1. Satellite Trajectory Control (n = 4, m = 2, p = 2, q = 1)

Total CPU time: 2.32 seconds

Matrices are given in complex number.

0 0 1 0 0 0 0 0

A = 0.3578 0 0 0 0 0 0.8525 0

0 0 0 0 0 0 1 0

0 0 -0.5596 0 0 0 0 0

0 0 0 0

B = 1.3411 0 0 0

0 0 0 0

0 0 1.0867 0

C = 0.1234 0 0.7934 0 0.8322 0 0.7979 0

0.3434 0 0.4232 0 0.0233 0 0.9232 0

-0.8945 0.4472

-0.8945 -0.4472

Poles = -5.0 0

-7.0 0

-3.0 0

%Solution No. 1

F{1}=[

-9.748975485330462e+01+2.109258881810700e+01*i

]

G{1}=[

2.104799069626041e+02-2.191861126364918e+02*i 9.699353867517590e+01-3.704026547514427e+02*i

]

H{1}=[

6.756813084019736e+01+3.565811988163494e+01*i

-6.417453616621243e+01-4.373503169106266e+01*i

]

K{1}=[

-2.290757069097127e+02+2.484350839892216e+01*i -2.331677887970709e+02+1.708717187386861e+02*i

2.342144735186220e+02+1.421044871691706e+00*i 2.528772027687453e+02-1.452669238238088e+02*i

]

%Solution No. 2

F{2}=[

-9.748975485332527e+01-2.109258881807931e+01*i

]

G{2}=[

2.104799069627051e+02+2.191861126364492e+02*i 9.699353867531062e+01+3.704026547514499e+02*i

]

H{2}=[

6.756813084019640e+01-3.565811988166475e+01*i

-6.417453616620843e+01+4.373503169109284e+01*i

]

K{2}=[

-2.290757069097583e+02-2.484350839883989e+01*i -2.331677887971661e+02-1.708717187386201e+02*i

2.342144735186598e+02-1.421044871779827e+00*i 2.528772027688352e+02+1.452669238237323e+02*i

]

%Solution No. 3

F{3}=[

1.159923143488741e+02+1.832427207052007e+02*i

]

G{3}=[

9.280462512545370e+01+2.606617390353373e+01*i -1.092268110802379e+02-5.344162804611599e+01*i

]

H{3}=[

6.212115768723651e+02-1.422865849840187e+03*i

-1.139539313436313e+02-1.499669525274109e+02*i

]

K{3}=[

-2.151745643496482e+02-6.549178701387477e+02*i 1.196114679268929e+02+8.624236677339381e+02*i

-8.133984634894836e+01-1.623608469963932e+01*i 9.849342166390244e+01+3.809160616508618e+01*i

]

%Solution No. 4

F{4}=[

1.448064562997523e+02-3.505642453853494e-13*i

]

G{4}=[

3.288498812603783e+01-1.122973666315728e-13*i -2.681282670151737e+02+4.602788086968863e-13*i

]

H{4}=[

-5.366563851587962e+02+1.424090736015156e-12*i

3.597755877728642e+02-9.151265804746549e-13*i

]

K{4}=[

-1.193231913028700e+02+4.437839743029536e-13*i 9.901888691405292e+02-1.938793632224967e-12*i

8.088733155287443e+01-2.888277727848179e-13*i -6.645986927699139e+02+1.226664512015890e-12*i

]

%Solution No. 5

F{5}=[

7.180250261060708e+01+3.132347159546074e-13*i

]

G{5}=[

-5.435510152127455e+01+4.235476435453059e-13*i -7.032771582342006e+01-5.081484905712730e-13*i

]

H{5}=[

-3.030859703417912e+01-1.776453855187470e-13*i

8.089316246008686e+01+4.422948913468620e-13*i

]

K{5}=[

2.567919572291180e+01-1.413708331847972e-13*i 2.681480391807477e+01+2.604898654571612e-13*i

-5.977018491001014e+01+4.016946256233110e-13*i -7.905209041624015e+01-6.567702248162184e-13*i

]

%Solution No. 6

F{6}=[

6.290869861970219e+00+6.495660240882938e+01*i

]

G{6}=[

-1.436117250134585e+01+3.313961703117094e+02*i -3.027483148540888e+02-7.300340885628166e+02*i

]

H{6}=[

3.110711030816350e+01-7.231224287886150e+01*i

5.313483522204642e+00+3.587516607936282e+01*i

]

K{6}=[

2.102045914150968e+02-3.421395492468785e+02*i -1.110235692753333e+02+9.501391706191929e+02*i

-6.298544120963641e-01+1.836033843135441e+02*i -1.825937792228395e+02-3.980732316100309e+02*i

]

%Solution No. 7

F{7}=[

6.290869862115027e+00-6.495660240895381e+01*i

]

G{7}=[

-1.436117250072968e+01-3.313961703124531e+02*i -3.027483148559162e+02+7.300340885639306e+02*i

]

H{7}=[

3.110711030807263e+01+7.231224287911117e+01*i

5.313483522293833e+00-3.587516607942414e+01*i

]

K{7}=[

2.102045914148498e+02+3.421395492482011e+02*i -1.110235692738112e+02-9.501391706217879e+02*i

-6.298544117041729e-01-1.836033843139249e+02*i -1.825937792239330e+02+3.980732316105344e+02*i

]

%Solution No. 8

F{8}=[

1.159923143487299e+02-1.832427207054476e+02*i

]

G{8}=[

9.280462512549082e+01-2.606617390366372e+01*i -1.092268110802580e+02+5.344162804629165e+01*i

]

H{8}=[

6.212115768743164e+02+1.422865849840082e+03*i

-1.139539313435458e+02+1.499669525275108e+02*i

]

K{8}=[

-2.151745643489848e+02+6.549178701393828e+02*i 1.196114679259047e+02-8.624236677346203e+02*i

-8.133984634896032e+01+1.623608469970188e+01*i 9.849342166390646e+01-3.809160616517110e+01*i

]

REFERENCES:

D.C. Dorf and R.H. Bishop:
Modern Control Systems. Addison-Wesley, 1998.

T. Kailath:
Linear Systems. Prentice-Hall, 1980.