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System modeled by Eigenvectors

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See the attached file.
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.

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