Robot Arm

Robot Arm is a case study from [1] for input-to-state stability study.

Dynamics

$$\left \{ \begin{array}{l} \dot x_0 = x_2 \\ \dot x_1 = x_3 \\ \dot x_2 = \frac{-2 x_1 x_2 x_3 – 2 x_0-2 x_2+4}{x_1^2+1}\\ \dot x_3 = x_1 x_2^2 – x_1 – x_3 +1\end{array} \right.$$

Properties

Please see details in the attached file

Reachtube generated by C2E2

Link to the example file: Robot.hyxml

reference:

[1] Angeli, David, Eduardo D. Sontag, and Yuan Wang. “A characterization of integral input-to-state stability.” Automatic Control, IEEE Transactions on 45, no. 6 (2000): 1082-1097.