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Unformatted text preview: . (c) Compute a value for the initial state x ( ) : = ± x 1 ( ) x 2 ( ) x 3 ( ) ² ′ such that the solution to ˙ x = Ax , y = ± 1 1 1 ² x is equal to y ( t ) = te − 2 t , ∀ t ≥ . 1 Hint: To solve (c), start by writing y ( t ) as a function of x 1 ( ) , x 2 ( ) , x 3 ( ) and then determine values for these constants to get the desired output. 4. Compute a matrix A ( t ) such that Φ ( t , t ) = 1 e t 2 − t 2 2 − 1 e t 2 − t 2 2 is the state transition matrix of the homogeneous ODE ˙ x = A ( t ) x 2...
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 Fall '09
 abamieh
 Characteristic polynomial, 1 k

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