an iterative method for nonsymmetric systems with multiple right hand sides we propose a method for the solution of linear systems ax b where a is a large possibly sparse nonsymmetric matrix of order n and b is an arbitrary rectangular matrix of order n times s with s of moderate size the method uses a single krylov subspace per step as a generator of approximations a projection process and a richardson acceleration technique it thus combines the advantages of recent hybrid methods with those for solving symmetric systems with multiple right hand sides numerical experiments indicate that in several cases the method has better practical performance and significantly lower memory requirements than block versions of nonsymmetric solvers and other proposed methods for the solution of systems with multiple right hand sides

effective digital implementation of fuzzy control systems based on approximate discrete time models this paper addresses an effective digital implementation of fuzzy control systems via an intelligent digital redesign idr approach the purpose of idr is to effectively convert an existing continuous time fuzzy controller to an equivalent sampled data fuzzy controller in the sense of the state matching the authors show that under reasonable assumptions the idr based on the exact discrete time models can be reduced to the idr based on the approximate discrete time models the state matching error between the closed loop trajectories is carefully analyzed using the integral quadratic functional approach the estimation of the state matching error is presented using the linear matrix inequality lmi techniques the problem of designing the sampled data fuzzy controller to minimize the estimation as well as to guarantee the stability is formulated and solved as the convex optimization problem with lmi constraints it is also shown that the resulting sampled data fuzzy controller recovers the performance of the continuous time fuzzy controller as the sampling period approaches zero a numerical example is used to demonstrate the effectiveness of the proposed design technique

a smooth transition model between kinetic and diffusion equations this paper presents a model which provides a smooth transition between a kinetic and a diffusion domain the idea is to use a buffer zone in which both diffusion and kinetic equations will be solved the solution of the original kinetic equation will be recovered as the sum of the solutions of these two equations we use an artificial connecting function which makes the equation on each domain degenerate at the end of the buffer zone thus no boundary condition is needed at the transition point this model avoids the delicate issue of finding the interface condition or iteration in a typical domain decomposition method that couples a kinetic equation with hydrodynamic equations a new asymptotic preserving method for this model is introduced and numerical examples are used to validate this new model and the new numerical method

discretization of the multiscale semiconductor boltzmann equation by diffusive relaxation schemes in this paper we derive diffusive relaxation schemes for the linear semiconductor boltzmann equation that work in both the kinetic and diffusive regimes similar to our earlier approach for multiscale transport equations we use the even and odd parity formulation of the kinetic equation and then reformulate it into the diffusive relaxation system drs in order to handle the implicit anisotropic collision term efficiently we utilize a suitable power series expansion based on the wild sum which yields a time discretization uniformly stable with any desired order of accuracy yet is explicitly solvable with the correct drift diffusion limit the velocity discretization is done with the gauss hermite quadrature rule equivalent to a moment expansion method asymptotic analysis and numerical experiments show that the schemes have the usual advantages of a diffusive relaxation scheme for multiscale transport equations and are asymptotic preserving

new convergence results on the global gmres method for diagonalizable matrices in the present paper we give some new convergence results of the global gmres method for multiple linear systems in the case where the coefficient matrix a is diagonalizable we derive new upper bounds for the frobenius norm of the residual we also consider the case of normal matrices and we propose new expressions for the norm of the residual

an asymptotic preserving two dimensional staggered grid method for multiscale transport equations we propose a two dimensional asymptotic preserving scheme for linear transport equations with diffusive scalings it is an extension of the time splitting developed by jin pareschi and toscani siam j numer anal 38 2000 pp 913 936 but uses spatial discretizations on staggered grids which preserves the discrete diffusion limit with a more compact stencil the first novelty of this paper is that we propose a staggering in two dimensions that requires fewer unknowns than one could have naively expected the second contribution of this paper is that we rigorously analyze the scheme of jin pareschi and toscani we show that the scheme is ap and obtain an explicit cfl condition which couples a hyperbolic and a parabolic condition this type of condition is common for asymptotic preserving schemes and guarantees uniform stability with respect to the mean free path in addition we obtain an upper bound on the relaxation parameter which is the crucial parameter of the used time discretization se

a conjugate gradient algorithm for the treatment of multiple incident electromagnetic fields an iterative method based on the conjugate gradient cg algorithm is developed for the efficient treatment of equations involving multiple excitations examples show that significant time savings can be obtained as compared to treating each excitation individually with the conjugate gradient algorithm however these savings are not obtained without the drawback of increased memory requirements to store the additional excitations residuals and solutions the efficiency of this algorithm tends to increase as additional excitations are added

asymptotic induced domain decomposition methods for kinetic and drift diffusion semiconductor equations this paper deals with domain decomposition methods for kinetic and drift diffusion semiconductor equations in particular accurate coupling conditions at the interface between the kinetic and drift diffusion domain are given the cases of slight and strong nonequilibrium situations at the interface are considered and numerical examples are shown

a new asymptotic preserving scheme based on micro macro formulation for linear kinetic equations in the diffusion limit we propose a new numerical scheme for linear transport equations it is based on a decomposition of the distribution function into equilibrium and nonequilibrium parts we also use a projection technique that allows us to reformulate the kinetic equation into a coupled system of an evolution equation for the macroscopic density and a kinetic equation for the nonequilibrium part by using a suitable time semi implicit discretization our scheme is able to accurately approximate the solution in both kinetic and diffusion regimes it is asymptotic preserving in the following sense when the mean free path of the particles is small our scheme is asymptotically equivalent to a standard numerical scheme for the limit diffusion model a uniform stability property is proved for the simple telegraph model various boundary conditions are studied our method is validated in one dimensional cases by several numerical tests and comparisons with previous asymptotic preserving schemes

an asymptotic induced scheme for nonstationary transport equations in the diffusive limit an asymptotic induced scheme for nonstationary transport equations with the diffusion scaling is developed the scheme works uniformly for all ranges of mean free paths it is based on the asymptotic analysis of the diffusion limit of the transport equation a theoretical investigation of the behavior of the scheme in the diffusion limit is given and an approximation property is proven moreover numerical results for different physical situations are shown and the uniform convergence of the scheme is established numerically

fuzzy model based control of a quadrotor abstract this paper focuses on a fuzzy model based design problem for the hovering control of a class of nonlinear quadrotors the concerned problem turns into an exponential stabilization of an augmented error system to incorporate the tracking of the desired three dimensional position and yaw angle and the stabilization of roll and pitch motions the augmented error dynamics under the proposed control scheme can be viewed as an interconnected system it is shown that the interconnected system is exponential stable if its subsystems systems are so this property makes the separate design of the available control inputs possible then sufficient linear matrix inequality lmi conditions for its local exponential stabilizability are derived in the sense of lyapunov stability criterion an example is given to illustrate the effectiveness of the proposed design methodology

sampled data observer based output feedback fuzzy stabilization of nonlinear systems exact discrete time design approach this paper presents a new direct discrete time design methodology of a sampled data observer based output feedback fuzzy controller for a class of nonlinear system that is exactly modeled in takagi sugeno s form at least locally a fundamental yet challenging issue in this direction is the unavailability of the exact discrete time model of the nonlinear plant in a closed form in contrast to the earlier works that are based on an approximate discrete time model thus the stability obtained in the design step is not preserved in the implementation step we employ an exact discrete time fuzzy model in an integral form sufficient asymptotic stabilization conditions are investigated in the discrete time lyapunov sense we then show that the resulting sampled data controller indeed asymptotically stabilizes the nonlinear plant an example is provided to illustrate the effectiveness of the proposed methodology

implicitly restarted global fom and gmres for nonsymmetric matrix equations and sylvester equations the global gmres and global fom algorithm are recently proposed by jbilou et al for solving the linear equations with multiple right hand sides k jbilou a messaoudi h sados global fom and gmres algorithms for matrix equations appl numer math 31 1999 49 63 like gmres for the linear equations they generally uses restarting which slows the convergence however some information can be retained at the time of the restart and used in the next cycle we present algorithms that use implicit restarting in order to retain this information as morgan have proposed recently r b morgan implicitly restarted gmres and arnoldi methods for nonsymmetric systems of equations siam j matrix anal appl 21 2000 1112 1135 at the same time we prove that global gmres and global fom methods for matrix equations are equivalent with the corresponding methods for linear equations and propose implicitly restarted global fom and gmres numerical examples show that our methods are efficient

asymptotic analysis and coupling conditions for kinetic and hydrodynamic equations abstract this article is concerned with domain decomposition for kinetic and hydrodynamic equations coupling conditions at the interface between the equations are developed and investigated in particular for nonequilibrium situations at the interface new coupling conditions are developed by considering interface layers this leads to kinetic half space problems a fast procedure to solve these problems is given

brief paper stability connection between sampled data fuzzy control systems with quantization and their approximate discrete time model this paper concerns the stability of a sampled data takagi sugeno t s fuzzy control system with quantization when a controller design is based on an approximate discrete time model of the plant without quantization the motivations come from the facts that digital devices for interfacing a plant with a controller quantize signals and an exact discrete time model of the t s fuzzy system is generally not amenable to synthesis process we show that the concerned system is lagrange stabilizable by the controller asymptotically stabilizing the approximate discrete time model a constructive design algorithm for the developed stability analysis is proposed in terms of linear matrix inequalities

robust digital control of fuzzy systems with parametric uncertainties lmi based digital redesign approach this paper presents a new intelligent digital redesign idr method for uncertain nonlinear systems which are represented by a takagi sugeno t s fuzzy model the term idr involves converting an analog controller into an equivalent digital one in the sense of state matching the idr problem can be reduced to finding the digital fuzzy gains minimizing the norm distance between the closed loop states of the analog and digital control systems the uncertainties in the plant dynamics are considered in the idr condition that plays an important role in the performance improvement also the robust stability is well guaranteed in the proposed idr procedure its constructive conditions are expressed as linear matrix inequalities lmis two numerical examples the chaotic lorenz system and the qi system are demonstrated to visualize the feasibility of the proposed methodology

asymptotic stability of digitally redesigned control systems this paper analyses an asymptotic stability of a digitally redesigned control system when the states of the analogue and the digital control systems are approximately matched at every sampling point the digital redesign is a simple method of converting a given analogue controller to an equivalent digital controller in the sense of state matching the concerned state matching technique is to minimise the norm distance between the discretised closed loop system matrix of linear analogue control system and that of linear digital control system it is shown that i there exists an upper bound of the norm distance to guarantee the asymptotic stability of the digitally redesigned control system and ii the trajectories of the linear analogue and the linear digital control systems coincide at every sampling point if the norm distance is zero also a robustness result is provided in the case that nonlinear perturbations occur in the analogue and the digital control systems moreover design conditions for the

a new implementation of the cmrh method for solving dense linear systems the cmrh method h sadok methodes de projections pour les systemes lineaires et non lineaires habilitation thesis university of lille1 lille france 1994 h sadok cmrh a new method for solving nonsymmetric linear systems based on the hessenberg reduction algorithm numer algorithms 20 1999 303 321 is an algorithm for solving nonsymmetric linear systems in which the arnoldi component of gmres is replaced by the hessenberg process which generates krylov basis vectors which are orthogonal to standard unit basis vectors rather than mutually orthogonal the iterate is formed from these vectors by solving a small least squares problem involving a hessenberg matrix like gmres this method requires one matrix vector product per iteration however it can be implemented to require half as much arithmetic work and less storage moreover numerical experiments show that this method performs accurately and reduces the residual about as fast as gmres with this new implementation we show that the cmrh method is the only method with long term recurrence which requires not storing at the same time the entire krylov vectors basis and the original matrix as in the gmres algorithm a comparison with gaussian elimination is provided

the block cmrh method for solving nonsymmetric linear systems with multiple right hand sides abstract cmrh method changing minimal residual with hessenberg process is an iterative method for solving nonsymmetric linear systems this method is similar to qmr method but based on the hessenberg process instead of the lanczos process on dense matrices the cmrh method is less expensive and requires less storage than other krylov methods this paper presents a block version of the cmrh algorithm for solving linear systems with multiple right hand sides the new algorithm is based on the block hessenberg process and the iterates are characterized by a block version of the quasi minimization property we analyze its main properties and show that under the condition of full rank of block residual the block cmrh method cannot break down finally some numerical examples are presented to show the efficiency of the new method in comparison with the traditional cmrh method and a comparison with the block gmres method is also provided

weighted and flexible versions of block cmrh method for solving nonsymmetric linear systems with multiple right hand sides abstract block krylov subspace methods are the most popular algorithms for solving large nonsymmetric linear systems with multiple right hand sides one of them is the block cmrh method this method generates a non orthogonal basis of the krylov subspace through the block hessenberg process to accelerate the convergence of the block cmrh method we will introduce two new methods first we present the block cmrh method with weighting strategy in this method the block cmrh method uses a different product at each restart second we introduce a flexible version of the block cmrh algorithm that allows varying preconditioning at every step of the algorithm numerical experiments illustrate the benefits of the presented methods

fuzzy stabilization of nonlinear systems under sampled data feedback an exact discrete time model approach this paper addresses stabilization problems for a nonlinear system via a sampled data fuzzy controller the nonlinear system is assumed to be exactly modeled in takagi sugeno s form at least locally unlike the conventional direct discrete time design approach based on an approximate discrete time model the sampled data fuzzy controllers are designed based on an exact discrete time model sufficient design conditions are formulated in terms of linear matrix inequalities it is shown that whenever the exact discrete time fuzzy model is asymptotically stabilizable via the sampled data fuzzy controller uniformly bounded in the state then so is the original nonlinear system a numerical example is given to illustrate the effectiveness of the proposed methodology

decentralized sampled data h fuzzy filter for nonlinear large scale systems this paper presents a decentralized sampled data h fuzzy filter design method for nonlinear large scale systems which are represented by a takagi sugeno t s fuzzy model based on the t s fuzzy model the error system between the nonlinear large scale system and the filter is obtained the discretization process of the error system is accomplished with the exact discrete time approach to eliminate the exact approximate mismatch by using the discrete time lyapunov sense the sufficient condition of the asymptotic stability for the error system is given and a prescribed level of the h norm is ensured to guarantee the h fuzzy filter performance finally numerical examples are given to show the effectiveness of the proposed methods

a block gcrot m k method for linear systems with multiple right hand sides this study is mainly focused on iterative solution to multiple linear systems with several right hand sides for solving such systems efficiently we explore a new block gcrot m k bgcrot m k method which is derived by extending gcrot m k method jason e hicken david w zingg a simplified and flexible variant of gcrot for solving nonsymmetric linear systems siam j sci comput 32 2010 1672 1694 we analyze its main properties it is shown that under the condition of full rank of block residual the frobenius norm of the block residual generated by the proposed method is always nonincreasing moreover we also present its block flexible version bfgcrot m k finally numerical examples demonstrate that the bgcrot m k method and its flexible variant can achieve a smoothed residual and can be more competitive than some other block solvers

moment methods for the semiconductor boltzmann equation on bounded position domains galerkin methods for the semiconductor boltzmann equation based on moment expansions for a discretization in the velocity direction are studied for the moment equations boundary conditions are proposed which are analogues to inflow and respectively reflecting boundary conditions for the boltzmann equation stability and an error estimate are proved for an expansion in terms of hermite polynomials finally an adaptive numerical implementation is introduced and results of numerical experiments are presented

an asymptotic preserving numerical scheme for kinetic equations in the low mach number limit a numerical scheme for the nonstationary boltzmann equation in the incompressible navier stokes limit is developed the scheme is induced by the asymptotic analysis of the navier stokes limit for the boltzmann equation it works uniformly for all ranges of mean free paths in the limit the scheme reduces to the chorin projection method for the incompressible navier stokes equation numerical results for different physical situations are shown and the uniform convergence of the scheme is established numerically

analysis of projection methods for solving linear systems with multiple right hand sides we analyze a class of krylov projection methods but mainly concentrate on a specific conjugate gradient cg implementation by smith peterson and mittra ieee transactions on antennas and propogation 37 1989 pp 1490 1493 to solve the linear system ax b where a is symmetric positive definite and b is a multiple of right hand sides this method generates a krylov subspace from a set of direction vectors obtained by solving one of the systems called the seed system by the cg method and then projects the residuals of other systems orthogonally onto the generated krylov subspace to get the approximate solutions the whole process is repeated with another unsolved system as a seed until all the systems are solved we observe in practice a superconvergence behavior of the cg process of the seed system when compared with the usual cg process we also observe that only a small number of restarts is required to solve all the systems if the right hand sides are close to each other these two features together make the method particularly effective in this paper we give theoretical proof to justify these observations furthermore we combine the advantages of this method and the block cg method and propose a block extension of this single seed method

on global iterative schemes based on hessenberg process for ill posed sylvester tensor equations abstract this paper is concerned with studying the performance of some global iterative schemes based on hessenberg process to solve the sylvester tensor equation ste furthermore we briefly mention the implementation of flexible versions under certain conditions we devote part of the work to derive upper bounds for condition number of matrices with a special kronecker product structure which can be helpful to obtain error bounds related to perturbation analysis of the mentioned ste in addition we propose using the tikhonov regularization technique in conjunction with the tensor form of the flexible hessenberg process when the ste is ill posed numerical examples are examined for two test problems arising from discretization of three dimensional partial differential equations we also present some experimental results related to restoration of color images

improvement on nonquadratic stabilization of discrete time takagi sugeno fuzzy systems multiple parameterization approach this paper presents the relaxed nonquadratic stabilization conditions of discrete time takagi sugeno t s fuzzy systems to do this we propose a new fuzzy controller and lyapunov function by generalizing the nonparallel distributed compensation non pdc control law and nonquadratic lyapunov function respectively by exploiting po lya s theorem and algebraic properties of a homogeneous polynomials of normalized fuzzy weighting functions an infinite family of sufficient conditions for the asymptotic stabilizability is derived these conditions are formulated in the format of linear matrix inequalities lmis and hence are numerically tractable via convex programming techniques finally an example is given to illustrate advantages of the proposed method

technical communique further studies on lmi based relaxed stabilization conditions for nonlinear systems in takagi sugeno s form this paper further studies stabilization of nonlinear systems represented by a takagi sugeno t s discrete fuzzy model by extending a nonquadratic lyapunov function and applying a nonparallel distributed compensation non pdc law a new stabilization conclusion is presented that is a generalization of some previous results in the literature the new conclusion under a special situation is also suitable for a pdc law which presents to be more relaxed than some existing results an example is provided to demonstrate the effectiveness of the new conclusions

global scd algorithm for real positive definite linear systems with multiple right hand sides abstract in the present paper we present the left conjugate direction lcd method for linear systems with multiple right hand sides we define the method by using left and right conjugate direction matrices and petrov galerkin condition the method has no breakdown for real positive definite systems the method reduces to the usual cg type method when a is symmetric positive definite we also show how to apply these methods for solving the lyapunov matrix equation finally a numerical experiment is given to illustrate the result

a new fuzzy lyapunov function for relaxed stability condition of continuous time takagi sugeno fuzzy systems this paper presents a new fuzzy lyapunov function flf for the stability analysis of continuous time takagi sugeno t s fuzzy systems unlike conventional flfs the proposed one depends not only on the fuzzy weighting functions of the t s fuzzy systems but on their first order time derivatives as well based on the proposed flf a sufficient stability condition is derived in the form of linear matrix inequalities depending on the upper bounds on the second order time derivative of the fuzzy weighting functions as well as the first order ones finally some examples demonstrate that the proposed condition can provide less conservative results than the previous ones in the literature

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

global lsmr gl lsmr method for solving general linear systems with several right hand sides abstract the global solvers are an attractive class of iterative solvers for solving linear systems with multiple right hand sides in this paper first a new global method for solving general linear systems with several right hand sides is presented this method is the global version of the lsmr algorithm presented by fong and saunders 2011 then some theoretical properties of the new method are discussed finally numerical experiments from real applications are used to confirm the effectiveness of the proposed method

a hybrid method for anisotropic elliptic problems based on the coupling of an asymptotic preserving method with the asymptotic limit model this paper presents a hybrid numerical method to solve efficiently a class of highly anisotropic elliptic problems the anisotropy is aligned with one coordinate axis and its strength is described by a parameter e 0 1 which can largely vary in the study domain our hybrid model is based on asymptotic techniques and couples spatially an asymptotic preserving model with its asymptotic limit model the latter being used in regions where the anisotropy parameter e is small adequate coupling conditions link the two models the aim of this hybrid procedure is to reduce the computational time for problems where the region of small e values extends over a significant part of the domain and this is due to the reduced complexity of the limit model

a block idr s method for nonsymmetric linear systems with multiple right hand sides the idr s based on the induced dimension reduction idr theorem is a new class of efficient algorithms for large nonsymmetric linear systems idr 1 is mathematically equivalent to bicgstab at the even idr 1 residuals and idr s with s 1 is competitive with most bi cg based methods for these reasons we extend the idr s to solve large nonsymmetric linear systems with multiple right hand sides in this paper a variant of the idr theorem is given at first then the block idr s an extension of idr s based on the variant idr s theorem is proposed by analysis the upper bound on the number of matrix vector products of block idr s is the same as that of the idr s for a single right hand side in generic case i e the total number of matrix vector products of idr s may be m times that of of block idr s where m is the number of right hand sides numerical experiments are presented to show the effectiveness of our proposed method

a new family of global methods for linear systems with multiple right hand sides the global bi conjugate gradient gl bcg method is an attractive matrix krylov subspace method for solving nonsymmetric linear systems with multiple right hand sides but it often show irregular convergence behavior in many applications in this paper we present a new family of global a biorthogonal methods by using short two term recurrences and formal orthogonal polynomials which contain the global bi conjugate residual gl bcr algorithm and its improved version finally numerical experiments illustrate that the proposed methods are highly competitive and often superior to originals

digitalizing a fuzzy observer based output feedback control intelligent digital redesign approach this paper concerns an intelligent digital redesign idr technique for a takagi sugeno fuzzy observer based output feedback control fobofc system the term idr involves converting an existing analog control into an equivalent digital counterpart in the sense of state matching the idr problem is herein viewed as a minimization problem of the norm distances between nonlinearly interpolated linear operators to be matched its constructive condition with global rather than local state matching is formulated in terms of bilinear matrix inequalities the main features of the proposed method are that the state estimation error in the plant dynamics is considered in the idr condition that plays a crucial role in the performance improvement the stability property is preserved by the proposed idr algorithm the separation principle is shown when the premise variables are measurable finally the idr condition for a more general fobofc an estimated premise variable case is conducted a numerical example is demonstrated to visualize the feasibility of the developed methodology

an adaptive domain decomposition procedure for boltzmann and euler equations in this paper we present a domain decomposition approach for the coupling of boltzmann and euler equations particle methods are used for both equations this leads to a simple implementation of the coupling procedure and to natural interface conditions between the two domains adaptive time and space discretizations and a direct coupling procedure lead to considerable gains in cpu time compared to a solution of the full boltzmann equation several test cases involving a large range of knudsen numbers are numerically investigated

a numerical method for kinetic semiconductor equations in the drift diffusion limit an asymptotic induced scheme for kinetic semiconductor equations with the diffusion scaling is developed the scheme is based on the asymptotic analysis of the kinetic semiconductor equation it works uniformly for all ranges of mean free paths the velocity discretization is done using quadrature points equivalent to a moment expansion method numerical results for different physical situations are presented

space time discretization of series expansion methods for the boltzmann transport equation the approximate solution of the boltzmann transport equation via galerkin type series expansion methods leads to a system of first order differential equations in space and time for the expansion coefficients this system is extremely stiff close to the fluid dynamical regime for small knudsen numbers and exhibits a mildly dispersive behavior due to the acceleration of waves by the external force the electric field in this paper a class of difference methods is presented and analyzed which represent a generalization of the well known scharfetter gummel exponential fitting approach for the drift diffusion equations it is shown that by using appropriate operator splitting methods for the time discretization one obtains stability properties which are only mildly dependent on the knudsen number and essentially independent of the size of the electric field

hybrid state space fuzzy model based controller with dual rate sampling for digital control of chaotic systems we develop a hybrid state space fuzzy model based controller with dual rate sampling for digital control of chaotic systems a takagi sugeno ts fuzzy model is used to model the chaotic dynamic system and the extended parallel distributed compensation technique is proposed and formulated for designing the fuzzy model based controller under stability conditions the optimal regional pole assignment technique is also adopted in the design of the local feedback controllers for the multiple ts linear state space models the proposed design procedure is as follows an equivalent fast rate discrete time state space model of the continuous time system is first constructed by using fuzzy inference systems to obtain the continuous time optimal state feedback gains the constructed discrete time fuzzy system is then converted into a continuous time system the developed optimal continuous time control law is finally converted into an equivalent slow rate digital control law using the proposed intelligent digital redesign method the main contribution of the paper is the development of a systematic and effective framework for fuzzy model based controller design with dual rate sampling for digital control of complex such as chaotic systems the effectiveness and the feasibility of the proposed controller design method is demonstrated through numerical simulations on the chaotic chua circuit

convergence of moment methods for linear kinetic equations numerical methods for linear kinetic equations based on moment expansions for a discretization in the velocity direction are examined the moment equations are hyperbolic systems which can be shown to converge to the kinetic equation as the order of the expansion tends to infinity and to a drift diffusion model as the knudsen number tends to zero a discretization of the moment equations with respect to time and space is presented a stability result is proven and some aspects of an implementation are discussed in particular an adaptive procedure is described where the order of the expansion is determined locally results of numerical experiments are presented

a new discrete time robust stability condition a new robust stability condition for uncertain discrete time systems with convex polytopic uncertainty is given it enables to check stability using parameter dependent lyapunov functions which are derived from lmi conditions it is shown that this new condition provides better results than the classical quadratic stability besides the use of a parameter dependent lyapunov function this condition exhibits a kind of decoupling between the lyapunov and the system matrices which may be explored for control synthesis purposes a numerical example illustrates the results

a block qmr algorithm for non hermitian linear systems with multiple right hand sides abstract many applications require the solution of multiple linear systems that have the same coefficient matrix but differ in their right hand sides instead of applying an iterative method to each of these systems individually it is often more efficient to employ a block version of the method that generates iterates for all the systems simultaneously in this paper we propose a block version of freund and nachtigal s quasi minimal residual qmr method for the iterative solution of non hermitian linear systems the block qmr method uses a novel lanczos type process for multiple starting vectors which was recently developed by aliaga boley freund and hernandez to compute suitable basis vectors for the underlying block krylov subspaces we describe the basic block qmr method and also give important implementation details in particular we show how to incorporate deflation to drop converged linear systems and to delete linearly and almost linearly dependent vectors in the underlying block krylov sequences numerical results are reported that illustrate typical features of the block qmr method

generalized global conjugate gradient squared algorithm in this paper a generalized global conjugate gradient squared method for solving nonsymmetric linear systems with multiple right hand sides is presented the method can be derived by using products of two nearby global bicg polynomials and formal orthogonal polynomials of which global cgs and global bicgstab are just particular cases we also show to apply the method for solving the sylvester matrix equation finally numerical examples are given to illustrate the effectiveness of the proposed method

an improved digital redesign for sampled data fuzzy control systems this paper proposes an improved digital redesign dr technique for sampled data fuzzy controllers in nonlinear systems based on a takagisugeno ts fuzzy model to improve the performance of the dr technique two methodologies are used a state matching error cost function and a continuous time fuzzy lyapunov function using these two methodologies a novel dr technique is proposed to guarantee both the stability and state matching conditions of the sampled data fuzzy control system further the proposed dr technique is represented as an optimal problem using the linear matrix inequality lmi format finally some simulation examples are provided to verify the effectiveness of the proposed technique in comparison with previous techniques

convergence properties of block gmres and matrix polynomials abstract this paper studies convergence properties of the block gmres algorithm when applied to nonsymmetric systems with multiple right hand sides a convergence theory is developed based on a representation of the method using matrix valued polynomials relations between the roots of the residual polynomial for block gmres and the matrix e pseudospectrum are derived and illustrated with numerical experiments the role of invariant subspaces in the effectiveness of block methods is also discussed

the block least squares method for solving nonsymmetric linear systems with multiple right hand sides abstract in this paper we present the block least squares method for solving nonsymmetric linear systems with multiple right hand sides this method is based on the block bidiagonalization we first derive two algorithms by using two different convergence criteria the first one is based on independently minimizing the 2 norm of each column of the residual matrix and the second approach is based on minimizing the frobenius norm of residual matrix we then give some properties of these new algorithms finally some numerical experiments on test matrices from harwell boeing collection are presented to show the efficiency of the new method

ga based intelligent digital redesign of fuzzy model based controllers intelligent digital redesign involves converting a continuous time fuzzy model based controller into an equivalent discrete time counterpart for the digital control of continuous time nonlinear systems by using the takagi sugeno ts fuzzy models in this paper the authors present a new global state matching intelligent digital redesign method for nonlinear systems by using genetic algorithms gas more precisely the intelligent digital redesign problem is converted to an equivalent optimization problem and then gas are adopted to find a solution the search space in which each problem variable is defined for gas are systematically obtained by the interval arithmetic operations the proposed method results in global matching of the states of the analogously controlled system with those of the digitally controlled system while the conventional intelligent digital redesign method does not the chen s chaotic system is used as an illustrative example to show the effectiveness and the feasibility of the developed method the proposed method provides a new approach for the digital redesign of a class of fuzzy model based controllers

lmi based relaxed nonquadratic stabilization conditions for nonlinear systems in the takagi sugeno s form this paper presents the stabilization analysis for a class of nonlinear systems that are represented by a takagi and sugeno ts discrete fuzzy model takagi and sugeno ieee trans systems man cybern 15 1 1985 116 the main result given here concerns their stabilization using new control laws and new nonquadratic lyapunov functions new relaxed conditions and linear matrix inequality based design are proposed that allow outperforming previous results found in the literature two examples are also provided to demonstrate the efficiency of the approaches

asymptotically complexity diminishing schemes acds for kinetic equations in the diffusive scaling abstract in this work we develop a new class of numerical schemes for collisional kinetic equations in the diffusive regime the first step consists in reformulating the problem by decomposing the solution in the time evolution of an equilibrium state plus a perturbation then the scheme combines a monte carlo solver for the perturbation with an eulerian method for the equilibrium part and is designed in such a way to be uniformly stable with respect to the diffusive scaling and to be consistent with the asymptotic diffusion equation moreover since particles are only used to describe the perturbation part of the solution the scheme becomes computationally less expensive and is thus an asymptotically complexity diminishing scheme acds as the solution approaches the equilibrium state due to the fact that the number of particles diminishes accordingly this contrasts with standard methods for kinetic equations where the computational cost increases or at least does not decrease with the number of interactions at the same time the statistical error due to the monte carlo part of the solution decreases as the system approaches the equilibrium state the method automatically degenerates to a solution of the macroscopic diffusion equation in the limit of infinite number of interactions after a detailed description of the method we perform several numerical tests and compare this new approach with classical numerical methods on various problems up to the full three dimensional case

a new intelligent digital redesign for t s fuzzy systems global approach this paper proposes a novel and efficient global intelligent digital redesign technique for a takagi sugeno t s fuzzy system the term of intelligent digital redesign involves converting an existing analog fuzzy model based controller into an equivalent digital counterpart in the sense of state matching the proposed method should be notably discriminated from the previous works in that it allows us to globally match the states of the overall closed loop t s fuzzy system with the predesigned analog fuzzy model based controller and those with the digitally redesigned fuzzy model based controller and further to examine the stabilizability by the redesigned controller in the sense of lyapunov the key idea is that the global intelligent digital redesign problem is viewed as a convex minimization problem of the norm distance between nonlinearly interpolated linear operators to be matched sufficient conditions for the global state matching and the stability of the digitally controlled system are formulated in terms of linear matrix inequalities lmis a complex nonlinear system duffing like chaotic oscillator is simulated and demonstrated to validate the feasibility and effectiveness of the proposed digital redesign technique which implies the safe applicability to the digital control system

micro macro schemes for kinetic equations including boundary layers we introduce a new micro macro decomposition of collisional kinetic equations in the specific case of the diffusion limit which naturally incorporates the incoming boundary conditions the idea is to write the distribution function f in all its domain as the sum of an equilibrium adapted to the boundary which is not the usual equilibrium associated with f and a remaining kinetic part this equilibrium is defined such that its incoming velocity moments coincide with the incoming velocity moments of the distribution function a consequence of this strategy is that no artificial boundary condition is needed in the micro macro models and the exact boundary condition on f is naturally transposed to the macro part of the model this method provides an asymptotic preserving numerical scheme that generates a very good approximation of the space boundary values at the diffusive limit without any mesh refinement in the boundary layers our numerical results are in very good agreement with the exact so c

global least squares method gl lsqr for solving general linear systems with several right hand sides abstract in this paper we propose a new method for solving general linear systems with several right hand sides this method is based on global least squares method and reduces the original matrix to the lower bidiagonal form we derive a simple recurrence formula for generating the sequence of approximate solutions x k some theoretical properties of the new method are discussed and we also show that how this method can be implemented for the sylvester equation finally some numerical experiments on test matrices are presented to show the efficiency of the new method