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    System modeled by Eigenvectors

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    Consider the system modeled by:

    x' = Ax + Bu , y = Cx + Du

    -5 1 -1
    A = , B = , C=[1 0] , D=0
    1 -5 1

    a) Determine the transition matrix eAt using the eigenvalues and eigenvectors method

    b) Find x(t) and y(t) if the input is a unit step function when x(0)=[3 -1]T

    c) Determine the controller u(t) if x(0) = and

    2e-21+ e-12
    x(3) =
    -2e-21+ e-12.

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    Solution Summary

    Eigenvectors are used to model electrical engineering systems. The transition matrix is used of an eigenvalue method.