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# Dynamic model of an inverted pendulum (part 6)

This page is part of a serie of articles on how to write the model of an inverted pendulum. We strongly recommand to read the previous pages for a better understanding.

## State space representation

Based on the previous result, it is now possible to write the state space model of the system. Let's define $$X$$ the state of the system:

$$X=\begin{pmatrix} x_1 \\ \Theta_2 \\ \dot{x_1} \\ \dot{\Theta_2} \end{pmatrix}$$

The state space representation is:

$$\dot{X}=\begin{pmatrix} \dot{x_1} \\ \dot{\Theta_2} \\ \left[A^{-1}.B\right] \end{pmatrix}$$