Consider the state space model with state equation
\frac{d\mathbf{x}}{dt} = \begin{bmatrix}-1 & 1 \3 & 2\end{bmatrix}\mathbf{x}(t) + \begin{bmatrix} 1\-1\end{bmatrix}u(t).
If state feedback u(t) = -\begin{bmatrix} K_1 & K_2 \end{bmatrix}\mathbf{x}(t) is used (and the reference is zero) then the closed-loop state equation is:

Question

Consider the state space model with state equation 
  \frac{d\mathbf{x}}{dt} = \begin{bmatrix}-1 & 1 \3 & 2\end{bmatrix}\mathbf{x}(t) + \begin{bmatrix} 1\-1\end{bmatrix}u(t). 
 If state feedback   u(t) = -\begin{bmatrix} K_1 & K_2 \end{bmatrix}\mathbf{x}(t)  is used (and the reference is zero) then the closed-loop state equation is:

Answer

\frac{d\mathbf{x}}{dt} = \begin{bmatrix} -1+K_1 & 1+K_2\3-K_1 & 2-K_2\end{bmatrix}\mathbf{x}(t)

Answer

\frac{d\mathbf{x}}{dt} = \begin{bmatrix} -1-K_1 & 1-K_2\3+K_1 & 2+K_2\end{bmatrix}\mathbf{x}(t)

Answer

\frac{d\mathbf{x}}{dt} = \begin{bmatrix} -1+K_1 & 1-K_1\3+K_2 & 2-K_2\end{bmatrix}\mathbf{x}(t)

Crowdly

Consider the state space model with state equation \frac{d\mathbf{x}}{dt} = \...

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