
and find the new system and input matrices A and B where
_z
1
_z
2
¼ A
z
1
z
2
þ B
F
1
F
2
Hint: Find H
1
and H
2
in terms of z
1
and z
2
.
(c) Find the new output matrix C where
V
T
¼ C
z
1
z
2
2.18 Write the state equations for the syst em of three railroad cars in Exercise 2.16. Choose the
outputs to be the positions of each car.
2.19 An ecosystem consists of three species whose populations are denoted by F, S, and G. The
growth rates of each specie are given by
Growth rate of F ¼
1
F
dF
dt
¼ a cS u
F
Growth rate of S ¼
1
S
dS
dt
¼k þ lF m
G
u
S
Growth rate of G ¼
1
G
dG
dt
¼e þ sS þ u
G
Write the system in state variable form
_
x ¼f(x, u) y ¼g(x, u) with the state x ¼[FSG]
T
, input ...