Control Systems

The ratio of the Laplace transform of the output to the Laplace transform of the input, assuming zero initial conditions.

Because the Laplace-domain ratio of output to input is only well-defined for LTI systems with zero initial conditions; otherwise extra terms from initial energy appear.

Their transfer functions multiply: the overall transfer function is the product G1(s)·G2(s).

Their transfer functions add (or subtract, per the summing-junction signs): G1(s) ± G2(s).

T(s) = G/(1 + GH). For positive feedback it becomes G/(1 − GH).

The loop gain is the product GH, the gain around the entire loop with the loop opened; the term 1 + GH is the return difference.