Question: Find decoupled state equations for the system described as [ begin{aligned} {left[begin{array}{l} dot{x}_{1} dot{x}_{2} end{array}ight] } & =left[begin{array}{rr} 0 & 1 -6 &
Find decoupled state equations for the system described as
\[
\begin{aligned}
{\left[\begin{array}{l}
\dot{x}_{1} \\
\dot{x}_{2}
\end{array}ight] } & =\left[\begin{array}{rr}
0 & 1 \\
-6 & -5
\end{array}ight]\left[\begin{array}{l}
x_{1} \\
x_{2}
\end{array}ight]+\left[\begin{array}{ll}
1 & 0 \\
0 & 1
\end{array}ight]\left[\begin{array}{l}
u_{1} \\
u_{2}
\end{array}ight] \\
y & =\left[\begin{array}{ll}
0 & 1
\end{array}ight]\left[\begin{array}{l}
x_{1} \\
x_{2}
\end{array}ight]
\end{aligned}
\]
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This system of equations is a statespace representation of a dynamic system often used in control theory where x1 and x2 are state variables and u1 an... View full answer
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