Nonlinear control

1. Necessary and sufficient conditions for controllability of homogeneous systems.
   Reference: Small-time local controllability of homogeneous systems.
2. A beautiful geometric formulation of stabilisation using linearisation..
   Reference: Geometric Jacobian linearization and LQR theory.
3. A feedback-invariant formulation for control-affine systems, and a manner, using jet bundle geometry, for generating variations of trajectories.
   Reference: Jet bundles and algebro-geometric characterisations for controllability of affine systems.
4. An example where the geometry of the system plays an interesting part in stabilisation.
   Reference: An example with interesting controllability and stabilisation properties.
5. The geometry of Jacobian linearisation and controllability of linearisation along a trajectory.
   Reference: Jacobian linearisation in a geometric setting.
6. Have you ever wondered what sliding mode control is? I did.
   Reference: Geometric sliding mode control: The linear and linearised theory.
7. A method, based on the Campbell-Baker-Hausdorff formula, for generating a large class of control variations.
   Reference: Local controllability of families of vector fields.
8. A general setting for control, and second-order controllability conditions within this framework.
   Reference: Geometric local controllability: second-order conditions.