状態空間 (制御理論)
[ x 1 ̇ ( t ) x 2 ̇ ( t ) ] = [ 0 1 − k 2 m − k 1 m ] [ x 1 ( t ) x 2 ( t ) ] + [ 0 1 m ] u ( t ) {\displaystyle \left[{\begin{matrix}\mathbf {\dot {x_{1}}} (t)\\\mathbf {\dot {x_{2}}} (t)\end{matrix}}\right]=\left[{\begin{matrix}0&1\\-{\frac {k_{2}}{m}}&-{\frac {k_{1}}{m}}\end{matrix}}\right]\left[{\begin{matrix}\mathbf {x_{1}} (t)\\\mathbf {x_{2}} (t)\end{matrix}}\right]+\left[{\begin{matrix}0\\{\frac {1}{m}}\end{matrix}}\right]\mathbf {u} (t)} y ( t ) = [ 1 0 ] [ x 1 ( t ) x 2 ( t ) ] {\displaystyle \mathbf {y} (t)=\left[{\begin{matrix}1&0\end{matrix}}\right]\left[{\begin{matrix}\mathbf {x_{1}} (t)\\\mathbf {x_{2}} (t)\end{matrix}}\right]}
ここで、
x 1 ( t ) {\displaystyle x_{1}(t)} は物体の位置を表す。