Week 02
Linearizing Nonlinear Systems
I use the saved simulation video as a starting point to revisit state-space control, observers, and digital control.
What I connect in this unit
Linearization of a nonlinear system is a local approximation for small perturbations around an operating point. Jacobians supply first-order state and input sensitivities, while neglected higher-order terms limit the model's valid region.
Concept map
- Operating points
- Jacobians
- Small perturbations
- Model validity range
Technical anchor
Expand f(x,u) at (x0,u0) to obtain δx'=Aδx+Bδu, with A=∂f/∂x and B=∂f/∂u evaluated there. For an equilibrium linearization, first verify f(x0,u0)=0.
How I review it
Overlay the nonlinear function and its first-order approximation on both sides of the operating point, identify where their error grows, and avoid claims beyond that range.
Connection to the full course
Unit 2 of 12. This study sequence connects the system flow visible in the video with standard control topics; it is not a claim about lecture weeks.