
F(s) is the Laplace transform of the continuous-time system transition matrix F(t), used to obtain
the state response in the time domain. Inverting (sI A) results in
F(s) ¼
f
11
(s) f
12
(s) f
13
(s) f
14
(s)
f
21
(s) f
22
(s) f
23
(s) f
24
(s)
f
31
(s) f
32
(s) f
33
(s) f
34
(s)
f
41
(s) f
42
(s) f
43
(s) f
44
(s)
2
6
6
6
6
4
3
7
7
7
7
5
(4:237)
where
f
11
(s) ¼
1
D(s)
[(s þ0:015)(s þ 0:32)(s þ 1:7)] (4:238)
f
12
(s) ¼
1
D(s)
[0:003(s þ 1:2)] (4:239)
f
13
(s) ¼
1
D(s)
[0:15(s þ 0:015)] (4:240)
f
14
(s) ¼
1
D(s)
[0:5(s þ 0:015)(s þ 0:32)] (4:241)
f
21
(s) ¼
1
D(s)
[0:8(s þ 0:32)(s þ 1:7)] (4:242)
f
22
(s) ¼
1
D(s)
[s
3
þ 2:97s
2
þ 2:388s þ 0:4928](4:243)
f
23
(s) ¼
1
D(s)
[0:12](4:244)
f
24
(s) ¼
1
D(s)
[0:4(s þ 0:32)] (4:245)
f
31
(s) ¼
1
D(s