In *Control theory from the geometric viewpoint* by Agrachev and Sachkov, the authors mention the concept of control-affine (affine in control $u_i$) systems:
$$\dot{x} = (f_0 + \sum_{i=1}^{m} u_i f_i)x $$

I would like to have some sources on the topic, preferably a survey of the field, overview or a textbook. My primary questions are:

- What are main results?
- When can a CA system be linearized?
- What are specific criteria for controllability, observability, optimality of control?
- Other generalizations of results for linear systems.
- Some good examples.