Question: Consider the following discrete-time system in state-space form: [ left[begin{array}{c} x_{1}(k+1) x_{2}(k+1) end{array}ight]=left[begin{array}{cc} 0 & -1 0 & -1 end{array}ight]left[begin{array}{l} x_{1}(k) x_{2}(k)
Consider the following discrete-time system in state-space form:
\[
\left[\begin{array}{c}
x_{1}(k+1) \\
x_{2}(k+1)
\end{array}ight]=\left[\begin{array}{cc}
0 & -1 \\
0 & -1
\end{array}ight]\left[\begin{array}{l}
x_{1}(k) \\
x_{2}(k)
\end{array}ight]+\left[\begin{array}{c}
0 \\
10
\end{array}ight] u(k) .
\]
Use state feedback to relocate all of the system's poles to 0.5.
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