k be the class of n times n band toeplitz matrices a a i j such that a i j 0 if i j geqq k or j i geqq h k leqq h and mathcal s n k the subclass of mathcal b n k k made up by symmetric matrices we show that operatorname rk bf f mathcal b n h k n h 1 if the field bf f contains a primitive n 1 h th root of unity operatorname brk bf f mathcal b n h k n k 1 operatorname rk bf r mathcal s n k operatorname brk bf r mathcal s n k n 2 lfloor k 1 2 rfloor if bf r is the real field and k leqq n 2

a subalgebra of lie algebra a2 and its associated two types of loop algebras as well as hamiltonian structures of integrable hierarchy in this paper a subalgebra a2 of the lie algebra a2 is constructed which gives a corresponding loop algebra a 2 by properly choosing the gradation of the basis elements it follows that an isospectral problem is established and a new liouville integrable hamiltonian hierarchy is obtained by making use of a matrix transformation a subalgebra a2 of the lie algebra a1 is presented which possesses the same communicative operations of basis elements as those in a2 again we expand the lie algebra a1 into a high dimensional loop algebra g and a type of expanding integrable system of the hierarchy obtained above is worked out furthermore hamiltonian structures of hierarchy are presented by use of the quadratic form identity

hamiltonian structure of the super evolution equation the constrained variational calculus proposed in previous papers y zheng y li and d chen sci sinica a 24 138 1986 g tu kexue tangbao 29 1227 1984 is generalized to the supersymmetric case utilizing this method to some super akns system which has soliton solutions and conserved quantities their equations of motion with the hamiltonian structure can be written as a 4 4 matrix this is the supersymmetric symplectic matrix and hn are hamiltonians of the system the conserved quantities worked out in recent literature are just the first few terms of our analytic expression

linear aperiodic array synthesis using an improved genetic algorithm a novel algorithm on beam pattern synthesis for linear aperiodic arrays with arbitrary geometrical configuration is presented in this paper linear aperiodic arrays are attractive for their advantages on higher spatial resolution and lower sidelobe however the advantages are attained at the cost of solving a complex non linear optimization problem in this paper we explain the improved genetic algorithm iga that simultaneously adjusts the weight coefficients and inter sensor spacings of a linear aperiodic array in more details and extend the investigations to include the effects of mutual coupling and the sensitivity of the peak sidelobe level psl to steering angles numerical results show that the psl of the synthesized beam pattern has been successfully lowered with the iga when compared with other techniques published in the literature in addition the computational cost of our algorithm can be as low as 10 of that of a recently reported genetic algorithm based synthesis method the excellent performance of iga makes it a promising optimization algorithm where expensive cost functions are involved

new nonlinear evolution equations related to some superloop algebras constructs hierarchies of nonlinear evolution equations on the superloop algebras related to the super lie algebras b 0 1 and sl 2 1 the hierarchy associated with sl 2 1 contains a generalisation of the super nonlinear schrodinger equation with a cubic non derivative interaction term in complex anticommuting fields in all cases the author gives a recursive procedure for constructing involutive integrals of local polynomials

an approach to stability criteria of neural network control systems this paper discusses stability of neural network nn based control systems using lyapunov approach first it is pointed out that the dynamics of nn systems can be represented by a class of nonlinear systems treated as linear differential inclusions ldi next stability conditions for the class of nonlinear systems are derived and applied to the stability analysis of single nn systems and feedback nn control systems furthermore a method of parameter region pr representation which graphically shows the location of parameters of nonlinear systems is proposed by introducing new concepts of vertex point and minimum representation from these concepts an important theorem which is useful for effectively finding a lyapunov function is derived stability criteria of single nn systems are illustrated in terms of pr representation finally stability of feedback nn control systems which consist of a plant represented by an nn and an nn controller is analyzed

relaxed stabilization criterion for t s fuzzy systems by minimum type piecewise lyapunov function based switching fuzzy controller this paper proposes the minimum type piecewise lyapunov function based switching fuzzy controller that switches accompanying the piecewise lyapunov function by applying this switching fuzzy controller with the minimum type piecewise lyapunov function the relaxed stabilization criterion is obtained for continuous takagi sugeno t s fuzzy systems some conditions of the relaxed stabilization criterion are represented by bilinear matrix inequalities bmis which contain some bilinear terms as the product of a full matrix and a scalar according to the literature the path following method is very effective for this kind of bmi problem hence it is utilized to obtain solutions of the criterion xie et al in 1997 chose two types i e minimum type and maximum type of piecewise lyapunov functions as the lyapunov function candidates the reasons for why this study only chooses the minimum type piecewise lyapunov function as the lyapunov function candidate are illustrated moreover the numerical example shows the relaxation of the proposed criterion

a discrete variational identity on semi direct sums of lie algebras the discrete variational identity under general bilinear forms on semi direct sums of lie algebras is established the constant involved in the variational identity is determined through the corresponding solution to the stationary discrete zero curvature equation an application of the resulting variational identity to a class of semi direct sums of lie algebras in the volterra lattice case furnishes hamiltonian structures for the associated integrable couplings of the volterra lattice hierarchy

fuzzy model based control of complex plants in the field of fuzzy modeling the takagi sugeno fuzzy model has been used to approximate accurately the dynamics of complex plants the paper addresses two control design problems associated with state space realizations of such fuzzy models first we treat the stability robustness of fuzzy model based controllers against modeling uncertainty second we develop observer based control schemes and further investigate the behavior of estimated state feedback in both cases we provide sufficient conditions that guarantee stability of the closed loop the results are demonstrated on the fuzzy model of a gas furnace process

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

adiabatic elimination for classical fermionic systems presents the reduction to a normal form of a grassmannian differential equation describing a classical fermionic system in the neighbourhood of an instability as an application of the method presented the author shows that the anticommuting version of the normal form associated with a the hopf bifurcation a simple pair of imaginary eigenvalues leads to the overdamped grassmann harmonic oscillator and b the resonant hopf bifurcation 1 1 a double pair of semisimple imaginary eigenvalues corresponds exactly to the thirring model for grassmann solitons

a deformation of the general zero curvature equations associated to simple lie algebras we construct deformations and rational reductions for all the general zero curvature equations associated to simple complex lie algebras known as akns equations for sl 2 c

a hierarchy of generalized akns equations n hamiltonian structures and finite dimensional involutive systems and integrable systems an eigenvalue problem and the associated hierarchy of nonlinear soliton equations are proposed in this paper in particular a representative system of generalized akns soliton equations in the hierarchy is given namely qt 12 qxx q2r 2 q2rx 2 rqqx 2 2q3r2 rt 12 rxx qr2 2 r2qx 2 qrrx 2 2q2r3 n hamiltonian structures are also established for all the hirarchy of generalized akns soliton equations based on n 1 pairs of hamiltonian pairs and then the eigenvalue problem is nonlinear as a finite dimensional completely integrable hamiltonian system under the bargmann constraint between the potentials and the eigenvalue functions and its involutive system is also given finally the involutive solutions of the hierarchy of generalized akns soliton equations are found in particular the involutive solutions of the system of generalized schrodinger equations are given

a special class of structured matrices constructed with the kronecker product and its use for difference equations abstract starting from a sequence of specific orthogonal matrices and using the matricial kronecker product we build classes of matrices sk k 1 2 which are shown to possess a certain affiliation with toeplitz and hankel matrices being completely determined by the first row elements their eigenvalues as well as an inversion formula are easily derived therefrom s matrices as they are termed in general may arise through the application of finite difference methods to boundary value problems

on the backlund transformation and hamiltonian properties of superevaluation equations backlund and darboux backlund transformations are deduced for the superevaluation equations recently deduced by kupershmidt b kuperschmidt a super k dv equation an integrable system preprint utsi tullahoma 1984 phys lett a 102 213 1983 j phys a 17 l 863 1984 and gurses h gurses and o oguz phys lett a 108 437 1985 by a extension of the technique of bpt m boiti f pempinelli and g z tu nuovo cimento b 79 231 1984 to anticommuting variables the bi hamiltonian structure and hence the form of the recursion operator for the lie backlund symmetry for such equations are deduced incidentally some explicit forms of the lie backlund symmetry are also deduced

transformation techniques for toeplitz and toeplitz plus hankel matrices ii algorithms abstract this paper is a continuation of g heinig a bojanczyk linear algebra appl 254 1997 193 226 where transformations mapping toeplitz and toeplitz plus hankel matrices into generalized cauchy matrices were studied in the present paper fast algorithms for lu factorization and inversion of generalized cauchy matrices are discussed it is shown that the combination of transformation pivoting techniques leads to algorithms for indefinite toeplitz and toeplitz plus hankel matrices that are more stable than the classical ones special attention is paid to the symmetric and hermitian cases

a supertrace identity and its applications to superintegrable systems a supertrace identity on lie superalgebras is established it provides a tool for constructing super hamiltonian structures of zero curvature equations associated with lie superalgebras applications in the case of the lie superalgebra b 0 1 present super hamiltonian structures of a super akns soliton hierarchy and a super dirac soliton hierarchy

a multiple lyapunov function approach to stabilization of fuzzy control systems this paper addresses stability analysis and stabilization for takagi sugeno fuzzy systems via a so called fuzzy lyapunov function which is a multiple lyapunov function the fuzzy lyapunov function is defined by fuzzily blending quadratic lyapunov functions based on the fuzzy lyapunov function approach we give stability conditions for open loop fuzzy systems and stabilization conditions for closed loop fuzzy systems to take full advantage of a fuzzy lyapunov function we propose a new parallel distributed compensation pdc scheme that feedbacks the time derivatives of premise membership functions the new pdc contains the ordinary pdc as a special case a design example illustrates the utility of the fuzzy lyapunov function approach and the new pdc stabilization method

h synchronization of chaotic systems using output feedback control design this article investigates the h synchronization problem for a general class of chaotic systems based on lyapunov theory linear matrix inequality lmi and linear matrix equality lme formulation the output feedback controller is established to not only guarantee stable synchronization of both master and slave systems but also reduce the effect of external disturbance to an h norm constraint two illustrative examples are provided to demonstrate the effectiveness of the developed theoretical results

an approach to generate superextensions of integrable systems an algorithm to generate integrable systems is extended to the super case some new examples of superextensions of integrable systems are illustrated we also generalize the trace identity due to tu to the super case and use it to establish hamiltonian structures of superextensions of integrable systems under consideration

a powerful approach to generate new integrable systems in this paper an effective algorithm to generate integrable systems is given as a result many new integrable equations are derived in a systematic way

fast triangular factorization of the sum of quasi toeplitz and quasi hankel matrices abstract the literature contains several recent fast algorithms for the triangular factorization of strongly regular toeplitz plus hankel matrices in this paper we study the rather more general sum of quasi toeplitz and quasi hankel matrices both hermitian and non hermitian quasi toeplitz and quasi hankel matrices are those that are congruent to toeplitz and hankel matrices in a special sense the derivation is based on the concept of displacement structure and its intimate relation to the schur reduction procedure for triangular factorization various special cases covering displacement ranks from two to eight are considered several other problems e g factorization of the inverse matrix solution of exact or overdetermined linear systems can be reduced to the direct factorization problem

exponential rm h _ infty synchronization of general discrete time chaotic neural networks with or without time delays this brief studies exponential h synchronization of a class of general discrete time chaotic neural networks with external disturbance on the basis of the drive response concept and h control theory and using lyapunov krasovskii or lyapunov functional state feedback controllers are established to not only guarantee exponential stable synchronization between two general chaotic neural networks with or without time delays but also reduce the effect of external disturbance on the synchronization error to a minimal h norm constraint the proposed controllers can be obtained by solving the convex optimization problems represented by linear matrix inequalities most discrete time chaotic systems with or without time delays such as hopfield neural networks cellular neural networks bidirectional associative memory networks recurrent multilayer perceptrons cohen grossberg neural networks chua s circuits etc can be transformed into this general chaotic neural network to be h synchronization controller designed in a unified way finally some illustrated examples with their simulations have been utilized to demonstrate the effectiveness of the proposed methods

transformation techniques for toeplitz and toeplitz plus hankel matrices part i transformations transformations of the form a c1ac2 are investigated that transform toeplitz and toeplitz plus hankel matrices into generalized cauchy matrices c1 and c2 are matrices related to the discrete fourier transformation or to various real trigonometric transformations combining these results with pivoting techniques in part ii algorithms for toeplitz and toeplitz plus hankel systems will be presented that are more stable than classical algorithms

a nonlinear integrable couplings of c kdv soliton hierarchy and its infinite conservation laws abstract a kind of nonlinear integrable couplings of c kdv soliton hierarchy is constructed then we present the infinitely many conservation laws for the nonlinear integrable couplings of the c kdv soliton hierarchy

displacement structure theory and applications in this survey paper we describe how strands of work that are important in two different fields matrix theory and complex function theory have come together in some work on fast computational algorithms for matrices with what we call displacement structure in particular a fast triangularization procedure can be developed for such matrices generalizing in a striking way an algorithm presented by schur 1917 j reine angew math 147 1917 pp 205 232 in a paper on checking when a power series is bounded in the unit disc this factorization algorithm has a surprisingly wide range of significant applications going far beyond numerical linear algebra we mention among others inverse scattering analytic and unconstrained rational interpolation theory digital filter design adaptive filtering and state space least squares estimation

fast direct solution methods for symmetric banded toeplitz systems based on the sine transform we present new fast direct methods for solving a large symmetric banded toeplitz system of order n with bandwidth p we make use of structured matrices which can be diagonalized by the discrete sine transform matrix sometimes called matrices a first method writes the toeplitz matrix as the sum of a matrix and a low rank matrix a second method embeds the toeplitz matrix in a larger matrix of order m the methods are similar to jain ieee trans acoust speech signal process 26 1978 121 and linzer linear algebra appl 170 1992 1 who worked with circulant matrices both algorithms consist in solving two systems and two smaller systems a system of order n can be solved in o n log n by using a discrete sine transform if n 1 has small prime factors therefore the second algorithm is preferable since we can choose m such that m 1 has small prime factors on the other hand in the second method the smaller systems can become large when m differs too much from n w hile in the first method the order is always p 1 in both methods the small systems have low displacement rank so we can use fast methods to solve them 2002 elsevier science inc all rights reserved

neural network based control design an lmi approach we address a neural network based control design for a discrete time nonlinear system our design approach is to approximate the nonlinear system with a multilayer perceptron of which the activation functions are of the sigmoid type symmetric to the origin a linear difference inclusion representation is then established for this class of approximating neural networks and is used to design a state feedback control law for the nonlinear system based on the certainty equivalence principle the control design equations are shown to be a set of linear matrix inequalities where a convex optimization algorithm can be applied to determine the control signal further the stability of the closed loop is guaranteed in the sense that there exists a unique global attraction region in the neighborhood of the origin to which every trajectory of the closed loop system converges finally a simple example is presented so as to illustrate our control design procedure

bifurcation control of a chaotic system the viability of controlling chaos by controlling associated bifurcations is demonstrated in the context of a thermal convection loop model washout filter aided feedback controls are employed to delay and to extinguish chaos in the model and to target preferred equilibrium points an important feature of the control laws is that they do not result in any change in the set of equilibria even in the presence of model uncertainty

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

kac moody lie algebras and soliton equations ii lax equations associated with a1 1 the soliton equations associated with sl 2 eigenvalue problems polynomial in the eigenvalue parameter are given a unified treatment they are shown to be generated by a single family of commuting hamiltonians on a subalgebra of the loop algebra of sl 2 the conserved densities and fluxes of the usual anks hierarchy are identified with conserved densities and fluxes for the polynomial eigenvalue problems the hamiltonian structures of the soliton equations associated with the polynomial eigenvalue problems are given a unified treatment

preconditioning of block toeplitz matrices by sine transforms the iterative solution of a block toeplitz linear system by the conjugate gradient method is analyzed the preconditioning step being solved by means of a discrete sine transform convergence properties are established and compared to the behavior of the block circulant preconditioner recently proposed in the literature as in the scalar case the new approach takes advantage if the system is ill conditioned

sine transform based preconditioners for symmetric toeplitz systems abstract the optimal circulant preconditioner for a given matrix a is defined to be the minimizer of c a f over the set of all circulant matrices c here f is the frobenius norm optimal circulant preconditioners have been proved to be good preconditioners in solving toeplitz systems with the preconditioned conjugate gradient method in this paper we construct an optimal sine transform based preconditioner which is defined to be the minimizer of b a f over the set of matrices b that can be diagonalized by sine transforms we will prove that for general n by n matrices a these optimal preconditioners can be constructed in o n 2 real operations and in o n real operations if a is toeplitz we will also show that the convergence properties of these optimal sine transform preconditioners are the same as that of the optimal circulant ones when they are employed to solve toeplitz systems numerical examples are given to support our convergence analysis

on liouville integrability of zero curvature equations and the yang hierarchy sufficient conditions for a zero curvature equation ut vx u v 0 being liouville integrable are investigated in the case that the equation is integrable an explicit formula of the poisson bracket h lambda h mu for hamiltonians h is proposed the yang hierarchy is derived and shown to be liouville integrable

nonlinear schrodinger equations and simple lie algebras we associate a system of integrable generalised nonlinear schrodinger nls equations with each hermitian symmetric space these nls equations are considered as reductions of more general systems this time associated with a reductive homogeneous space the nonlinear terms are related to the curvature and torsion tensors of the appropriate geometrical space the hamiltonian structure is investigated using r matrix techniques and shown to be canonical for all these equations throughout the reduction procedure this hamiltonian structure does not degenerate each of the above systems of equations is gauge equivalent to a generalised ferromagnet reductions of the latter are discussed in terms of the corresponding nls type equations

on the complete solution of the hirota satsuma system through the dressing operator technique the authors have applied the dressing operator method of zakharov et al for obtaining the complete solution of the hirota satsuma coupled system this method helps one essentially to solve the inverse problem associated with a fourth order differential operator also the method of the dressing operator has the distinct advantage of generating solutions other than soliton by varying the boundary condition in an appropriate fashion