A Stability Criterion Based on the Return Difference

A simple stability criterion based on the return difference is established: Draw the phase plot of the return difference 1 + GH(jω) vs. ω, if and only if θ(∞)-∞(0) = (n + 2m) π/2, the system is stable, where n is the number of poles of GH(jω) at the origin and m is that in the right half plane; θ(∞) and θ(0) are the phase angles of "1 + GH(iω)" at ω = ∞ and at ∞ = 0, respectively.