finite dimensional controllers for linear distributed parameter systems exponential stability using residual mode filters abstract modal control has often been proposed as a way to design stabilizing low order controllers for distributed parameter systems dps however it is well known that such controllers designed from a reduced order modal model do not necessarily stabilize the actual dps in this paper we prove that exponential closed loop stability can always be achieved by the addition of a residual mode filter of sufficiently large dimension

on the error estimates of several newton like methods1partial supported by the national natural science foundation of china and by natural science foundation of zhejiang province 1 in this paper convergence theorems and error estimates for several newton like iteration methods under new kantorovitch ostrowski type conditions using the information of higher derivatives at initial point s are established we get not only the convergence speed estimates of iterative sequence x n but also the estimates of f x n 1 f x n

relaxing convergence conditions for newton s method the classical kantorovich theorem on newton s method assumes that the first derivative of the operator involved satisfies a lipschitz condition 0 f x f y l x y in this paper we weaken this condition assuming that 0 f x f x0 x x0 for a given point x0

finite dimensional adaptive observers applied to distributed parameter systems the application of finite dimensional adaptive observers to distributed parameter systems is addressed ultimate boundedness of the parameter and state errors are proved in the case of residuals which have finite energy over a finite time interval provided the plant input is definitely exciting in the absence of definite excitation an error growth rate of proportional to t sup 1 2 is proved the results are obtained without assuming plant stability or input boundedness

a newton method for systems of m equations in n variables the classical newton kantorovich method for solving systems of equations f x 0 uses the inverse of the jacobian of f at each iteration if the number of equations is dierent than the number of variables or if the jacobian cannot be assumed nonsingular a generalized inverse of the jacobian can be used in a newton method whose limit points are stationary points of kf x k 2 we study conditions for local convergence of this method prove quadratic convergence and implement an adaptive version this iterative method allowing a controlled increase of the ranks of the 2 inverses used in the iterations

a method for finding sharp error bounds for newton s method under the kantorovic assumptions this paper gives a method for finding sharpa posteriori error bounds for newton s method under the assumptions of kantorovich s theorem on the basis of this method new error bounds are derived and comparison is made among the known bounds of dennis 2 doring 4 gragg tapia 5 kantorovich 6 7 kornstaedt 9 lancaster 10 miel 11 13 moret 14 ostrowski 17 18 potra 19 and potra ptak 20

numerical treatment of sth order boundary value problems by solving second kind fredholm integral equations a nystrom method is proposed for solving fredholm integral equations equivalent to boundary value problems of order s with complete differential equations the stability and the convergence of the proposed procedure are proved some numerical examples are provided in order to illustrate the accuracy of the method and to compare the procedure with some other ones given in the literature

a variant of newton s method and its application abstract this paper details an existence and uniqueness theorem for solving an operator equation of the form f x 0 where f is a gateaux differentiable operator defined on an open convex subset of a banach space proved from the main theorem an earlier theorem of argyros follows as a consequence other corollaries constitute the semilocal versions of the theorems due to ozban and weerakoon and fernando in a general banach space our main theorem leads to the existence of solutions for a class of nonlinear urysohn type integral equations in the n dimensional euclidean space

on newton s method under holder continuous derivative a mysovskii type theorem for newton s method under k p holder continuous derivative is considered in this paper for the application studied by others the new condition is weaker than ones in the literature also we prove that the optimal convergent order is p 1 for 0 p 1

high order accuracy nonpolynomial spline solutions for 2μth order two point boundary value problems sixth order accurate method based on quintic nonpolynomial spline function for the numerical solution of 2 th order two point bvps where is a positive integer is presented by transforming the problem into a system of second order two point bvps the nonpolynomial spline function is used to drive some consistency relations for computing approximation to the solution of this problem the proposed approach gives better approximations than existing polynomial spline and finite difference methods and has a lower computational cost convergence analysis of the proposed method is discussed numerical examples are included to illustrate the practical usefulness of our method

solutions of twelfth order boundary value problems using thirteen degree spline abstract numerical solutions of the twelfth order linear special case boundary value problems are obtained using thirteen degree spline the end conditions are derived for the definition of spline siddiqi and twizell s s siddiqi e h twizell spline solutions of linear twelfth order boundary value problems j comput appl math 78 1997 371 390 presented the solutions of twelfth order boundary value problems using 12th degree spline where some unexpected results for the solution and its derivatives were obtained near the boundaries of the interval no such situation is observed in this method the algorithm developed approximates not only the solution but its higher order derivatives as well numerical illustrations are tabulated to demonstrate the practical usefulness of the method

newton method under weak lipschitz continuous derivative in banach spaces in the present paper a relax kantorovich type condition to guarantee the convergence of newton method with order 2 in banach space is obtained which takes the well known kantorovich and smale conditions as its special cases the relations between the new condition and the old ones are also studied

the numerical solution of third order boundary value problems using quintic splines we present a fourth order method based on quintic splines for the solution of third order linear and non linear boundary value problems bvps of the form y f x y a

adaptive optimal control of highly dissipative nonlinear spatially distributed processes with neuro dynamic programming highly dissipative nonlinear partial differential equations pdes are widely employed to describe the system dynamics of industrial spatially distributed processes sdps in this paper we consider the optimal control problem of the general highly dissipative sdps and propose an adaptive optimal control approach based on neuro dynamic programming ndp initially karhunen loeve decomposition is employed to compute empirical eigenfunctions eefs of the sdp based on the method of snapshots these eefs together with singular perturbation technique are then used to obtain a finite dimensional slow subsystem of ordinary differential equations that accurately describes the dominant dynamics of the pde system subsequently the optimal control problem is reformulated on the basis of the slow subsystem which is further converted to solve a hamilton jacobi bellman hjb equation hjb equation is a nonlinear pde that has proven to be impossible to solve analytically thus an adaptive optimal control method is developed via ndp that solves the hjb equation online using neural network nn for approximating the value function and an online nn weight tuning law is proposed without requiring an initial stabilizing control policy moreover by involving the nn estimation error we prove that the original closed loop pde system with the adaptive optimal control policy is semiglobally uniformly ultimately bounded finally the developed method is tested on a nonlinear diffusion convection reaction process and applied to a temperature cooling fin of high speed aerospace vehicle and the achieved results show its effectiveness

fuzzy boundary control design for a class of nonlinear parabolic distributed parameter systems this paper deals with the problem of fuzzy boundary control design for a class of nonlinear distributed parameter systems which are described by semilinear parabolic partial differential equations pdes both distributed measurement form and collocated boundary measurement form are considered a takagi sugeno t s fuzzy pde model is first applied to accurately represent the semilinear parabolic pde system based on the t s fuzzy pde model two types of fuzzy boundary controllers which are easily implemented since only boundary actuators are used are proposed to ensure the exponential stability of the resulting closed loop system sufficient conditions of exponential stabilization are established by employing the lyapunov direct method and the vector valued wirtinger s inequality and presented in terms of standard linear matrix inequalities finally the advantages and effectiveness of the proposed control methodology are demonstrated by the simulation results of two examples

a nystrom method for solving 2sth order boundary value problems a nystrom method is proposed for solving fredholm integral equations equivalent to special boundary value problems of order 2s the stability and the convergence of the proposed procedure is proved some numerical examples are provided in order to illustrate the accuracy of the method

septic spline solutions of sixth order boundary value problems septic spline is used for the numerical solution of the sixth order linear special case boundary value problem end conditions for the definition of septic spline are derived consistent with the sixth order boundary value problem the algorithm developed approximates the solution and their higher order derivatives the method has also been proved to be second order convergent three examples are considered for the numerical illustrations of the method developed the method developed in this paper is also compared with that developed in m el gamel j r cannon j latour a i zayed sinc galerkin method for solving linear sixth order boundary value problems mathematics of computation 73 247 2003 1325 1343 as well and is observed to be better

h sampled data fuzzy observer design for nonlinear parabolic pde systems this paper considers the h infty sampled data fuzzy observer sdfo design problem for nonlinear parabolic pde systems under spatially local averaged measurements slams initially the nonlinear pde system is accurately represented by the takagi sugeno t s fuzzy pde model then based on the t s fuzzy pde model a sdfo under slams is constructed for the state estimation to attenuate the effect of the exogenous disturbance and the design disturbance an h infty sdfo design under slams is developed in terms of linear matrix inequalities lmis by utilizing lyapunov functional and inequality techniques which can guarantees the exponential stability and satisfies an h infty performance for the estimation error fuzzy pde system lastly simulation results on the state estimation of the fitzhugh nagumo fhn equation are given to support the presented h infty sdfo design method

a new semilocal convergence theorem for newton s method abstract a new semilocal convergence theorem for newton s method is established for solving a nonlinear equation f x 0 defined in banach spaces it is assumed that the operator f is twice frechet differentiable and f satisfies a lipschitz type condition results on uniqueness of solution and error estimates are also given finally these results are compared with those that use kantorovich conditions

robust filter for nonlinear stochastic partial differential systems in sensor signal processing fuzzy approach this study addresses a robust h filter design problem for nonlinear stochastic partial differential systems nspdss with random external disturbance and measurement noise in the spatiotemporal domain for nspdss a robust h filter design through a set of sensor measurements needs to solve a complex second order hamilton jacobi integral inequality hjii in order to simplify the design procedure a fuzzy stochastic partial differential system based on a fuzzy interpolation approach is proposed to approximate the nspds then a fuzzy stochastic spatial state space model is developed to represent the fuzzy stochastic partial differential system via the semidiscretization finite difference scheme and the kronecker product based on this model a robust h filter design is proposed to achieve the robust state estimation via solving linear matrix inequalities lmis instead of a second order hjii the proposed robust fuzzy h filter efficiently attenuates the effect of spatiotemporal external disturbances and measurement noise on the state estimation of nspdss from the area energy point of view finally a robust h state estimation example of heat transfer system is given to illustrate the design procedure and to confirm the h filtering performance of the proposed robust filter design method

a cubically convergent newton type method under weak conditions under weak conditions we present an iteration formula to improve newton s method for solving nonlinear equations the method is free from second derivatives permitting f x 0 in some points and per iteration it requires two evaluations of the given function and one evaluation of its derivative analysis of convergence demonstrates that the new method is cubically convergent some numerical examples illustrate that the algorithm is more efficient and performs better than classical newton s method

two conditions concerning newton s method in this note we compare two conditions concerning newton s method and find out that even under some weaker condition one has the convergence of the newton s method and a better error bound than the relative strong condition

nonic spline solutions of eighth order boundary value problems nonic spline is used for the numerical solutions of the eighth order linear special case boundary value problems the end conditions are derived for the definition of spline the algorithm developed not only approximates the solutions but their higher order derivatives as well the method presented in this paper has also been proved to be second order convergent two examples compared with those considered by inc et al m inc d j evans an efficient approach to approximate solutions of eighth order boundary value problems int j comput math 81 6 2004 685 692 and siddiqi et al s s siddiqi e h twizell spline solution of linear eighth order boundary value problems comput methods appl mech eng 131 1996 309 325 show that the method developed in this paper is more efficient

on the continuous realization of iterative processes many important mathematical problems are solved by iterative methods many of these iterative schemes may be regarded as the discrete realization of certain continuous dynamical systems this paper summarizes some of the recent developments in the continuous realization of several popular basic iterative methods

on a theorem of l v kantorovich concerning newton s method we study the problem of approximating a locally unique solution of an operator equation using newton s method the well known convergence theorem of l v kantorovich involves a bound on the second frechet derivative or the lipschitz frechet differentiability of the operator involved on some neighborhood of the starting point here we provide local and semilocal convergence theorems for newton s method assuming the frechet differentiability only at a point which is a weaker assumption a numerical example is provided to show that our result can apply to solve a scalar equation where the above mentioned ones may not

on the convergence of newton s method for a class of nonsmooth operators we provide an analog of the newton kantorovich theorem for a certain class of nonsmooth operators this class includes smooth operators as well as nonsmooth reformulations of variational inequalities it turns out that under weaker hypotheses we can provide under the same computational cost over earlier works s m robinson newton s method for a class of nonsmooth functions set valued anal 2 1994 291 305 a semilocal convergence analysis with the following advantages finer error bounds on the distances involved and a more precise information on the location of the solution in the local case not examined in s m robinson newton s method for a class of nonsmooth functions set valued anal 2 1994 291 305 we can show how to enlarge the radius of convergence and also obtain finer error estimates numerical examples are also provided to show that in the semilocal case our results can apply where others s m robinson newton s method for a class of nonsmooth functions set valued anal 2 1994 291 305 fail whereas in the local case we can obtain a larger radius of convergence than before s m robinson newton s method for a class of nonsmooth functions set valued anal 2 1994 291 305

parametric cubic spline solution of two point boundary value problems in this paper we use parametric cubic spline function to develop a numerical method which is fourth order for a specific choice of the parameter for computing smooth approximations to the solution for second order boundary value problems some numerical evidence is also included to demonstrate the superiority of our method

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

a new semilocal convergence theorem for newton s method in banach space using hypotheses on the second frechet derivative a new global kantorovich type convergence theorem for newton s method in banach space is provided for approximating a solution of a nonlinear equation it is assumed that a solution exists and the second frechet derivative of the operator involved satisfies a lipschitz condition our convergence condition differs from earlier ones and therefore it has theoretical and practical value finally a simple numerical example is provided to show that our results apply where earlier ones fail

a new semilocal convergence theorem for newton s method involving twice frechet differentiability at only one point in this study we provide a new semilocal convergence theorem for newton s method it is assumed that an operator is twice continuously frechet differentiable at only one point finally a simple numerical example is given to show that our results can apply but earlier similar ones fail

guaranteed cost fuzzy state observer design for semilinear parabolic pde systems under pointwise measurements abstract this paper studies the guaranteed cost fuzzy state observer gcfso design via pointwise measurement sensors for a class of distributed parameter systems described by semilinear parabolic partial differential equations pdes initially a takagi sugeno t s fuzzy model is employed to accurately represent the original pde system in a local region then based on the t s fuzzy model a fuzzy state observer is constructed for the state estimation by augmenting the state estimation error system with the fuzzy pde system and utilizing lyapunov technique and wirtinger s inequality a fuzzy state observer design with a guaranteed cost is developed in terms of linear matrix inequalities lmis the resulting fuzzy observer can exponentially stabilize the augmented system while providing an upper bound on the cost function of state estimation error moreover a suboptimal gcfso design problem is also addressed to make the upper bound as small as possible finally the numerical simulation results on two examples demonstrate the effectiveness of the proposed method

observers and initial state recovering for a class of hyperbolic systems via lyapunov method a b s t r a c t recently the problem of estimating the initial state of some linear infinite dimensional systems from measurements on a finite interval was solved by using the sequence of forward and backward observers ramdani tucsnak and weiss 2010 in the present paper we introduce a direct lyapunov approach to the problem and extend the results to the class of semilinear systems governed by wave and beam equations with boundary measurements from a finite interval we first design forward observers and derive linear matrix inequalities lmis for the exponential stability of the estimation errors further we obtain simple finite dimensional conditions in terms of lmis for an upper bound t on the minimal time that guarantees the convergence of the sequence of forward and backward observers on 0 t for the initial state recovering this t represents also an upper bound on the observability time for observation times bigger than t these lmis give upper bounds on the convergence rate of the iterative algorithm in the norm defined by the lyapunov functions in our approach t is found as the minimal dwelling time for the switched exponentially stable forward and backward estimation error systems with the different lyapunov functions liberzon 2003 the efficiency of the results is illustrated by numerical examples 2013 elsevier ltd all rights reserved

on solving nonlinear equations with simple singularities or nearly singular solutions the paper begins with a review of the convergence theory for newton s method near simple and other regular singularities followed by a brief discussion of the inherent difficulty of singular problems and the effect of rounding errors on the achievable solution accuracy then several ways to accelerate the slow convergence of newton s method are described in some detail these are richardson extrapolation overrelaxation bordering by a singularity condition and appending the usual linear model by a quadratic term the last two approaches require limited second derivative information which can be obtained analytically by differencing or through secant updating numerical comparisons reported in the final sections lead to the conclusion that the collection of the additional information pays off in terms of speed and accuracy

on a numerical treatment for the curve tracing of the homotopy method a newton like iteration scheme is proposed for the tracing of an implicitly defined smooth curve this scheme originates from the study of the continuous newton raphson method for underdetermined systems and hence inherits the characteristic property of orthogonality its domain of attraction is formed and makes it possible to trace this curve more efficiently

convergence of newton s method for singular smooth and nonsmooth equations using adaptive outer inverses we present a local convergence analysis of generalized newton methods for singular smooth and nonsmooth operator equations using adaptive constructs of outer inverses we prove that for a solution x of f x 0 there exists a ball s s x r r 0 such that for any starting point x 0 in s the method converges to a solution bar x in s of gamma f x 0 where gamma is a bounded linear operator that depends on the frechet derivative of f at x 0 or on a generalized jacobian of f at x 0 point bar x may be different from x when x is not an isolated solution moreover we prove that the convergence is quadratic if the operator is smooth and superlinear if the operator is locally lipschitz these results are sharp in the sense that they reduce in the case of an invertible derivative or generalized derivative to earlier theorems with no additional assumptions the results are illustrated by a system of smooth equations and a system of nonsmooth equations each of which is equivalent to a nonlinear complementarity problem

convergence analysis of some algorithms for solving nonsmooth equations this paper presents convergence analysis of some algorithms for solving systems of nonlinear equations defined by locally lipschitzian functions for the directional derivative based and the generalized jacobian based newton methods both the iterates and the corresponding function values are locally superlinearly convergent globally a limiting point of the iterate sequence generated by the damped directional derivative based newton method is a zero of the system if and only if the iterate sequence converges to this point and the stepsize eventually becomes one provided that the system is strongly bd regular and semismooth at this point in this case the convergence is superlinear a general attraction theorem is presented which can be applied to two algorithms proposed by han pang and rangaraj a hybrid method which is both globally convergent in the sense of finding a stationary point of the norm function of the system and locally quadratically convergent is also presented

qualitative analysis of newton s flow the newton flow of a parameter dependent mapping is analysed in a neighbourhood of a singular point it is shown that the liapunov schmidt reduction process yields an invariant exponentially attracting manifold of the newton flow if the singular point is a fold then a normal form of the reduced 2 d newton flow is given moreover numerical experiments suggest that discrete versions of the normal form seem to be useful for an understanding of the performance of the ordinary newton method in a neighbourhood of the fold

indices of convexity and concavity application to halley method we define an index to measure the convexity of a convex function f at each point we use this index to establish conditions on the convergence of the halley method in the complex plane and in banach spaces

robust estimation and filtering in the presence of bounded noise optimal algorithms for robust estimation and filtering are constructed the noise is considered a deterministic variable belonging to a set described by a norm previous results obtained for complete one to one and approximate information by m milanese and r tempo ibid vol 30 p 730 8 1985 are extended to partial and approximate information this information is considered useful in dealing with dynamic systems not completely identifiable and or with two different sources of noise such as process and measurement noise for different norms characterizing the noise optimal algorithms in a min max sense are shown in particular for hilbert norms a linear optimal algorithm is the well known minimum variance estimator for l sub infinity norm an optimal algorithm computable by linear programming is presented state estimation is formalized in the context of the general theory for stable systems an approximate state estimation is obtained by neglecting higher order powers an upper bound determining the approximation introduced is derived a numerical example illustrates the application of the theory

a note on the kantorovich theorem for newton iteration abstract in this paper a new theorem for the newton method convergence is obtained its condition is different from that of the kantorovich theorem and therefore it has theoretical and practical value

spectral galerkin methods for the primary two point boundary value problem in modelling viscoelastic flows the essential character of the primary elliptic hyperbolic operator encountered in the modelling of viscoelastic flows is encaptured in a non linear fifth order two point boundary value problem in one dimension expansions in terms of beam functions and chebyshev polynomials are used to compute solutions to the primary two point boundary value problem within a spectral galerkin formulation an investigation of the performance of the methods with respect to the level of non linearity is carried out accurate results are obtained with chebyshev polynomials for high levels of non linearity whereas the behaviour of beam function expansions proves far more sensitive to the level of non linearity

error bounds for newton s iterates derived from the kantorovich theorem in this paper it is shown that the upper and lower bounds of the errors in the newton iterates recently obtained by potra ptak 11 and miel 7 with the use of nondiscrete induction and majorizing sequence respectively follow immediately from the kantorovich theorem and the kantorovich recurrence relations it is also shown that the upper and lower bounds of miel are finer than those of potra ptak

guaranteed cost design for controlling semilinear parabolic pde systems with mobile collocated actuators and sensors this paper investigates the guaranteed cost design problem for controlling a class of semilinear parabolic partial differential equation pde systems using mobile collocated actuators and sensors

a newton kantorvich theorem for equations involving m frechet differentiable operators and applications in radiative transfer abstract in this study we approximate a locally unique solution of a nonlinear operator equation in banach space using newton s method a complete error analysis showing the quadratic convergence of our method is also given our new theorem uses lipschitz or holder continuity assumptions on m frechet differentiable operators where m 2 is a positive integer a numerical example is given to show that our results provide a better information on the location of the solution as well as finer error bounds on the distances involved than earlier results a second numerical example shows how to solve a nonlinear integral equation appearing in radiative transfer

the theory of newton s method we review the most important theoretical results on newton s method concerning the convergence properties the error estimates the numerical stability and the computational complexity of the algorithm we deal with the convergence for smooth and nonsmooth equations underdetermined equations and equations with singular jacobians only those extensions of the newton method are investigated where a generalized derivative and or a generalized inverse is used

the theory of smale s point estimation and its applications abstract the main result of this paper is that we exact smale s point estimation theory i e without assuming k p z 1 p k z k k 2 being bounded by the point estimation convergence theorem of the ne method is set up by making use of the majorizing method the proof of the theorem is simple and precise while the required point estimation conditions are weaker than all those of known point estimation convergence theorems another result of this paper is an application of the above new theory to the durand kerner method we compare the point estimation conditions for the durand kerner method with other known point estimation conditions numerical results show that our results have evident advantages

third order convergence theorem by using majorizing function for a modified newton method in banach space abstract following the ideas of frontini and sormani we present a modified newton method in banach space which is used to solve the nonlinear operator equation we establish the newton kantorovich convergence theorem for the modified newton method with third order convergence in banach space by using majorizing function we also get the error estimate finally two examples are provided to show the application of our theorem

a third order method for fixed points in banach spaces this paper deals with a third order stirling like method used for finding fixed points of nonlinear operator equations in banach spaces the semilocal convergence of the method is established by using recurrence relations under the assumption that the first frechet derivative of the involved operator satisfies the holder continuity condition a theorem is given to establish the error bounds and the existence and uniqueness regions for fixed points the r order of the method is also shown to be equal to at least 2p 1 for p 0 1 the efficacy of our approach is shown by solving three nonlinear elementary scalar functions and two nonlinear integral equations by using both stirling like method and newton like method it is observed that our convergence analysis is more effective and give better results

weak convergence conditions for inexact newton type methods abstract we establish a new semilocal convergence results for inexact newton type methods for approximating a locally unique solution of a nonlinear equation in a banach spaces setting we show that our sufficient convergence conditions are weaker and the estimates of error bounds are tighter in some cases than in earlier works 15 31 special cases and numerical examples are also provided in this study

on newton s method under mild differentiability conditions and applications in this study we are concerned with the problem of approximating a locally unique solution of a nonlinear operator equation in a banach space we examine the convergence of the newton kantorovich method by assuming that the frechet derivative of the nonlinear operator involved is only holder continuous many results exist already in the literature to cover the stronger case when the operator is lipschitz continuous moreover we use this study to counter some claims made by galperin and waksman on related work of ours furthermore we use our results to solve a two point boundary value problem appearing in kinetic theory of gasses elasticity and other applied areas

solutions of tenth order boundary value problems using eleventh degree spline abstract numerical solutions of the tenth order linear special case boundary value problems are obtained using eleventh degree spline the end conditions consistent with the bvp are also derived siddiqi and twizell s s siddiqi e h twizell spline solutions of linear tenth order boundary value problems int j comput math 68 1998 345 362 presented the solutions of tenth order boundary value problems using tenth degree spline where some unexpected results for the solution and higher order derivatives were obtained near the boundaries of the interval no such unexpected situation is observed in this method near the boundaries of the interval and the results are better in the whole interval the algorithm developed approximates the solutions and their higher order derivatives numerical illustrations are tabulated to compare the errors with those considered by siddiqi and twizell s s siddiqi e h twizell spline solutions of linear tenth order boundary value problems int j comput math 68 1998 345 362 and the method is observed to be better

observer design for takagi sugeno descriptor models this paper considers observer design for nonlinear descriptor systems we propose approaches based on takagi sugeno ts models an extended estimation vector is used in order to keep the descriptor structure of the observer the design conditions are expressed as linear matrix inequalities the proposed observer structure via an intermediate variable as estimated variable is able to recover the previous observer results for ts descriptors moreover through a direct extension via so called finsler s lemma relaxed conditions are obtained numerical examples show the effectiveness of the proposed approaches

adaptive observer for a class of parabolic pdes the problem of state observation based on spatially sampled output measurements is addressed for a class of infinite dimensional systems modelled by a semi linear heat equation augmented with a structured uncertain part involving a set of unknown parameters an adaptive observer is designed that provides online estimates of the system spatially distributed state and unknown parameters based on sampled data in space sufficient conditions for the observer to be exponentially convergent are established these include an ad hoc persistent excitation condition as well as a condition on how the observer gain must be selected in relation with the space sampling interval

comparison of brown s and newton s method in the monotone case in many cases when newton s method applied to a nonlinear sytemf x 0 produces a monotonically decreasing sequence of iterates brown s method converges monotonically too we compare the iterates of brown s and newton s method in these monotone cases with respect to the natural partial ordering it turns out that in most of the cases arising in applications brown s method then produces better iterates than newton s method

on the local convergence of fast two step newton like methods for solving nonlinear equations a local convergence analysis is presented for a fast two step newton like method tsnlm for solving nonlinear equations in a banach space setting the tsnlm unifies earlier methods such as newton s secant newton like chebyshev secant chebyshev newton steffensen stirling s and other single or multistep methods numerical examples and a comparative study of these methods validating our theoretical results are also given in the concluding section of this paper

a nonsmooth version of newton s method newton s method for solving a nonlinear equation of several variables is extended to a nonsmooth case by using the generalized jacobian instead of the derivative this extension includes the b derivative version of newton s method as a special case convergence theorems are proved under the condition of semismoothness it is shown that the gradient function of the augmented lagrangian forc2 nonlinear programming is semismooth thus the extended newton s method can be used in the augmented lagrangian method for solving nonlinear programs

a newton like method and its application abstract in this paper we prove an existence and uniqueness theorem for solving the operator equation f x g x 0 where f is a gateaux differentiable continuous operator while the operator g satisfies a lipschitz condition on an open convex subset of a banach space as corollaries a theorem of tapia on a weak newton s method and the classical convergence theorem for modified newton iterates are deduced an existence theorem for a generalized euler lagrange equation in the setting of sobolev space is obtained as a consequence of the main theorem we also obtain a class of gateaux differentiable operators which are nowhere frechet differentiable illustrative examples are also provided

extending the domain of starting points for newton s method under conditions on the second derivative abstract in this paper we propose a center lipschitz condition for the second frechet derivative together with the use of restricted domains in order to improve the domain of starting points for newton s method in addition we compare the new result with an older one and see that the former improves the latter

switching type h filter design for t s fuzzy systems with unknown or partially unknown membership functions this paper is concerned with the h filter design problem for takagi sugeno t s fuzzy systems with unknown or partially unknown membership functions if the membership functions are allowed to be unknown or partially unknown then a fuzzy system may describe a wide class of nonlinear systems however in this case the filter design of fuzzy systems which is based on parallel distributed compensator strategy is infeasible to tackle this difficulty a switching mechanism which depends on the lower and upper bounds of the unknown membership functions is introduced to construct the h filter with varying gains some examples given in the simulation section show that the proposed method can achieve a better disturbance attenuation performance than a simple fixed gain filter design approach

convergence of newton like methods for singular operator equations using outer inverses we present a semilocal kantorovich type analysis for newton like methods for singular operator equations using outer inverses we establish sharp generalizations of the kantorovich theory and the mysovskii theory for operator equations when the derivative is not necessarily invertible the results reduce in the case of an invertible derivative to well known theorems of kantorovich and mysovskii with no additional assumptions unlike earlier theorems which impose strong conditions the strategy of the analysis is based on banach type lemmas and perturbation bounds for outer inverses which show that the set of outer inverses to a given bounded linear operator admits selections that behave like bounded linear inverses in contrast to inner inverses or generalized inverses which do not depend continuously on perturbations of the operator we give two examples to illustrate our results and compare them with earlier results and another numerical example to relate our results to computational issues