What are the main techniques for nonlinear control system design?

Nonlinear control techniques include: Lyapunov-based design (prove stability by finding Lyapunov function, design control to make its derivative negative), feedback linearization (cancel nonlinearities using measured states, apply linear control), sliding mode control (force trajectory onto sliding surface, robust to uncertainties), backstepping (recursive design for cascaded systems), and gain scheduling (interpolate between linear controllers designed at operating points). Model predictive control handles nonlinear models directly. Analysis uses describing functions, phase plane, and center manifold theory.