2. Numerical Example A (n = 6, m = 2, p = 2, q = 1)
Total CPU time: 3 seconds
Matrices are given in complex number.
0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0 -1 0
A = 0 0 1 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 1 0 0 0 0 0
0 0 0 0 -1 0 0 0 1 0 0 0
-1 0 -3 0
0 0 0 0
B = 0 0 1 0
0 0 -1 0
0 0 -1 0
0 0 0 0
C = 0 0 0 0 1 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 1 0
-0.1 0
-1.5 0
Poles = -0.9 0
-0.7 0
-6.0 0
-3.5 0
-8.0 0
%Solution No. 1
F{1}=[
7.477287846756940e+01+2.728674330937002e+02*i
]
G{1}=[
4.965871721002973e+02+4.374521730646446e+02*i -4.628452522763754e+02+1.147426032605264e+02*i
]
H{1}=[
1.846707722127365e+02+5.083453428956880e+02*i
3.031794622473183e+01-1.200322035489404e+02*i
]
K{1}=[
1.015363754915874e+03+7.567864482174076e+02*i -8.652241045147512e+02+2.906491323022162e+02*i
-9.547287846760622e+01-2.728674330937206e+02*i 2.011686776535216e+02+5.536081376366627e+01*i
]
%Solution No. 2
F{2}=[
3.199265715516323e+02-1.548765332057977e+02*i
]
G{2}=[
2.487577530781561e+02+2.616178585610839e+01*i -8.215121581135115e+01-5.315759856207782e+01*i
]
H{2}=[
1.622813189326907e+03-1.924766465580797e+03*i
-2.945871472467236e+02+4.422917801244651e+02*i
]
K{2}=[
1.685596108645322e+03-5.483491533511044e+02*i -6.857792609523018e+02-1.065335313789688e+02*i
-3.406265715516261e+02+1.548765332057818e+02*i 1.465555028609590e+02+6.201382224233811e+00*i
]
%Solution No. 3
F{3}=[
3.700426673515059e+02-5.751200273721160e-37*i
]
G{3}=[
1.349864376666484e+02-2.102467921882523e-37*i -5.986703477727053e+01+9.260262325463762e-38*i
]
H{3}=[
2.530566165894360e+03-3.929595352241036e-36*i
-1.069761676445779e+03+1.660879086501155e-36*i
]
K{3}=[
9.248416695982899e+02-1.436546872444680e-36*i -4.066720073655953e+02+6.327021005205896e-37*i
-3.907426673515100e+02+6.071695406717201e-37*i 1.722405095387777e+02-2.674189370303932e-37*i
]
%Solution No. 4
F{4}=[
-1.569401692074347e+01-2.913834370565495e-37*i
]
G{4}=[
-1.563082831754350e+01-3.297869322655579e-37*i 2.133071330565473e+02+5.007507560868619e-36*i
]
H{4}=[
5.981772081343235e+01+1.204086596378784e-36*i
-4.427894613550870e+00-8.635982099626995e-38*i
]
K{4}=[
6.279802588629813e+01+1.363804024669587e-36*i -8.832762189962114e+02-2.071707079326163e-35*i
-5.005983079256266e+00-9.947602287161490e-38*i 7.349383868089529e+01+1.531082463054382e-36*i
]
%Solution No. 5
F{5}=[
2.110603980992597e+01-3.756872517073130e-38*i
]
G{5}=[
2.311484540677111e+01-4.053110943782212e-38*i -4.193923681216096e+01+6.988903369652432e-38*i
]
H{5}=[
4.829219406844260e+02-7.523476634595503e-37*i
-3.845839601411206e+01+5.814560823516235e-38*i
]
K{5}=[
5.242342437765735e+02-8.115273243777475e-37*i -9.341492213882619e+02+1.394213026031765e-36*i
-4.180603980992174e+01+6.269406664409022e-38*i 7.487003103245937e+01-1.075707761935145e-37*i
]
%Solution No. 6
F{6}=[
-2.015358804668081e+02-4.026018887985202e-35*i
]
G{6}=[
-3.837832596569949e+01-8.162913119068724e-36*i -1.534669036615372e+02-3.055708729801036e-35*i
]
H{6}=[
-8.134121343332920e+02-1.616697698399795e-34*i
9.173623257276732e+02+1.823502264495430e-34*i
]
K{6}=[
-1.583919749733504e+02-3.278373954810061e-35*i -6.186501628423116e+02-1.227043712671164e-34*i
1.808358804667722e+02+3.697823361187740e-35*i 6.972140122165179e+02+1.383997883670813e-34*i
]
%Solution No. 7
F{7}=[
3.199265715525333e+02+1.548765332070819e+02*i
]
G{7}=[
2.487577530793235e+02-2.616178585556132e+01*i -8.215121581181972e+01+5.315759856208922e+01*i
]
H{7}=[
1.622813189329064e+03+1.924766465589500e+03*i
-2.945871472469713e+02-4.422917801263274e+02*i
]
K{7}=[
1.685596108650497e+03+5.483491533566807e+02*i -6.857792609548521e+02+1.065335313780135e+02*i
-3.406265715525750e+02-1.548765332070651e+02*i 1.465555028614683e+02-6.201382223975287e+00*i
]
%Solution No. 8
F{8}=[
7.477287846755218e+01-2.728674330934444e+02*i
]
G{8}=[
4.965871720999467e+02-4.374521730641991e+02*i -4.628452522759800e+02-1.147426032605170e+02*i
]
H{8}=[
1.846707722126949e+02-5.083453428951437e+02*i
3.031794622467361e+01+1.200322035488356e+02*i
]
K{8}=[
1.015363754915120e+03-7.567864482164575e+02*i -8.652241045138999e+02-2.906491323021912e+02*i
-9.547287846758258e+01+2.728674330934559e+02*i 2.011686776533629e+02-5.536081376356833e+01*i
]
REFERENCES:
J. Rosenthal and X.A. Wang:
Output Feedback Pole Placement with Dynamic Compensators.
IEEE Trans. Automat. Contr. 41(6):830-843, 1996.