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Where

Mathinline

body	A

,

Mathinline

body	B

,

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body	C

, and

Mathinline

body	D

are matrices.

Example:

Say we have a system that can be described with

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body	\ddot{\theta} = k\dot{\theta} + n\theta + u(t)

and

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body	y(t) = \theta

To model this, let

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body	x = \left[_{\dot{\theta}}^{\theta}\right]

.

We need to find matrices

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body	A

and

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body	B

such that

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body	\left[_\ddot{\theta}^\dot{\theta}\right] = A\left[_\dot{\theta}^\theta\right] + Bu(t)

.

We find that

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body	A = \begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix}

.

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