Robustness and Stability Margins in Linear Time-Invariant SISO Feedback Control Systems

This paper discusses the link between the stability margins and the stability robustness of linear time-invariant SISO feedback control systems. For this purpose, a system which implements the unitary feedback control for a number of variables (outputs) is considered. In this case, obviously, the plot of the loop-frequency-response function G(jω) and, consequently, the stability margins depend on the particular output considered. Naturally, applying the Nyquist criterion, the system turns out to be stable or unstable no matter which G(jω) (that is which output) is considered. Consequently, since, in general, the plots of various G(jω)'s present different distances from the critical point, it means that this is an on-off stability criterion. In other words, what can be said is that the Nyquist criterion only states whether the system is stable or not, but it doesn't supply exhaustive information on stability as often assumed in many text books and papers, especially in the ones dealing with automatic control in aerospace. In particular, they correlate the stability margins to robustness and not only to overshoot as they should.