Modern Control Engineering

Example Problems and Solutions 819

Hence, Equation (10–137) may be written as follows:

Define

Then Equation (10–137) can be written as

=Cf 1 f 2 pfqvq+ 1 pvnDc

A 11

0

A 12

A 22

d

CAf 1 Af 2 pAfqAvq+ 1 pAvnD

E

aq+1q+ 1







anq+ 1

p

p

aq+1n







ann

U=A 22

E

0







0

p

p

0







0

U=A 21 =(n-q)*q zero matrix

F

a1q+ 1

a2q+ 1







aqq+ 1

p

p

p

a1n

a2n







aqn

V=A 12

F

a 11

a 21







aq1

p

p

p

a1q

a2q







aqq

V=A 11

=Cf 1 f 2 pfqvq+ 1 pvnD

a 11

a 21







aq1

0







0

p

p

p

p

p

a1q

a2q







aqq

0







0

a1q+ 1

a2q+ 1







aqq+ 1

aq+1q+ 1







anq+ 1

p

p

p

p

p

a1n

a2n







aqn

aq+1n







ann

CAf 1 Af 2 pAfqAvq+ 1 pAvnD