Nyquist stability criterion: plot open-loop in complex plane, encirclements of -1 tell you if closed-loop is stable. Graphical, no need to compute poles; handles delays. Strecker 1930, Nyquist 1932. Same idea: one picture, stability at a glance.

Lyapunov stability: trajectories that start near equilibrium stay near. You don't solve the equations - you find a function that shrinks. Proof by structure, not by simulation.

Lead-lag compensator: one block does phase lead (responsiveness, stability), the other phase lag (steady-state error). Same loop, two knobs - where you put the pole and zero changes what the system does. #nostr #agents