comparison between h sub 2 and h sub infinity controllers the h sub infinity performances of a controller designed by h sub 2 methodology and a controller designed by h sub infinity methodology are quantitatively compared it is shown that the ratio of the h sub infinity performance of the two is no greater than 2k for the one block problem where k is the total number of right half plane transmission zeros for two subsystems namely the subsystem between the disturbance and the measurement and the subsystem between the control signal and the controlled output it is also shown that there are systems which can give a ratio arbitrarily close to the upper bound however those systems are of a pathological type some possible generalizations to two and four block problems are discussed

effects of an endoscope and fluid with variable viscosity on peristaltic motion the influence of an inserted endoscope and fluid with variable viscosity on the peristaltic motion has been investigated under zero reynolds number the problem is formulated using a perturbation expansion in terms of a variant wave number the effects of curvature viscosity radius of an endoscope and amplitude of the wave on the pressure rise and friction forces on the inner and outer tubes are analyzed peristaltic and augmented pumping are discussed the results show that the pressure rise increases with increasing wave number amplitude ratio and radius ratio also it decreases with increasing viscosity parameter further it is independent of wave number amplitude ratio radius ratio and viscosity parameter at certain values of flow rate a comparison with previous studies is given

characterization of the solution to the optimal h model reduction problem abstract in this paper the h norm approximation of a given stable proper rational transfer function by a lower order stable proper rational transfer function is studied the solution method is based on the authors observation that the h model reduction problem can be converted into a hankel norm model reduction problem a simple characterization of the solution to the optimal h model reduction problem is developed

applications of the numerical inversion of the laplace transform to unsteady problems of the third grade fluid abstract in this article we have effectively used the numerical inversion of laplace transform to study some time dependent problems of the third grade fluid to do so we have considered three different types of unsteady flows of the third grade fluid namely a unsteady flow over a flat rigid plate with porous medium b unsteady mhd flow in a porous medium c unsteady mhd flow in a non porous space with hall currents the solution to the governing equation in each case is obtained by using the standard laplace transform however to transform the obtained solutions from laplace space back to the original space we have used the numerical inversion of the laplace transform graphical results for each case have been presented to show the effects of different parameters involved and to show how the fluid flow evolves with time

hp adaptive finite elements in electromagnetics a model problem for the steady state form of maxwell s equations is considered the problem is formulated in a weak form using a lagrange multiplier laying down a foundation for a general class of novel hp adaptive fe approximations a convergence proof for curvilinear elements is presented the proposed method is illustrated and verified by a series of 2d experiments which include elements with curved boundaries and nonhomogeneous media

l optimization and hankel approximation an important l infty optimization problem arising in feedback system design is shown to be equivalent to an optimal hankel norm approximation problem this enables the problem to be solved using state space methods based on balanced realizations

reductions and solutions for the unsteady flow of a fourth grade fluid on a porous plate the unsteady unidirectional flow of an incompressible fourth grade fluid over an infinite porous plate is studied the flow is induced due to the motion of the plate in its own plane with an arbitrary velocity symmetry reductions are performed to transform the governing nonlinear partial differential equations into ordinary differential equations the reduced equations are then solved analytically and numerically the influence of various physical parameters of interest on the velocity profile are shown and discussed through several graphs a comparison of the present analysis shows excellent agreement between analytical and numerical solutions

solving the inverse problem of identifying an unknown source term in a parabolic equation the inverse problem of determining an unknown source term in a parabolic equation with the leading coefficient depending on time and space variables under a final overdetermination condition is considered the series pattern solution of the problem is obtained by using the weighted homotopy analysis method wham a description of the method for solving the problem and identifying the unknown source term is derived finally several examples are presented to illustrate this method

analytic solution for mhd flow of a third order fluid in a porous channel the present study investigates the channel flow of a third order fluid the fluid is electrically conducting in the presence of a magnetic field applied transversely to the porous walls of a channel expression for velocity is developed by an analytic method namely the homotopy analysis method ham convergence of the obtained solution is properly checked the feature of the analytic solution as function of the physical parameters of the problem are discussed with the help of graphs it is observed that unlike the flow of second grade fluid the obtained solution for a third order fluid is non similar also the behavior of hartmann number on the velocity is different to that of the reynold s number

l sub 2 optimal filter reduction a closed loop approach this paper is concerned with the problem of order reduction of a full order kalman filter for a stable linear signal model so that the steady state filtering error variance associated with the reduced order filter is minimized by an orthogonal parameterization the above problem is formulated to minimize the filtering error variance over a set of orthogonal matrices both continuous and iterative algorithms are derived to compute an optimal reduced order filter the algorithms are shown to possess good properties including the desirable convergence property the proposed algorithms are simple and effective numerical examples are presented to demonstrate the effectiveness and the significant advantages of the proposed algorithms over the existing open loop methods such as the well known balanced truncation method

a non iterative method for computing the infimum in h optimization this paper presents a simple and non iterative procedure for the computation of the exact value of the infimum in the singular h optimization problem and is an extension of our earlier work the problem formulation is general and does not place any restriction on the direct feedthrough terms between the control input and the controlled output variables and between the disturbance input and the measurement output variables our method is applicable to a class of singular h optimization problems for which the transfer functions from the control input to the controlled output and from the disturbance input to the measurement output have no invariant zeros on the jw axis and also satisfy certain geometric conditions the computation of the infimum in our method involves solving two well defined riccati and two lyapunov equations

spectral analysis in linear process identification a new look at an old problem the problem of estimating the transfer function frequency response of a linear process by means of a modified spectral analysis method is treated a method of determining the maximum time lags of the correlation functions which makes use of the available a priori physical knowledge about the process and the input signal is proposed this leads in a natural way to the use of an asymmetrical window technique some simulation results are used to illustrate the method based on the asymptotic properties of the estimate the input design is studied finally it will be shown that this work can be used for the estimation of an upper bound of the model uncertainty in the frequency domain

numerical solitons of generalized korteweg de vries equations abstract we propose a numerical method for finding solitary wave solutions of generalized korteweg de vries equations by solving the nonlinear eigenvalue problem on an unbounded domain the artificial boundary conditions are obtained to make the domain finite we specially discuss the soliton solutions of the k m n equation and kdv k m n equation furthermore for the mixed models of linear and nonlinear dispersion the collision behaviors of soliton soliton and soliton antisoliton are observed

all optimal hankel norm approximations of linear multivariable systems and their l error bounds the problem of approximating a multivariable transfer function g s of mcmillan degree n by s of mcmillan degree k is considered a complete characterization of all approximations that minimize the hankel norm is derived the solution involves a characterization of all rational functions s f s that minimize where s has mcmillan degree k and f s is anticavisal the solution to the latter problem is via results on balanced realizations all pass functions and the inertia of matrices all in terms of the solutions to lyapunov equations it is then shown that where k 1 g s is the k l st hankel singular value of g s and for one class of optimal hankel norm approximations the method is not computationally demanding and is applied to a 12 state model

peristaltic transport of fractional maxwell fluids in uniform tubes applications in endoscopy this paper presents the effect of endoscope on peristaltic transport of fractional maxwell fluids through the gap between two concentric uniform tubes under the assumptions of large wavelength and low reynolds number the inner tube is an endoscope and the outer tube has a sinusoidal wave traveling down its wall i e the inner tube is rigid and outer tube is flexible solutions for the problem are obtained by two numerical methods named as homotopy perturbation method and variational iteration method the impacts of endoscope relaxation time and fractional parameters on pressure per wavelength and friction force on inner and outer tubes per wavelength are discussed with the help of computational results which are presented in graphical form on the basis of the present study it is revealed that pressure diminishes with increase in the magnitude of first fractional parameter ratio of tube radii and relaxation time whereas it enhances with increasing the magnitude of second fractional parameter and amplitude ratio the study further reveals the important fact that the effects of all pertinent parameters except ratio of tube radii on friction force at inner tube are similar in magnitude but opposite in direction to that of pressure and the effects of same parameters on friction force at outer tube are similar in magnitude but opposite in direction to that of pressure

exact solutions of a third grade fluid flow on a porous plate in this paper the exact solutions for an unsteady flow of an incompressible fluid of third grade occupying space over an infinite porous plate are obtained for a given velocity component translational type symmetries are employed to reduce the non linear equations governing the flow under discussion to two ordinary differential equations with and without dispersion terms graphs representing the solutions are discussed and appropriate conclusions drawn

principal component analysis in linear systems controllability observability and model reduction kalman s minimal realization theory involves geometric objects controllable unobservable subspaces which are subject to structural instability specifically arbitrarily small perturbations in a model may cause a change in the dimensions of the associated subspaces this situation is manifested in computational difficulties which arise in attempts to apply textbook algorithms for computing a minimal realization structural instability associated with geometric theories is not unique to control it arises in the theory of linear equations as well in this setting the computational problems have been studied for decades and excellent tools have been developed for coping with the situation one of the main goals of this paper is to call attention to principal component analysis hotelling 1933 and an algorithm golub and reinsch 1970 for computing the singular value decompositon of a matrix together they form a powerful tool for coping with structural instability in dynamic systems as developed in this paper principal component analysis is a technique for analyzing signals singular value decomposition provides the computational machinery for this reason kalman s minimal realization theory is recast in terms of responses to injected signals application of the signal analysis to controllability and observability leads to a coordinate system in which the internally balanced model has special properties for asymptotically stable systems this yields working approximations of x c x bar o the controllable and unobservable subspaces it is proposed that a natural first step in model reduction is to apply the mechanics of minimal realization using these working subspaces

hierarchal vector basis functions of arbitrary order for triangular and tetrahedral finite elements new vector finite elements are proposed for electromagnetics the new elements are triangular or tetrahedral edge elements tangential vector elements of arbitrary polynomial order they are hierarchal so that different orders can be used together in the same mesh and p adaption is possible they provide separate representation of the gradient and rotational parts of the vector field explicit formulas are presented for generating the basis functions to arbitrary order the basis functions can be used directly or after a further stage of partial orthogonalization to improve the matrix conditioning matrix assembly for the frequency domain curl curl equation is conveniently carried out by means of universal matrices application of the new elements to the solution of a parallel plate waveguide problem demonstrates the expected convergence rate of the phase of the reflection coefficient for tetrahedral elements to order 4 in particular the full order elements have only the same asymptotic convergence rate as elements with a reduced gradient space such as the whitney element however further tests reveal that the optimum balance of the gradient and rotational components is problem dependent

brief paper positivity preserving h model reduction for positive systems this paper is concerned with the model reduction of positive systems for a given stable positive system our attention is focused on the construction of a reduced order model in such a way that the positivity of the original system is preserved and the error system is stable with a prescribed h performance based upon a system augmentation approach a novel characterization on the stability with h performance of the error system is first obtained in terms of linear matrix inequality lmi then a necessary and sufficient condition for the existence of a desired reduced order model is derived accordingly furthermore iterative lmi approaches with primal and dual forms are developed to solve the positivity preserving h model reduction problem finally a compartmental network is provided to show the effectiveness of the proposed techniques

probability one homotopy algorithms for solving the coupled lyapunov equations arising in reduced order h2 h modeling estimation and control optimal reduced order modeling estimation and control with respect to combined h 2 h criteria give rise to coupled lyapunov and riccati equations to develop reliable numerical algorithms for these problems this paper focuses on the coupled lyapunov equations which appear as a subset of the synthesis equations in particular this paper systematically examines the requirements of probability one homotopy algorithms to guarantee global convergence homotopy algorithms for nonlinear systems of equations construct a continuous family of systems and solve the given system by tracking the continuous curve of solutions to the family the main emphasis is on guaranteeing transversality for several homotopy maps based upon the pseudogramian formulation of the coupled lyapunov equations and variations based upon canonical forms these results are essential to the probability one homotopy approach by guaranteeing good numerical properties in the computational implementation of the homotopy algorithms

approximation of fir by iir digital filters an algorithm based on balanced model reduction an algorithm for the approximation of finite impulse response fir filters by infinite impulse response iir filters is presented the algorithm is based on a concept of balanced model reduction the matrix inversions normally associated with this procedure are notoriously error prone due to ill conditioning of the special matrix forms required this difficulty is circumvented here by directly formulating a reduced state space system description which is input output equivalent to the system that would more conventionally be obtained following the explicit step of constructing an interim balanced realization examples of fir by iir filter approximations are included

peristaltic motion of a burger s fluid in a planar channel abstract this investigation deals with the peristaltic motion of an incompressible non newtonian fluid in a planar channel for long wavelength the mechanical properties of the material are represented by the constitutive equation for a burger s fluid perturbation solutions are developed for stream function the axial velocity and pressure rise over a wavelength the influence of various emerging parameters on the flow is shown through graphs and discussed

the influence of slip condition on thin film flow of a fourth grade fluid by the homotopy analysis method this paper provides an investigation regarding slip effects on thin film flow of a fourth grade fluid down a vertical cylinder the nonlinear problem that arises is solved for both exact and ham homotopy analysis method solutions exact and ham solutions are also compared finally we briefly describe the flow characteristics to include the effects of emerging parameters

multiobjective h sub 2 h sub spl infin control for a linear time invariant system with several disturbance inputs and controlled outputs we show how to minimize the nominal h sub 2 norm performance in one channel while keeping bounds on the h sub 2 norm or h sub spl infin norm performance implying robust stability in the other channels this multiobjective h sub 2 h sub spl infin problem in an infinite dimensional space is reduced to sequences of finite dimensional convex optimization problems we show how to compute the optimal value and how to numerically detect the existence of a rational optimal controller if it exists we reveal how the novel trick of optimizing the trace norm of the youla parameter over certain convex constraints allows one to design a nearly optimal controller whose youla parameter is of the same order as the optimal one

optimal hankel model reduction for nonminimal systems a basis free descriptor system representation is shown to facilitate the computation of all minimum degree and optimal kth order all pass extensions and hankel norm approximants the descriptor representation has the same simple form for both the optimal and suboptimal cases the method makes hankel model reduction practical for nonminimal and nearly nonminimal systems by eliminating the ill conditioned calculation of a minimal balanced realization a simple numerically sound method based on singular value decomposition enables the results to be expressed in state space form

magnetohydrodynamic flow of an oldroyd 6 constant fluid a study is made of the steady flow in an incompressible magnetohydrodynamic oldroyd 6 constant fluid by the motion of an infinite plate the analytical solution of the non linear problem is obtained by the homotopy analysis method the manner in which the various material parameters affect the structure of the velocity profile is delineated also a comparison of the present solution is made with the solution of an oldroyd 3 constant fluid

mhd flow of a third grade fluid in a porous half space with plate suction or injection an analytical approach the present work deals with the modeling and solution of the unsteady flow of an incompressible third grade fluid over a porous plate within a porous medium the flow is generated due to an arbitrary velocity of the porous plate the fluid is electrically conducting in the presence of a uniform magnetic field applied transversely to the flow lie group theory is employed to find symmetries of the modeled equation these symmetries have been applied to transform the original third order partial differential equation into third order ordinary differential equations these third order ordinary differential equations are then solved analytically and numerically the manner in which various emerging parameters have an effect on the structure of the velocity is discussed with the help of several graphs

formulation and solution of structured total least norm problems for parameter estimation the total least squares tls method is a generalization of the least squares ls method for solving overdetermined sets of linear equations ax spl ap b the tls method minimizes spl par e r spl par sub f where r b a e x so that b r spl isin range a e given a spl isin c sup m spl times n with m spl ges n and b spl isin c sup m spl times 1 the most common tls algorithm is based on the singular value decomposition svd of a b however the svd based methods may not be appropriate when the matrix a has a special structure since they do not preserve the structure previously a new problem formulation known as structured total least norm stln and the algorithm for computing the stln solution have been developed the stln method preserves the special structure of a or a b and can minimize the error in the discrete l sub p norm where p 1 2 or spl infin in this paper the stln problem formulation is generalized for computing the solution of stln problems with multiple right hand sides ax spl ap b it is shown that these problems can be converted to ordinary stln problems with one right hand side in addition the method is shown to converge to the optimal solution in certain model reduction problems furthermore the application of the stln method to various parameter estimation problems is studied in which the computed correction matrix applied to a or a b keeps the same toeplitz structure as the data matrix a of a b respectively in particular the l sub 2 norm stln method is compared with the ls and tls methods in deconvolution transfer function modeling and linear prediction problems

model reduction of large scale systems by least squares abstract in this paper we introduce an approximation method for model reduction of large scale dynamical systems this is a projection which combines aspects of the svd and krylov based reduction methods this projection can be efficiently computed using tools from numerical analysis namely the rational krylov method for the krylov side of the projection and a low rank smith type iteration to solve a lyapunov equation for the svd side of the projection for discrete time systems the proposed approach is based on the least squares fit of the r 1 th column of a hankel matrix to the preceding r columns where r is the order of the reduced system the reduced system is asymptotically stable matches the first r markov parameters of the full order model and minimizes a weighted h 2 error the method is also generalized for moment matching at arbitrary interpolation points application to continuous time systems is achieved via the bilinear transformation numerical examples prove the effectiveness of the approach the proposed method is significant because it combines guaranteed stability and moment matching together with an optimization criterion

an algebraic multigrid method for the finite element analysis of large scattering problems an efficient iterative solver is proposed for the linear matrix equation that arises in the analysis of large scattering problems by the frequency domain finite element method a krylov method is preconditioned by a technique that approximately solves equivalent problems in two auxiliary spaces a space of scalar functions and a space of piecewise linear nodal vector functions on each space the traditional algebraic multigrid method is employed further the shifted laplace idea is used to improve the performance of the solver as the frequency increases results are reported for a waveguide cavity filter and three free space scatterers a conducting sphere a metallic frequency selective surface and a metamaterial lens made of split ring resonators containing dielectric and metal

couette and poiseuille flows of an oldroyd 6 constant fluid with magnetic field abstract in this paper we develop a set of differential equations describing the steady flow of an oldroyd 6 constant magnetohydrodynamic fluid the fluid is electrically conducting in the presence of a uniform transverse magnetic field the developed non linear differential equation takes into account the effect of the material constants and the applied magnetic field we presented the solution for three types of steady flows namely i couette flow ii poiseuille flow and iii generalized couette flow homotopy analysis method ham is used to solve the non linear differential equation analytically it is found from the present analysis that for steady flow the obtained solutions are strongly dependent on the material constants non newtonian parameters which is different from the model of oldroyd 3 constant fluid numerical solutions are also given and compared with the solutions by ham

model reduction via balanced state space representations a model reduction procedure based on balanced state space representations is studied in this paper the reduced order model is examined from the point of view of stability controllability and observability both continuous time and discrete time systems are considered

goal oriented error estimation and h adaptivity for maxwell s equations goal oriented error estimates based on dual solutions are derived for the s parameters of a waveguide cavity resonator and a computationally cheap method is proposed to compute these numerical results show that the error estimators are relatively accurate usually well within a factor 2 from the exact errors adaptive mesh refinement based on these estimates recovers optimal convergence rates for complete and incomplete first and second order curl conforming finite elements of nedelec type despite singularities at reentrant corners it is also shown numerically that the convergence rate is independent of the element order when singularities are present and the mesh is refined uniformly

a lyapunov theory for linear time delay systems some relationships between a lyapunov based stability test and linear control system models with time delays are explored the main result is a generalization of the result that if a b is a reachable pair of matrices then square a is a stability matrix if and only if there is a positive definite matrix k such that ak ka bb

shape optimization for radar cross sections by a gradient method a gradient method for optimization of shape and materials for radar cross section rcs reduction is derived from maxwell s equations the method uses the adjoint problem and finds the derivatives of the rcs with respect to all design parameters from a single solution of the scattering problem the method is tested in two dimensional test problems to minimize the rcs in specified angular intervals at a single frequency and finds configurations with strongly reduced rcs in a small number of iterations in the absence of other constraints the optimal shapes of perfectly electrically conducting pec scatterers have sharp corners pointing in the directions where the rcs is minimized and shapes optimized at a single or small number of frequencies exhibit corrugations with about half the wavelength of the incident wave the corrugations can be suppressed by means of penalty functions and this gives only moderate increases of the rcs after such regularization the optimal shapes agree well with expectations from geometrical optics they have almost flat surfaces whose normals lie outside the intervals chosen for rcs optimization and sharp edges at locations where the surface normal points into the intervals in which the rcs is minimized shape optimization of pec wing profiles aiming at both good aerodynamical properties and low rcs show give conflicting requirements on the shape copyright 2004 john wiley sons ltd

hierarchic hp edge element families for maxwell s equations on hybrid quadrilateral triangular meshes we construct and study a set of hierarchic basis functions for the galerkin discretisation of the space h curl 169 suitable for hybrid meshes containing both quadrilateral and triangular elements with arbitrary non uniform order polynomial approximation we investigate the conditioning and dispersive behaviour of the elements in addition numerical examples are shown which demonstrate the accuracy of the space for computing solutions of the time harmonic maxwell s equations that have singularities

a posteriori error indicators for maxwell s equations abstract in this paper we shall analyze a class of a posteriori error indicators for an electromagnetic scattering problem for maxwell s equations in the presence of a bounded inhomogeneous and anisotropic scatterer problems of this type arise when computing the interaction of electromagnetic radiation with biological tissue we briefly recall existence and uniqueness theory associated with this problem then we show how a posteriori error indicators can be derived using an adjoint equation approach the error indicators use both the jump in normal and tangential components of the field across faces in the mesh

conjugation interpolation and model matching in h abstract the notion of conjugation is introduced to give a unified framework of algebraic operations connected to the analytic aspects of transfer functions two classes of conjugations are shown to be important one is the lossless conjugation that performs inner outer factorization and the other is the j lossless conjugation that solves the model matching problem related to h 8 control the solution of the model matching problem obtained by j lossless conjugation is regarded as the state space version of the directional interpolation theory and is much simpler than those obtained via the nehari approximation

brief paper on the stability of a reduced order filter based on dominant singular value decomposition of the system dynamics the stability of a reduced order filter rof the gain of which is constructed on the basis of a subspace of dominant singular vectors of the system dynamics is examined a definition of s detectability is introduced it is found that the observability of all unstable and neutral singular vectors s detectability is a sufficient condition for the existence of a stable filter

a new family of mixed finite elements in ir 3 we introduce two families of mixed finite element on conforming inh div and one conforming inh curl these finite elements can be used to approximate the stokes system

hankel norm approximation for well posed linear systems the sub optimal hankel norm approximation problem is solved for a well posed linear system with generating operators a b c and transfer function g satisfying some mild assumptions in the special case of the sub optimal nehari problem an explicit parameterization of all solutions is obtained in terms of the system parameters a b c and g 0

characterization and computation of the solution to the optimal l sub spl infin approximation problem the characterization of the solution to the problem of approximating a given stable proper rational transfer function in l sub spl infin norm sense by a rational function with prescribed number of stable and unstable modes is developed a simple state space suboptimal computational algorithm for the solution is presented

model reduction for state space symmetric systems in this paper the model reduction problem for state space symmetric systems is investigated first it is shown that several model reduction methods such as balanced truncation balanced truncation which preserves the dc gain optimal and suboptimal hankel norm approximations inherit the state space symmetric property furthermore for single input and single output siso state space symmetric systems we prove that the h norm of its transfer functions can be calculated via two simple formulas moreover the siso state space symmetric systems are equivalent to systems with zeros interlacing the poles zip under mild conditions

a new parametrization of h suboptimal controllers elementary state space concepts are used to derive a transparent solution to the h control problem on an infinite horizon the main contribution of this solution is a novel representation of suboptimal controllers in terms of a pair of parametric riccati equations with a coupling constraint unlike the classical parametrization in terms of linear fractional transformation this state space representation has a homogeneous riccati formulation which should help to make the most of the suboptimal controller diversity potential applications include the design of reduced order controllers and more generally the selection of suboptimal controllers to meet or optimize additional constraints

a stable state space realization in the formulation of h norm computation in the two block hinftyoptimization problem usually we are given the state space realizations of the proper rational matrices r 1 s and r 2 s whose poles are all the open right half plane two problems are studied in the note the first is the evaluation of phi s r 1 s at s s k k 1 2 n where phi s is an inner function whose zeros s k k 1 2 n are the poles of r 1 s this evaluation is essential if chang and pearson s method is used for computing the optimal hinftynorm the problem is solved in state space via the solutions of lyapunov equations neither polynomial matrix manipulations nor numerical pole zero cancellations are involved in the evaluation the second problem is to find a stable state space realization of s s u s r 2 s where u s is an inner matrix this problem arises in the spectral factorization of gamma 2 r 2 ast r 2 doyle and chu had a method for constructing stable s s based on a minimal realization of r 2 s an alternate method is proposed the alternate method does not require a minimal realization of r 2 s and only a lyapunov equation is involved

h sub spl infin norm approximation of systems by constant matrices and related results in this work the h sub spl infin norm approximation of a given stable proper rational transfer function by a constant matrix is considered a new improved bound on h sub spl infin norm of a given stable transfer function is derived optimal approximation for relaxation systems is given

separation in the flow through peristaltic motion of a carreau fluid in uniform tube abstract the problem of separated flow trapping through peristaltic motion of an incompressible carreau fluid in uniform tube has been investigated under long wavelength approximation neglecting the wave number and using a perturbation series in the weissenberg number wi was used to obtain explicit forms for the velocity field a relation between the flow rate and the pressure gradient and a relation between the friction force and the flow rate in terms of parameter weissenberg number wi power law index n and amplitude ratio a condition frequently used to predict separated flow in boundary layer theory is to set the vorticity equal to zero on the boundary we solve the problem numerically using newton raphson method to get separated flow points on the wall surface from our results the trapping region at the wall decreases with increasing volume flow rate and we found that there exist two values of longitudinal component of separated flow points one of them approaches to inlet of contraction and the other approaches to outlet of contraction also the magnitude of radial velocity of the fluid at the separated flow points for newtonian fluid is greater than non newtonian fluid and the magnitude of pressure rise at separated flow points approximately has the same values at the two values of the longitudinal component of separated flow points moreover the friction force at separated flow points declare reflux phenomena in the contraction region we discuss behavior of the vertical velocity the pressure rise and the friction force at separated flow points for the physical parameters of interest

on the homotopy analysis method for nonlinear problems a powerful easy to use analytic tool for nonlinear problems in general namely the homotopy analysis method is further improved and systematically described through a typical nonlinear problem i e the algebraically decaying viscous boundary layer flow due to a moving sheet two rules the rule of solution expression and the rule of coefficient ergodicity are proposed which play important roles in the frame of the homotopy analysis method and simplify its applications in science and engineering an explicit analytic solution is given for the first time with recursive formulas for coefficients this analytic solution agrees well with numerical results and can be regarded as a definition of the solution of the considered nonlinear problem

directional interpolation approach to h optimization and robust stabilization it is shown that under a mild condition h infty optimization and robust stabilization are equivalent to a directional interpolation problem which is a matrix extension of the classical pick nevanlinna interpolation problem a classical iterative method which is an extension of the schur nevanlinna algorithm is given for solving the problem this method does not require the inner outer factorization nor the balanced realization of the original plant a circuit theoretical parameterization of all solutions is derived that is expected to enhance the physical insight to the h infty optimal control and robust stabilization this parameterization has the degree much less than the one obtained previously

brief paper balanced truncation model reduction for systems with inhomogeneous initial conditions we present a rigorous approach to extend balanced truncation model reduction btmr to systems with inhomogeneous initial conditions we provide an estimate for the error between the input output maps of the original and of the reduced initial value system and we illustrate numerically the superiority of our approach over the naive application of btmr when btmr is applied to linear time invariant systems with inhomogeneous initial conditions it is crucial that the initial data are well represented by the subspaces generated by btmr this requirement is often ignored or it is avoided by making the restrictive assumption that the initial data are zero to ensure that the initial data are well represented by the btmr subspaces we add auxiliary inputs determined by the initial data

convolution and hankel operator norms for linear systems some norms are derived for convolution and hankel operators associated with linear time invariant systems in certain cases these norms are shown to be identical the tightest possible bound has been obtained for the absolute magnitude of the euclidean 2 or infinity norm of the time domain response of a multioutput system to certain classes of input disturbance

optimal sensitivity theory for multivariate distributed plants in this note we generalized the results of foias and tannenbaum 1986 a and foias et al 1987 on optimal sensitivity minimization to a much broader class of distributed plants we relate our results to certain kinds of hankel norm approximation problems that frequently appear in control engineering applications

peristaltically induced motion of a mhd third grade fluid in a deformable tube abstract we consider incompressible magnetohydrodynamic mhd third grade fluid confined in a circular cylindrical tube the tube surfaces are electrically non conducting travelling sinusoidal wave is imposed on the tube which induces peristaltic motion in the fluid the stream function axial velocity and pressure gradient are determined analytically for small deborah number the analysis consists of a perturbation expansion in terms of the deborah number up to o solutions for pressure rise and frictional force per wavelength are given through the use of numerical integration the general solution of highly non linear equation for the hydrodynamic third grade fluid is developed the results are finally compared with the third grade hydrodynamic and newtonian fluid cases it is found that the axial velocity increases by increasing deborah number but decreases for large values of hartmann number