5 Feedback control theory

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Stability of feedback systems

Definition: The feedback system is input-output stable if e,u, y are bounding signals whenever exogenous inputs are bounded (all transfer functions are BIBO stable)

We could try to find every possible transfer function in a system, but we want a way to test stability without

Definition: the characteristic polynomial of the feedback system is \(\pi(s) := N_p N_c + D_p D_c\) is the denominator of the four transfer functions from (r,d) to (e,u)