Control theory

Control theory studies dynamical input-output systems, feedback, stability, and response.

For a linear time-invariant system with zero initial data, the transfer function is the Laplace-domain ratio $G(s)=Y(s)/F(s)$. A rational causal system is BIBO stable when all poles lie in the open left half-plane.

Let $L$ be the open-loop transfer function. The winding of its Nyquist plot around $-1$, together with the number of unstable open-loop poles, determines the number of unstable zeros of $1+L$, which are the closed-loop poles.