Fixed-gain linear controller applied to nonlinear dynamics

The application of a fixed-gain linear controller to nonlinear dynamics can lead to suboptimal or even unstable behavior. This is because the linear controller is designed based on the assumption that the system dynamics are linear, and may not be able to account for the nonlinearities present in the actual system.

However, in some cases, a linear controller may still be effective if the nonlinearities are relatively small and the controller gain is carefully chosen to provide adequate stability margins. Additionally, some techniques such as linearization or feedback linearization can be used to approximate the nonlinear system dynamics with a linear model, which can then be controlled using a linear controller.