How a feedback controller is designed to drive a nonlinear plant to an asymptotically stable equilibrium, and how the design changes depending on what the controller can measure. State feedback assumes every state variable is available, and is approached by linearizing about an operating point, transforming to controllable-like canonical forms, solving inequalities read off the system equations, compensating constant input delay, and recursive Lyapunov design for cascades with input-to-state-stable uncertainty. Output feedback uses only the measured outputs, which is harder because nonlinear systems lack uniform observability and observable linearization, so it relies on reduced-order and dual observers, growth conditions on the unmeasured states, adaptive/universal controllers when growth rates are unknown, and nonlinear internal models that recast robust output regulation as a stabilization problem.
A 10-page literature survey of how nonlinear control systems are driven to an equilibrium point by feedback. It sets up the state-space model x-dot = f(x,t) with a locally Lipschitz f and an equilibr…