Find the state vector via the formal solution approach ( dot mathbf x left begin array ccc 1 0 0 0 1 0 1 2 3 end array ight mathbf x left begin array l 0 0 frac 1 4 end array ight u, u e t 3 sin t, quad mathbf x (0) left begin array l 0 1 0 end array ight )

Question: Find the state vector via the formal-solution approach. (dot{mathbf{x}}=left[begin{array}{ccc}1 & 0 & 0 0 & 1 & 0 -1 & -2 & -3end{array}

Find the state vector via the formal-solution approach.

$\dot{\mathbf{x}}=\left[\begin{array}{ccc}1 & 0 & 0 \\ 0 & 1 & 0 \\ -1 & -2 & -3\end{array}\right] \mathbf{x}+\left[\begin{array}{l}0 \\ 0 \\ \frac{1}{4}\end{array}\right] u, u=e^{-t / 3} \sin t, \quad \mathbf{x}(0)=\left\{\begin{array}{l}0 \\ 1 \\ 0\end{array}\right\}$

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To find the state vector using the formal solution approach well first solve the homogeneous equation dotmathbfx mathbfAmathbfx where mathbfA is the coefficient matrix and then add the particular solu... View full answer

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