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Prévia do material em texto

Problem 7.20PP
Show that the impulse response of the system {A. B, C. D) is given by 
h(t) = CeAB + D5(t),
where eAf is the matrix exponential defined by
-Al / . A V \ ” A‘l*
Step-by-step solution
step 1 of 1
Step 1 of 1 ^
Consider the state variable equations for the inhomogeneous case with a forcing function input
» (/)
i(0=A (/)x(0+B (r)«(/) (1)
The solution of {1) is
x(») = ®(/,»„)i„+|®(/,r)B(r)ii(r)x,+|e*Bii(r)x,+Cje*