Reduced order feedback control equations for linear time and frequency domain analysis

An algorithm was developed which can be used to obtain the equations. In a more general context, the algorithm computes a real nonsingular similarity transformation matrix which reduces a real nonsymmetric matrix to block diagonal form, each block of which is a real quasi upper triangular matrix. The algorithm works with both defective and derogatory matrices and when and if it fails, the resultant output can be used as a guide for the reformulation of the mathematical equations that lead up to the ill conditioned matrix which could not be block diagonalized

Controllability distributions and systems approximations: a geometric approach

Given a nonlinear system we determine a relation at an equilibrium between controllability distributions defined for a nonlinear system and a Taylor series approximation of it. The value of such a relation is appreciated if we recall that the solvability conditions as well as the solutions to some control synthesis problems can be stated in terms of geometric concepts like controlled invariant (controllability) distributions. The relation between these distributions at the equilibrium will help us to decide when the solvability conditions of this kind of problems are equivalent for the nonlinear system and its approximatio

Sympiler: Transforming Sparse Matrix Codes by Decoupling Symbolic Analysis

Sympiler is a domain-specific code generator that optimizes sparse matrix computations by decoupling the symbolic analysis phase from the numerical manipulation stage in sparse codes. The computation patterns in sparse numerical methods are guided by the input sparsity structure and the sparse algorithm itself. In many real-world simulations, the sparsity pattern changes little or not at all. Sympiler takes advantage of these properties to symbolically analyze sparse codes at compile-time and to apply inspector-guided transformations that enable applying low-level transformations to sparse codes. As a result, the Sympiler-generated code outperforms highly-optimized matrix factorization codes from commonly-used specialized libraries, obtaining average speedups over Eigen and CHOLMOD of 3.8X and 1.5X respectively.Comment: 12 page

Integration by parts identities in integer numbers of dimensions. A criterion for decoupling systems of differential equations

Integration by parts identities (IBPs) can be used to express large numbers of apparently different d-dimensional Feynman Integrals in terms of a small subset of so-called master integrals (MIs). Using the IBPs one can moreover show that the MIs fulfil linear systems of coupled differential equations in the external invariants. With the increase in number of loops and external legs, one is left in general with an increasing number of MIs and consequently also with an increasing number of coupled differential equations, which can turn out to be very difficult to solve. In this paper we show how studying the IBPs in fixed integer numbers of dimension d=n with $n \in \mathbb{N}$ one can extract the information useful to determine a new basis of MIs, whose differential equations decouple as $d \to n$ and can therefore be more easily solved as Laurent expansion in (d-n).Comment: 31 pages, minor typos corrected, references added, accepted for publication in Nuclear Physics

Vector like gauge theories with almost massless fermions on the lattice

A truncation of the overlap (domain wall fermions) is studied and a criterion for reliability of the approximation is obtained by comparison to the exact overlap formula describing massless quarks. We also present a truncated version of regularized, pure gauge, supersymmetric models. The mechanism for generating almost masslessness is shown to be a generalized see-saw which can also be viewed as a version of Froggatt-Nielsen's method for obtaining natural large mass hierarchies. Viewed in this way the mechanism preserving the mass hierarchy naturally avoids preserving even approximately axial U(1). The new insights into the source of the mass hierarchy suggest ways to increase the efficiency of numerical simulations of QCD employing the truncated overlap.Comment: 35 pages, TeX, 4 figures using eps

TRIANGULAR DECOUPLING THROUGH LINEAR STATE VARIABLE FEEDBACK

The paper studies the problem of triangular decoupling through l.s.v. f. using frequency-domain approaches. The interactor concept and the matrix fraction right description form are used to resolve the questions concerned with this problem and in turn an algorithm is given for triangularization of any right invertible proper system by using l.s.v.f. alone. The paper describes the use of triangular decoupling as an intermediate step for exact decoupling of systems having unstable decoupling zeros

A model-based method for organizing tasks in product development

"Revised November 1993."Includes bibliographical references (p. 18-20).Funded jointly by the National Science Foundation, General Motors Corporation and MIT Leaders for Manufacturing Program.Steven D. Eppinger ... [et al.]

Organizing the tasks in complex design projects

"October 1989, revised December 1989."Includes bibliographical references (leaves 16-19).by Steven D. Eppinger and Daniel E. Whitney

Trade-off between complexity and BER performance of a polynomial SVD-based broadband MIMO transceiver

In this paper we investigate non-linear precoding solutions for the problem of broadband multiple-input multiple output(MIMO) systems. Based on a polynomial singular value decomposition (PSVD) we can decouple a broadband MIMO channel into independent dispersive spectrally majorised single-input single-output (SISO) subchannels. In this contribution, the focus of our work is to explore the influence of approximations on the PSVD, and the performance degradation that can be expected as a result