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Find the transfer function from state space representation

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Consider the following system (see attachment) whose state space representation is as follows:

a) Find the transfer function of the system.
b) Compute eAt using the eigenvalues and eigenvectors method.
c) Compute eAt using the partial fraction method.
d) If u (t)=0 for t ≥ 0,compute x (t), y(t), and x(1) =[ -1 2]T
e) Assume that the initial conditions are zero. Using MATLAB ,Plot x(t), y(t), given that u(t)= -5 for 0 ≤ t ≤ 3 and u(t)=5 for 3 ≤ t ≤ 6

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Solution Preview

Consider the following system whose state space representation is as follows:

x'1(t) 5 2 x1(t) 1
= + u(t)
x'2(t) -2 5 x2(t) 1

y(t) = [ 1 5 ] ...

Solution Summary

The expert finds the transfer function from the state space representation.