Consider the system described in state variable form by x(t) = Ax(t) + Bu(t) y(t) = Cx(t)
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x(t) = Ax(t) + Bu(t)
y(t) = Cx(t)
where
and where k1 k2 and both k1 and k2 are real numbers.
(a) Compute the state transition matrix Φ(t, 0).
(b) Compute the eigenvalues of the system matrix A.
(c) Compute the roots of the characteristic polynomial.
(d) Discuss the results of parts (a)-(c) in terms of stability of the system.
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