The document discusses nonlinear systems and how they are often approximated as linear models within an acceptable operating range. It then describes how the nonlinear differential equations for a pendulum and inverted pendulum can be linearized by assuming small angles to develop linear models and transfer functions to represent the system response. The inverted pendulum is provided as an example of a commonly studied nonlinear control problem where the system is open-loop unstable unless a suitable force is applied to balance it.

1. ME 330 Control Systems SP 2011 Lecture 8