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