14,545 research outputs found

    Conditions for triangular decoupling control

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    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

    Controllability distributions and systems approximations: a geometric approach

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    Given a nonlinear system, a relation between controllability distributions defined for a nonlinear system and a Taylor series approximation of it is determined. Special attention is given to this relation at the equilibrium. It is known from nonlinear control theory 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. By dealing with a k-th Taylor series approximation of the system, the authors are able to decide when the solvability conditions of these kinds of problem are equivalent for the nonlinear system and its approximation. Some cases when the solution obtained from the approximated system is an approximation of an exact solution for the original problem are distinguished. Some examples illustrate the result

    Controllability distributions and systems approximations: a geometric approach

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    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

    Two Qubit Quantum Computing in a Projected Subspace

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    A formulation for performing quantum computing in a projected subspace is presented, based on the subdynamical kinetic equation (SKE) for an open quantum system. The eigenvectors of the kinetic equation are shown to remain invariant before and after interaction with the environment. However, the eigenvalues in the projected subspace exhibit a type of phase shift to the evolutionary states. This phase shift does not destroy the decoherence-free (DF) property of the subspace because the associated fidelity is 1. This permits a universal formalism to be presented - the eigenprojectors of the free part of the Hamiltonian for the system and bath may be used to construct a DF projected subspace based on the SKE. To eliminate possible phase or unitary errors induced by the change in the eigenvalues, a cancellation technique is proposed, using the adjustment of the coupling time, and applied to a two qubit computing system. A general criteria for constructing a DF projected subspace from the SKE is discussed. Finally, a proposal for using triangulation to realize a decoherence-free subsystem based on SKE is presented. The concrete formulation for a two-qubit model is given exactly. Our approach is novel and general, and appears applicable to any type of decoherence. Key Words: Quantum Computing, Decoherence, Subspace, Open System PACS number: 03.67.Lx,33.25.+k,.76.60.-kComment: 24 pages. accepted by Phys. Rev.

    On computing minimal realizations of periodic descriptor systems

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    Abstract: We propose computationally efficient and numerically reliable algorithms to compute minimal realizations of periodic descriptor systems. The main computational tool employed for the structural analysis of periodic descriptor systems (i.e., reachability and observability) is the orthogonal reduction of periodic matrix pairs to Kronecker-like forms. Specializations of a general reduction algortithm are employed for particular type of systems. One of the proposed minimal realization transformations for which the backward numerical stability can be proved

    Accurate multigrid solution of the Euler equations on unstructured and adaptive meshes

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    A method for accurately solving inviscid compressible flow in the subcritical and supercritical regimes about complex configurations is presented. The method is based on the use of unstructured triangular meshes in two dimensions, and special emphasis is placed on the accuracy and efficiency of the solutions. High accuracy is achieved by careful scaling of the artificial dissipation terms, and by reformulating the inner and outer boundary conditions for both the convective and dissipative operators. An adaptive grid refinement strategy is presented which enhances the solution accuracy for complex flows. When coupled with an unstructured multigrid algorithm, this method is shown to produce an efficient solver for flows about arbitrary configurations
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