Question: Assume that equation (9-25), Ackermann's formula for pole-assignment design, is the solution of (9-15). Based on this result, show that (9-48), Ackermann's formula for observer

Assume that equation (9-25), Ackermann's formula for pole-assignment design, is the solution of (9-15). Based on this result, show that (9-48), Ackermann's formula for observer design, is the solution of (9-46).

Equation 9-15a(z) = |zI = A + BK| = (z A)(z-A). (Z - A) - (9-15)

Equation 9-25K = [00 01][B AB.. A B A B a (A) (9-25)

Equation 9-48G = ag(A)| C CA CA-1 0 0 (9-48)

Equation 9-46a(z) = |zI - (A - GC)| = z" + an-12 zn-1 + +  + o (9-46)

a(z) = |zI = A + BK| = (z A)(z- A). (Z - ^) - (9-15)

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