oscillations of nonlinear partial difference systems abstract this paper studies the following two dimensional nonlinear partial difference systems t 1 2 x mn b mn g y mn 0 t 1 2 y mn a mn f x mn 0 where m n n0 0 1 2 t 1 2 1 2 i t 1 2 1 2 i 1ymn ym 1 n ymn 2ymn ym n 1 ymn iymn ymn 1ymn ym 1 n ymn 2ymn ym n 1 ymn amn and bmn are real sequences m n n0 and f g r r are continuous with uf u 0 and ug u 0 for all u 0 a solution xmn ymn of the system is oscillatory if both components are oscillatory some sufficient conditions for all solutions of this system to be oscillatory are derived

robust h sub spl infin and mixed h sub 2 h sub spl infin filters for equalization designs of nonlinear communication systems fuzzy interpolation approach generally it is difficult to design equalizers for signal reconstruction of nonlinear communication channels with uncertain noises in this paper we propose the h sub spl infin and mixed h sub 2 h sub spl infin filters for equalization detection of nonlinear channels using fuzzy interpolation and linear matrix inequality lmi techniques first the signal transmission system is described as a state space model and the input signal is embedded in the state vector such that the signal reconstruction estimation design becomes a nonlinear state estimation problem then the takagi sugeno fuzzy linear model is applied to interpolate the nonlinear channel at different operation points through membership functions since the statistics of noises are unknown the fuzzy h sub spl infin equalizer is proposed to treat the state estimation problem from the worst case robust point of view when the statistics of noises are uncertain but with some nominal or average information available the mixed h sub 2 h sub spl infin equalizer is employed to take the advantage of both h sub 2 optimal performance with nominal statistics of noises and the h sub spl infin robustness performance against the statistical uncertainty of noises using the lmi approach the fuzzy h sub 2 h sub spl infin equalizer detector design problem is characterized as an eigenvalue problem evp the evp can be solved efficiently with convex optimization techniques

summation formulae for spherical spinors the summation formulae for spinor spherical waves j l or 1 2 analogous to the well known summation formulae for ordinary spherical harmonics are derived the summation over magnetic quantum number gives a combination of unit and pauli matrices with coefficients depending on the legendre polynomials and their derivatives application to the full scattering solution of the dirac equation is also described

adaptive sliding mode observer design for a class of t s fuzzy descriptor fractional order systems this paper investigates the problem of sliding mode observer smo design for takagi sugeno t s fuzzy descriptor fractional order systems foss with fractional order 0 first an smo is designed for the t s fuzzy descriptor fos then a fuzzy fractional order integral type sliding surface is constructed by utilizing the fuzzy sliding surface the assumption that all local input matrices are identical in most existing results about sliding mode control smc for t s fuzzy systems can be removed then a new sufficient condition is proposed in terms of linear matrix inequalities lmis which guarantees the admissibility of the sliding mode dynamics moreover adaptive smc strategy is used such that the reachability condition can be guaranteed finally three examples are given to verify the effectiveness of our results

completeness of the dirac oscillator eigenfunctions completeness of the dirac oscillator eigenfunctions is proved in one and three spatial dimensions proofs are based on standard properties of the hermite and the generalized laguerre polynomials

oscillation of partial difference equations with variable coefficients for the partial difference equations am 1 n am n 1 am n pm nam k n 1 0 and am 1 n am n 1 am n i 1upi m n fi am ki n li 0 we shall obtain sufficient conditions for the oscillation of all solutions

robust spl hscr sub spl infin filtering for uncertain discrete time state delayed systems this paper addresses the problem of robust spl hscr sub spl infin filtering for linear discrete time systems subject to parameter uncertainties in the system state space model and with multiple time delays in the state variables the uncertain parameters are supposed to belong to a given convex bounded polyhedral domain a methodology is developed to design a stable linear filter that assures asymptotic stability and a prescribed spl hscr sub spl infin performance for the filtering error irrespective of the uncertainty and the time delays the proposed design is given in terms of linear matrix inequalities which has the advantage in that it can be implemented numerically very efficiently

domain decomposition using spectral expansions of steklov poincare operators a new domain decomposition method is described for solving elliptic boundary value problems on a region partitioned into nonoverlapping subdomains which are discretized independently using a galerkin finite element method the interdomain continuity requirements on the solution are imposed using an independent low dimensional set of interfacial basis functions which are separately derived for each subdomain by solving an eigenvalue problem for the steklov poincare operator on the complementary region the efficient numerical implementation of this method is described here for the two subdomain case and its convergence properties are studied for some test examples in specific examples involving constant coefficient problems on rectangular regions partitioned into rectangular subdomains the pointwise error of the discrete solution in the subdomain interior converges exponentially in the number of interfacial modes so that the present method is effectively a direct solution method in other examples

the embedding method for electromagnetics a new method is derived for solving maxwell s equations for a region of space region i joined onto region ii which may be a finite dielectric or an extended substrate this is based on a variational principle in which a trial field is defined explicitly only in region i the solution of maxwell s equations in region ii being included through an embedding operator defined on the boundary of region i with ii this operator is the inverse of a non local boundary impedance the method is applied to calculating the normal modes of an array of dielectric slabs semi infinite dielectrics separated by vacuum and modes confined in a three dimensional box with conducting walls plane wave basis functions are used to expand the electric field in region i and the method shows excellent convergence in all cases approximate solutions of laplace s equation can occur corrupting the solutions of maxwell s equations with finite frequency it is shown how these can be suppressed

domain decomposition using spectral expansions of steklov poincare operators ii a matrix formulation we describe a matrix formulation of the iterative domain decomposition method in natarajan siam j sci comput 16 1995 pp 470 495 from one point of view this method can be regarded as a preconditioning technique for the interface schur complement operator obtained from a decomposition into nonoverlapping subdomains from another point of view it can be viewed as a method of the schwarz type for overlapping subdomains but with an overlap between the physical space in one subdomain and the leading components of the eigenspace induced by the steklov poincare operator in the complementary domain

nonexistence of positive solutions of a class of nonlinear delay partial difference equations sufficient conditions are derived for the nonexistence of positive solutions of a class of positive nonlinear delay partial difference equations results are also obtained for the nonexistence of positive solutions of the dual equation

oscillation theorems for second order nonlinear partial difference equations 479 abstract the oscillation of the second order nonlinear partial difference equation t 1 2 c mn 1 y mn i 1 s a i m n f i y m 1 n 1 y mn 0 is investigated some sufficient conditions for the oscillation of all solutions of the above equation are obtained

algebraic properties of the dirac oscillator an algebraic representation independent analysis is presented for the dirac oscillator in an angular momentum basis the analysis is based on shift operators for energy and angular momentum and it is similar to that for a non relativistic isotropic harmonic oscillator the shift operators generate all the eigenkets of the dirac oscillator from a vacuum ket the shift operations yield energy eigenvalues and certain matrix elements the relationship to the factorization method is discussed

asynchronous output feedback control of networked nonlinear systems with multiple packet dropouts t s fuzzy affine model based approach this paper investigates the problem of robust output feedback control for a class of networked nonlinear systems with multiple packet dropouts the nonlinear plant is represented by takagi sugeno t s fuzzy affine dynamic models with norm bounded uncertainties and stochastic variables that satisfy the bernoulli random binary distribution are adopted to characterize the data missing phenomenon the objective is to design an admissible output feedback controller that guarantees the stochastic stability of the resulting closed loop system with a prescribed disturbance attenuation level it is assumed that the plant premise variables which are often the state variables or their functions are not measurable so that the controller implementation with state space partition may not be synchronous with the state trajectories of the plant based on a piecewise quadratic lyapunov function combined with an s procedure and some matrix inequality convexifying techniques two different approaches to robust output feedback controller design are developed for the underlying t s fuzzy affine systems with unreliable communication links the solutions to the problem are formulated in the form of linear matrix inequalities lmis finally simulation examples are provided to illustrate the effectiveness of the proposed approaches

robust h_ infty control for nonlinear stochastic systems a sliding mode approach this paper considers the sliding mode control for nonlinear stochastic systems modeled by ito stochastic differential equations it is noted that there exist state and exogenous disturbance dependent noise in the controlled systems by utilizing h infin disturbance attenuation technique a novel sliding mode control method is proposed such that the resultant system is asymptotically stable in probability with a prescribed h infin performance sufficient conditions for the solvability of these problems are derived via nonlinear hamilton jacobi hj type inequalities moreover it is shown that for a class of special nonlinear stochastic systems the h infin sliding mode control design can be obtained by solving linear matrix inequalities lmis finally a numerical simulation example is given

robust fuzzy design for nonlinear uncertain stochastic systems via sliding mode control this paper deals with the sliding mode control smc problem for nonlinear stochastic time delay systems by means of fuzzy approach the takagi sugeno t s fuzzy stochastic time delay model with parametric uncertainties and unknown nonlinearities is presented a sufficient condition for the exponential stability in mean square of the sliding motion is also derived moreover it is shown that when the linear matrix inequalities lmis with equality constraint are feasible the designs of both sliding surface and sliding mode controller can be easily obtained via convex optimization a simulation example illustrating the proposed method is given

operator formulation of wigner s r matrix theories for the schrodinger and dirac equations the r matrix theories for the schrodinger and dirac equations are formulated in the language of integral operators in the nonrelativistic theory the central role is played by an integral operator rb e relating function values to normal derivatives on a surface s of a closed volume v inside which the function satisfies the schrodinger equation at energy e in the relativistic theory the same role is played by two integral operators rb e and rb e linking on the surface s values of upper and lower components of spinor wave functions satisfying in the volume v the dirac equation at energy e systematic procedures for constructing the operators rb e and rb e generalizing the methods due to kapur and peierls and to wigner are presented

oscillation for nonlinear delay partial difference equations with positive and negative coefficients abstract we construct an important transform to obtain sufficient conditions for the oscillation of all solutions of the delay partial difference equations with positive and negative coefficients of the form m n a m n a m u n v a m 1 n a m n 1 a mn pa m k n l qa m k n l 0 and mn m n a m n a m u n v a m 1 n a m n 1 a mn p mn a m k n l q mn a m k n l 0 where m n 0 1 and k k l l are nonnegative integers p q 0 and u v are positive integers the coefficients mn qmn and pmn are assumed to be positive

universal fuzzy controllers based on generalized t s fuzzy models this paper investigates the universal fuzzy control problem based on generalized t s fuzzy models the universal approximation capability of the generalized t s fuzzy models is shown and an approach to robust controller design for general nonlinear systems based on this kind of generalized t s fuzzy models is developed the results of universal fuzzy controllers for two classes of nonlinear systems are then given and constructive procedures to obtain the universal fuzzy controllers are also provided an example is finally presented to show the effectiveness of our approach

nonlinear integral type sliding surface for both matched and unmatched uncertain systems this note presents a new nonlinear integral type sliding surface which incorporates a virtual nonlinear nominal control to achieve prescribed specifications first the plant with matched uncertainties is considered the resultant closed loop system during ideal sliding mode behaves exactly like the nominal plant under the nonlinear nominal control which completely nullifies the matched uncertainties and consequently satisfies the prescribed specifications second the stability analysis of the proposed sliding mode for the systems with unmatched uncertainties is performed to exploit the stability conditions numerical results demonstrate the validity of the proposed concept

adaptive fuzzy control for synchronization of nonlinear teleoperators with stochastic time varying communication delays in this paper adaptive fuzzy control is investigated for nonlinear teleoperators with time delays which ensures synchronization of positions and velocities of the master and slave manipulators and does not rely on the use of the scattering transformation compared with the previous passivity framework the communication delays are assumed to be stochastic time varying by feedback linearization the nonlinear dynamics of the teleoperation system is transformed into two subsystems local master slave position control with unmodeled dynamics and delayed motion synchronization then based on linear matrix inequalities lmi and markov jump linear systems adaptive fuzzy control strategies are developed for the nonlinear teleoperators with modeling uncertainties and external disturbances by using the approximation property of the fuzzy logic systems it is proven that the master slave teleoperation system is stochastically stable in mean square under specific lmi conditions and all the signals of the resulting closed loop system are uniformly bounded finally the extensive simulations are performed to show the effectiveness of the proposed method

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

dirichlet to neumann and neumann to dirichlet embedding methods for bound states of the dirac equation the embedding method inglesfield j e 1981 j phys c solid state phys 14 3795 is nowadays widely used for determining properties of bound and continuum eigenstates of the schrodinger equation recently crampin 2004 j phys condens matter 16 8875 extended inglesfield s formalism to systems described by the dirac equation in this paper we reformulate the embedding method for bound states of dirac particles in the language of the theory of surface integral operators which are natural analogues of the dirichlet to neumann dtn and neumann to dirichlet ntd operators used in the non relativistic theory a method of constructing kernels of these dirac counterparts of the dtn and ntd maps from solutions to an analogue of the steklov stekloff eigenproblem for an exterior dirac problem is presented a numerical example illustrating the utility of the dtn ntd embedding method is provided

integral sliding mode control for nonlinear systems with matched and unmatched perturbations we consider the problem of designing an integral sliding mode controller to reduce the disturbance terms that act on nonlinear systems with state dependent drift and input matrix the general case of both matched and unmatched disturbances affecting the system is addressed it is proved that the definition of a suitable sliding manifold and the generation of sliding modes upon it guarantees the minimization of the effect of the disturbance terms which takes place when the matched disturbances are completely rejected and the unmatched ones are not amplified a simulation of the proposed technique applied to a dynamically feedback linearized unicycle illustrates its effectiveness even in presence of nonholonomic constraints

nonsynchronized state estimation of multichannel networked nonlinear systems with multiple packet dropouts via t s fuzzy affine dynamic models this paper investigates the problem of robust h state estimation for a class of multichannel networked nonlinear systems with multiple packet dropouts the nonlinear plant is represented by takagi sugeno t s fuzzy affine dynamic models with norm bounded uncertainties and stochastic variables with general probability distributions are adopted to characterize the data missing phenomenon in output channels the objective is to design an admissible state estimator guaranteeing the stochastic stability of the resulting estimation error system with a prescribed h disturbance attenuation level it is assumed that the plant premise variables which are often the state variables or their functions are not measurable so that the estimator implementation with state space partition may not be synchronized with the state trajectories of the plant based on a piecewise quadratic lyapunov function combined with s procedure and some matrix inequality convexifying techniques two different approaches are developed to robust filtering design for the underlying t s fuzzy affine systems with unreliable communication links all the solutions to the problem are formulated in the form of linear matrix inequalities lmis finally simulation examples are provided to illustrate the effectiveness of the proposed approaches

delay dependent robust h sub spl infin and l sub 2 l sub spl infin filtering for a class of uncertain nonlinear time delay systems this note presents delay dependent robust h sub spl infin and l sub 2 l sub spl infin filter designs for a class of nonlinear systems with multiple time varying delays in the state and parameter uncertainties residing in a polytope the nonlinearities are assumed to satisfy global lipschitz conditions attention is focused on the design of robust full order and reduced order filters guaranteeing a prescribed noise attenuation level in an h sub spl infin or l sub 2 l sub spl infin sense the admissible filters can be obtained from the solution of convex optimization problems in terms of linear matrix inequalities which can be solved via efficient interior point algorithms

some summation formulae for spherical spinors two families of series with terms involving spherical spinors spinor spherical harmonics for a spin one half particle and are summed to closed forms involving the legendre function of the first kind and its derivatives with respect to an argument and or an index in particular it is shown that the closed forms of the series 0 n n are remarkably simple and with i denoting the 2 2 unit matrix and standing for the vector of pauli matrices integral eigenvalue equations solved by the spherical spinors with either n n or as kernels are provided it is pointed out that n n is the green function of the operator 1 i 1 2 while is the generalized reduced green function of the operator k 1 i k 1 2 with ir

universal fuzzy models and universal fuzzy controllers for stochastic nonaffine nonlinear systems this paper investigates the universal fuzzy model and universal fuzzy controller problems for stochastic nonaffine nonlinear systems the underlying mechanism of stochastic fuzzy logic is first discussed and a stochastic generalized fuzzy model with new stochastic fuzzy rule base is then given based on their function approximation capability these kinds of stochastic generalized fuzzy models are shown to be universal fuzzy models for stochastic nonaffine nonlinear systems under some sufficient conditions an approach to stabilization controller design for stochastic nonaffine nonlinear systems is then developed through their stochastic generalized takagi sugeno t s fuzzy approximation models then the results of universal fuzzy controllers for two classes of stochastic nonlinear systems along with constructive procedures to obtain the universal fuzzy controllers are also provided respectively finally a numerical example is presented to illustrate the effectiveness of the proposed approach

piecewise integral sliding mode control for t s fuzzy systems this paper addresses the issue of piecewise integral sliding mode control ismc for the takagi sugeno t s fuzzy systems ismc is chosen to stabilize the t s fuzzy system because of its superior capability in treating uncertainties individual integral sliding surfaces are designed in different operating regions of the t s fuzzy system conditions on the existence of the sliding mode in the associated region are given the chattering phenomenon around region boundaries is analyzed and the prevention of such chattering is discussed an illustrative example is finally given to show the efficiency of the proposed method

on the oscillation of two partial difference equations abstract this paper is concerned with two partial difference equations of the form a m 1 n a m n 1 a m n p m n a m k n l 0 and a m 1 n a m n 1 a m n i 1 u p i m n f i a m k i n l i 0 respectively we obtain sufficient conditions for the oscillation of all solutions of these equations

delay dependent hbox h _ infty filter design for discrete time fuzzy systems with time varying delays this paper investigates delay dependent hinfin filter design problems for discrete time fuzzy systems with time varying delays first a novel delay dependent piecewise lyapunov krasovskii functional ddplkf is proposed in which both the upper bound of delays and the delay interval are considered based on this ddplkf the delay dependent stability criteria for discrete time systems with constant or time varying delays are obtained respectively then delay dependent full order and reduced order hinfin filter design approaches are proposed the filter parameters can be obtained by solving a set of linear matrix inequalities lmis simulation examples are also given to illustrate the performance of the proposed approaches it is shown that our approaches are less conservative and that the corresponding hinfin filters can achieve better performance than the existing approaches

robust integral sliding mode control for uncertain stochastic systems with time varying delay this paper is concerned with sliding mode control for uncertain stochastic systems with time varying delay both time varying parameter uncertainties and an unknown nonlinear function may appear in the controlled system an integral sliding surface is first constructed then by means of linear matrix inequalities lmis a sufficient condition is derived to guarantee the global stochastic stability of the stochastic dynamics in the specified switching surface for all admissible uncertainties the synthesized sliding mode controller guarantees the reachability of the specified sliding surface finally a simulation example is presented to illustrate the proposed method

robust control by fuzzy sliding mode abstract most fuzzy controllers fcs for nonlinear second order systems are designed with a two dimensional phase plane in mind we show that the performance and the robustness of this kind of fc stems from their property of driving the system into the sliding mode sm in which the controlled system is invariant to parameter fluctuations and disturbances additionally the continuous distribution of the control values in the phase plane causes a behavior similar to that of a sliding mode controller smc with a boundary layer bl near the switching line this gives assured tracking quality even in the presence of high model uncertainties tracing the fc back to the principle of an smc one obtains evidence about the stability of the closed loop system the choice of the scaling factors for the crisp inputs and outputs can be guided by the comparison of the fc with the smc and with the modified smc respectively at the end of the paper an fc for a higher order system is proposed simulation results show the practicability of the method

lmi based sliding surface design for integral sliding mode control of mismatched uncertain systems we propose a linear matrix inequality lmi based sliding surface design method for integral sliding mode control of mismatched uncertain systems the uncertain system under consideration may have mismatched norm bounded uncertainties in the state matrix as well as the input matrix we give a sufficient condition for the existence of a sliding surface guaranteeing asymptotic stability of the full order sliding mode dynamics we also give an lmi characterization of the sliding surface together with an integral sliding mode control law guaranteeing the existence of a sliding mode from the initial time additionally we give an lmi condition of sliding surfaces guaranteeing the alpha stability constraint finally we give a simulation result to show the effectiveness of our method

a delay dependent approach to robust h sub spl infin filtering for uncertain discrete time state delayed systems a delay dependent approach to robust h sub spl infin filtering is proposed for linear discrete time uncertain systems with multiple delays in the state the uncertain parameters are supposed to reside in a polytope and the attention is focused on the design of robust filters guaranteeing a prescribed h sub spl infin noise attenuation level the proposed filter design methodology incorporates some recently appeared results such as moon s new version of the upper bound for the inner product of two vectors and de oliveira s idea of parameter dependent stability which greatly reduce the overdesign introduced in the derivation process in addition to the full order filtering problem the challenging reduced order case is also addressed by using different linearization procedures both full and reduced order filters can be obtained from the solution of convex optimization problems in terms of linear matrix inequalities which can be solved via efficient interior point algorithms numerical examples have been presented to illustrate the feasibility and advantages of the proposed methodologies

universal fuzzy integral sliding mode controllers based on t s fuzzy models this paper addresses the universal fuzzy integral sliding mode controllers problem for continuous time multi input multi output nonlinear systems based on takagi sugeno t s fuzzy models by using the approximation capability of t s fuzzy models the nonlinear systems are expressed by uncertain t s fuzzy models with norm bounded approximation errors a novel fuzzy dynamic integral sliding mode control dismc scheme is then developed for the nonlinear systems based on their t s fuzzy approximation models one of the key features of the new dismc scheme is that the restrictive assumption that all local linear systems share a common input matrix which is required in most existing fuzzy integral sliding mode control ismc approaches is removed furthermore the results of universal fuzzy ismcs for two classes of nonlinear systems along with constructive procedures to obtain the universal fuzzy ismcs are provided respectively finally the advantages and effectiveness of the proposed approaches are illustrated via a numerical example

a new design of delay dependent robust cal h _ bm infty filtering for discrete time t s fuzzy systems with time varying delay this paper investigates the problem of delay dependent robust h infin filtering design for a class of uncertain discrete time state delayed takagi sugeno t s fuzzy systems the state delay is assumed to be time varying and of an interval like type which means that both the lower and upper bounds of the time varying delay are available the parameter uncertainties are assumed to have a structured linear fractional form based on a novel fuzzy basis dependent lyapunov krasovskii functional combined with finsler s lemma and an improved free weighting matrix technique for delay dependent criteria a new sufficient condition for robust h infin performance analysis is first derived and then the filter synthesis is developed it is shown that by using a simple linearization technique incorporating a bounding inequality a unified framework can be developed such that both the full order and reduced order filters can be obtained by solving a set of linear matrix inequalities lmis which are numerically efficient with commercially available software finally simulation examples are provided to illustrate the advantages and less conservatism of the proposed approach

h sub spl infin fuzzy estimation for a class of nonlinear discrete time dynamic systems this paper studies h sub spl infin fuzzy filtering design for state estimation of nonlinear discrete time systems with bounded but unknown disturbances first the takagi and sugeno 1985 fuzzy model is proposed to represent a nonlinear system next using a linear matrix inequality lmi approach the h sub spl infin fuzzy filtering problems are characterized in terms of a linear matrix inequality problem lmip the lmip can be efficiently solved using convex optimization techniques simulation examples are given to illustrate the design procedure and the applicability of the proposed method the results indicate that the proposed method is suitable for practical applications

stability and stabilizability of fuzzy neural linear control systems this paper discusses stability analysis of fuzzy neural linear fnl control systems which consist of combinations of fuzzy models neural network nn models and linear models the authors consider a relation among the dynamics of nn models those of fuzzy models and those of linear models it is pointed out that the dynamics of linear models and nn models can be perfectly represented by takagi sugeno t s fuzzy models whose consequent parts are described by linear equations in particular the authors present a procedure for representing the dynamics of nn models via t s fuzzy models next the authors recall stability conditions for ensuring stability of fuzzy control systems in the sense of lyapunov the stability criteria is reduced to the problem of finding a common lyapunov function for a set of lyapunov inequalities the stability conditions are employed to analyze stability of fnl control systems finally stability analysis for four types of fnl control systems is demonstrated

a unified construction of variational r matrix methods i the schrodinger equation properties of two linear integral operators and relating function values to normal derivatives on a surface of a closed volume inside which the function satisfies the schrodinger equation at energy e are discussed variational principles for matrix elements and eigenvalues of these operators are constructed in a systematic way by using an approach of gerjuoy et al some of the variational principles derived were already known in the non relativistic r matrix theory of scattering but others seem to be new applications of the rayleigh ritz linear trial functions are presented

adaptive fuzzy logic control of dynamic balance and motion for wheeled inverted pendulums in this paper adaptive fuzzy logic control of dynamic balance and motion is investigated for wheeled inverted pendulums with parametric and functional uncertainties the proposed adaptive fuzzy logic control based on physical properties of wheeled inverted pendulums makes use of a fuzzy logic engine and a systematic online adaptation mechanism to approximate the unknown dynamics based on lyapunov synthesis the fuzzy control ensures that the system outputs track the given bounded reference signals to within a small neighborhood of zero and guarantees semi global uniform boundedness of all closed loop signals the effectiveness of the proposed control is verified through extensive simulations

oscillatory behavior of delay partial difference equations with positive and negative coefficients abstract we construct an important transform to obtain sufficient conditions for the oscillation of all solutions of delay partial difference equations with positive and negative coefficients of the form a m 1 n a m n 1 a mn p mn a m k 1 q mn a m k n l 0 where m n 0 1 and k k l l are nonnegative integers p q 0 the coefficients q mn and p mn are sequences of nonnegative real numbers

t s fuzzy based sliding mode controller design for discrete time nonlinear model and its applications abstract this paper investigates the takagi sugeno t s fuzzy based sliding mode control smc design of the discrete time nonlinear model by constructing a suitable fuzzy membership functions fmfs dependent lyapunov function the sufficient conditions are derived such that the resultant discrete time t s fuzzy model can achieve strictly q s r dissipative where q s and r are known matrices with compatible dimensions satisfying q 0 and r r t and is a positive constant then the desired control gain can be obtained by solving a set of linear matrix inequalities lmis besides that a fuzzy smc is designed to assure reaching condition a modified fuzzy sliding mode controller is also constructed to adapt input saturation finally simulation results are presented to demonstrate the applicability and effectiveness of the proposed approaches