coprime matrix fraction description via orthogonal structure theorem an algorithm to compute the coprime matrix fraction description from a given transfer function matrix w s is presented the algorithm is based on householder transformations to compute the minimal realization of w s and on the orthogonal version of the structure theorem of w a wolovich 1974 and of wolovich and p l falb 1969 to determine the coprime form the proposed method is numerically less expensive than a similar algorithm given by r v patel 1981 which uses singular value decomposition

a connection between state space and doubly coprime fractional representations explicit formulas for a doubly coprime fractional representation of the transfer function of a lumped lti system are given in terms of a stabilizable and detectable state space realization of the transfer function these formulas allow existing computational algorithms to be utilized for the purpose of computing doubly coprime factorizations several additional implications of this result are briefly discussed as are some immediate extensions and future research directions

on strong anomalous diffusion superdiffusive behavior i e x2 t t2 with 1 2 is in general not completely characterized by a unique exponent we study some systems exhibiting strong anomalous diffusion i e x t q tq q where 2 1 2 and q q is not a linear function of q this feature is different from the weak superdiffusive regime i e q const 1 2 occurring in random shear flows strong anomalous diffusion can be generated by nontrivial chaotic dynamics e g lagrangian motion in 2d time dependent incompressible velocity fields 2d symplectic maps and 1d intermittent maps typically the function q q is piecewise linear this is due to two mechanisms a weak anomalous diffusion for the typical events and a ballistic transport for the rare excursions in order to have strong anomalous diffusion one needs a violation of the hypothesis of the central limit theorem this happens only in a very narrow region of the control parameters space in the presence of strong anomalous diffusion one does not have a unique exponent and therefore one has the failure of the usual scaling p x t t f x t of the probability density this implies that the effective equation at large scale and long time for p x t obeys neither the usual fick equation nor other linear equations involving temporal and or spatial fractional derivatives

generalized matrix euclidean algorithms for solving diophantine equations and associated problems abstract based on the matrix fraction descriptions of multi variable control systems this paper presents the generalized matrix euclidean algorithms for solving diophantine equations and associated problems a chain rule is developed for finding the greatest common right left divisor of two square non square polynomial matrices and the irreducible right left matrix fraction description from the reducible or irreducible left right matrix fraction description also the development of multi variable pole assignment controllers are discussed for engineering applications

scaling of the density of state of the weighted laplacian in the presence of fractal boundaries spectral properties of the weighted laplace operator in the presence of fractal boundaries are numerically investigated for both neumann and dirichlet boundary conditions this corresponds to the characterization of heat and mass transport in microchannels with irregular and rough surfaces induced by the microfabrication process the axial velocity field with no slip boundary conditions representing the weighting function of the laplace operator influences the localization properties of the eigenfunctions and the scaling of the integrated density of state idos n the results indicate that n deviates from the form given by the modified weyl berry lapidus conjecture as it shows a correction of n df 4 to the leading order weil term numerical results are presented for koch and koch snowflake fractal boundaries the role of slip or no slip boundary conditions of the velocity field on the idos is also investigated 2010 the american physical society less

a fast algorithm for the division of two polynomial matrices a modification of the algorithm shown by q g wang and c h zhou see ibid vol ac 31 p 165 6 1968 is presented the performance of their algorithm is improved by the use of convolutions and therefore of fft techniques the present method is based on the fast inversion of block triangular toeplitz matrices and it is amenable to parallel implementation

on doubly coprime factorizations abstract this paper proposes a new doubly coprime factorization technique which forms a basis of algebraic control theory this enables us to generalize a previous result on doubly coprime factorization furthermore it is shown that all stabilizing compensators possess a simple model reference structure

a new total variational regularization method for nonlinear inverse problems in fluorescence molecular tomography abstract fluorescence molecular tomography fmt is an imaging way of in vivo optical imaging which is widely used in biomedical photon imaging for its higher sensitivity for years the propagation process of photons in tissue is simulated based on the equation of radiative transfer in this work we analyze an inverse problem in fmt which uses the reading of body surface detector to reconstruct the optical parameter distribution we propose a novel total variational regularization method to solve the absorption parameter inversion problem in fmt the proof of the proposed method is also provided finally numerical experiments demonstrate the feasibility of the proposed method

a convergence analysis of the landweber iteration for nonlinear ill posed problems in this paper we prove that the landweber iteration is a stable method for solving nonlinear ill posed problems for perturbed data with noise level delta we propose a stopping rule that yields the convergence rate o delta 1 2 under appropriate conditions we illustrate these conditions for a few examples

parameterization of reduced order compensator in the frequency domain after a brief survey of the relations between time and frequency domain representations of the observer based linear state feedback loop the parameterization of the compensator is discussed it is shown that the free parameters specified by the state feedback matrix k and the output error feedback matrix l in the time domain appear as coefficients in the polynomial matrices dtilde s and s characterizing the closed loop dynamics in the frequency domain these polynomial matrices can either be chosen arbitrarily pole placement problem or they may be derived as solutions from the corresponding optimal control or the optimal estimation problems respectively starting from the polynomial matrices dtilde s and s the doubly coprime fractional representations of the system and of the compensator transfer matrices can be computed directly without recurrence to the time domain results from these representations the right and left coprime compensator matrix fraction descriptions can easily be evalu

mixing enhancement by optimal flow advection we consider the problem of optimal mixing control our objective is to best enhance mixing by flow advection while the flow is optimized in the sense that it is almost steady and is of the least magnitude and the least rotation for this we define a mixing efficiency functional by penalizing the average of variance of a diffusive scalar the average of the flow and the average of its acceleration and strain tensor by variational principles we prove the existence of an optimal flow and derive optimality conditions that consist of a system of nonlinear advection diffusion equations wave equations and laplace s equation

proper stable transfer matrix factorizations and internal system descriptions the exact relations between coprime proper stable factorizations of p s and coprime polynomial matrix factorizations are derived and they directly lead to relations with internal descriptions of the plant in differential operator or state space form it is shown that obtaining any right or left proper stable coprime factorization is equivalent to state feedback stabilization or to designing a full order full state observer respectively solving the diophantine equation is shown to be equivalent to designing a full or reduced order observer of a linear functional of the state and to designing a stable inverse system and this suggests new computational methods to solve the diophantine

boundary feedback stabilization of homogeneous equilibria in unstable fluid mixtures we consider the problem of boundary feedback stabilization of homogeneous equilibria in unstable fluid mixtures that are governed by unstable linear reaction convection diffusion equations we extend boundary feedback control laws designed for the one dimensional reaction diffusion equation using the backstepping method to this higher dimensional case we show that under certain mathematical conditions on the velocity field boundary feedback controls similar to the ones for one dimensional equations also works for the higher dimensional case and exponentially stabilize the homogeneous equilibrium zero at any given decay rate

a polynomial matrix method for computing stable rational doubly coprime factorizations this paper proposes a new method for computing stable rational doubly coprime factorizations from a given transfer matrix in contrast to the well known method which requires a state space representation the proposed method makes full use of polynomial matrices and the whole operation is carried out directly in the frequency domain furthermore the paper clarifies the meaning of the obtained factorization as a controller by showing that this factorization coincides with the one by the state space method for a suitable choice of feedback and observer gains

advection diffusion in nonchaotic closed flows non hermitian operators universality and localization the qualitative spectral properties characterizing the advection diffusion operator in two dimensional steady incompressible flows can be obtained from the analysis of simple model flows on the torus the velocity field of which attains the simple expression mathbf v mathbf x mathbf 0 v y x mathbf for this class of simple flows the advection diffusion operator reduces to a one dimensional schr odinger operator in the presence of an imaginary potential which shares some spectral analogies with non hermitian quantum operators e g spectral invariance and is characterized by eigenfunction localization the latter property i e eigenfunction localization is strictly related to the occurrence of a universal scaling of the eigenvalue spectrum with the peclet number the scaling exponent of which depends exclusively on the local behavior of the potential close to its critical points the analysis is extended to a class of unbounded non hermitian operators which include the laplacian and the biharmonic operators coupled to an imaginary potential as special cases

conditions for triangular decoupling control the main purpose of this article is to explore the relationship of two existing conditions for the triangular decoupling problem the first one is the triangular diagonal dominance condition proposed by hung and anderson the second one is the stable coprime factorisation described condition proposed by gomez and goodwin which has been proven as a necessary and sufficient condition for the triangular decoupling problem this article proves that the two conditions are actually equivalent it also provides easy to use criteria for assessment of the solvability of the triangular decoupling problem

a recursive algorithm for coprime fractions and diophantine equations the computation of coprime fractions for proper rational matrices and the solving of the minimal design problem are important in the design of multivariable systems by using polynomial fractional terms a recursive algorithm which fully exploits the shift invariant property of the generalized resultants is developed to carry out these computations a method for solving the diophantine equation that is based on this algorithm is outlined this results in a significant reduction in computation as compared to the standard methods involving solution of linear algebraic equations some comparisons to existing methods show that the present algorithm is computationally more attractive with regard to efficiency and accuracy

numerical computation of a coprime factorization of a transfer function matrix abstract a new algorithm is presented for computing a coprime factorization of a transfer function matrix the method is based on reformulating the problem as a problem of constructing a minimal basis of the right nullspace of a matrix pencil b a due to the special structure and rank properties of the pencil obtained after transforming b a to generalized schur form the original problem can be easily solved in a numerically reliable way

the design of linear controllers with symbolic algebra abstract modern transfer function methods use quite a lot of abstract algebra in the design of control systems in computing the final results symbolic algebra turns out to be an important tool in this paper symbolic computation algorithms will be developed to enable computations directly in the theoretically useful transfer function rings a symbolic software package called hinf will be developed and used both for educational and theoretical purposes

a levenberg marquardt method based on sobolev gradients abstract we extend the theory of sobolev gradients to include variable metric methods such as newton s method and the levenberg marquardt method as gradient descent iterations associated with stepwise variable inner products in particular we obtain existence uniqueness and asymptotic convergence results for a gradient flow based on a variable inner product

a new approach for calculating doubly coprime matrix fraction descriptions using the concepts of state feedback in generalized state space explicit formulas for calculating doubly coprime matrix fraction descriptions mfds of the transfer matrix of a regular state space system and the polynomial generalized bezout identity elements corresponding to those coprime mfds are presented they can be easily calculated with the help of existing computational algorithms and software packages