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Question 5.9: Similarity Transformations on State Equations PROBLEM: Given...

Similarity Transformations on State Equations

PROBLEM: Given the system represented in state space by Eqs. (5.73),

\dot{x} =\left[\begin{matrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ -2 & -5 & -7 \end{matrix} \right] x + \left[\begin{matrix} 0 \\ 0 \\ 1 \end{matrix} \right] u

 

y=\left[\begin{matrix} 1 & 0 & 0\end{matrix} \right] x

transform the system to a new set of state variables, z, where the new state variables are related to the original state variables, x,

z_{1} =2x_{1}

 

z_{2} =3x_{1} +2x_{2}

 

z_{3} =x_{1} +4x_{2} +5x_{3}
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