Question

7. Determine conditions on $b_1$, $b_2$, $c_1$ and $c_2$ such that the following system is both controllable and observable $A = \begin{bmatrix} 1 & 1\\ 0 & 1 \end{bmatrix}$, $B = \begin{bmatrix} b_1\\ b_2 \end{bmatrix}$, $C = \begin{bmatrix} c_1 & c_2 \end{bmatrix}$

          7. Determine conditions on $b_1$, $b_2$, $c_1$ and $c_2$ such that the following system is both controllable
and observable
$A = \begin{bmatrix} 1 & 1\\ 0 & 1 \end{bmatrix}$,
$B = \begin{bmatrix} b_1\\ b_2 \end{bmatrix}$,
$C = \begin{bmatrix} c_1 & c_2 \end{bmatrix}$

7. Determine conditions on b1, b2, c1 and c2 such that the following system is both controllable
and observable
A =
< b m a t r i x >,
B =
< b m a t r i x >,
C =
< b m a t r i x >

Added by Catalina G.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

11/26/2022

Step 1

Step 1: The controllability matrix is given by \[W_c = [B, AB] = \begin{bmatrix} b_1 & b_2 \\ b_1 & b_2 \\ \end{bmatrix}\] Show more…

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Determine conditions on b_(1),b_(2),c_(1) and c_(2) such that the following system is both controllable and observable A=[[1,1],[0,1]],B=[[b_(1)],[b_(2)]],C=[[c_(1),c_(2)]] 7.Determine conditions on b,bz,c and c such that the following system is both controllable and observable 4=[] B C=[c1c]