Metodo De Ackerman Ing.Control

EJERCICIOҨ
M1=-7
M2=-4+2i
M3=-4-2i
ẋ1ẋ2ẋ3=-121210241x1x2x3+011u
ẋ1=-x1+2x2+x3
ẋ2=2x1+x2+u
ẋ1=2x1+4x2+x3+uy=100x1x2x3+[0]u
CONTROLABILIDAD
Ҩ=[BABA2B]
B=011
AB=-121210241011=315
A2B=-121210241-121210241011=7400528123011=4715
Ҩ=0341171515rank=(3)
detҨ=0+21+20-4+0+45=41-49=-8
ES COMPLETAMENTE CONTROLABLE
OBSERVABILIDAD
=CCACA2
C=[100]CA=1007400528123=[-121]
CA2=1007400528123=[740]
det=0+0+0-0+4+0=0-4=-4
rank=3 ∴
EL SISTEMA ES COMPLETAMENTE OBSERVABLE ES PLENO
METODO DE ACKERMANK=001Ҩ-1∅(A)
Ҩ-1=1detҨAdjҨT0341171515
Ҩ-1=-1815-35-15-75-1-45-20-4--321-4--4-3AdjҨ=-20-84-25-43174-3AdjҨT=
-20-2517-8-4443-3∅A=s+7s+4-2is+4+2i
s+7s2+4+2is+4-2is+16-4i2
s+7s2+8s+20
s3+8s2+20s
7s2+56s+140
∅A= s3+15s2+76s+140K=0015/225/8-17/811/2-1/2-1/2-3/83/8∅(A)
∅A=A3+15A2+76A+140I
A2=-121210241-121210241=1+4+2-2+2+4-1+0+1-2+2+04+1+02-8+24+616+12+128+3A2=7400528123
A2A=7400528123-121210241=-7+814+4710+45+82-8+24+616+12+128+3=118714132224011∅A=118714132224011+157400528123+76-121210241+140100010001
∅A=118714132224011+1056000753012018045+-761527615276015230476+140000140000140=K=0015/225/8-17/811/2-1/2-1/2-3/83/81702308316630432294524272
K=-12-38381702308316630432294524272
=-1702-4988+8828-2302-9128+15728-832-968+8168
K=[-37-32.548.5]