System modeled by Eigenvectors
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
3
c) Determine the controller u(t) if x(0) = and
-1
2e-21+ e-12
x(3) =
-2e-21+ e-12.
https://brainmass.com/engineering/electrical-engineering/system-modeled-eigenvectors-54771
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Solution Summary
Eigenvectors are used to model electrical engineering systems. The transition matrix is used of an eigenvalue method.
Real Life Applications of Complex or Imaginary Numbers
When solving a quadratic equation using the quadratic formula, it is possible for the b2 - 4ac term inside the square root (the discriminant) to be negative, thus forcing us to take the square root of a negative number. The solutions to the equation will then be complex numbers (i.e., involve the imaginary unit i).
Question:
In the real world, where might these so-called imaginary numbers be used?
When using a formula, we often know the value of one variable to a greater degree of accuracy than we know the others. I need help to understand, what affect, if any, does it make on our use of a formula if we know the value of one variable to a greater degree of accuracy than another? Please assist.
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