Mikhailov Stability Criterion for Time-Delayed Systems

摘要

The valid and invalid application of the Mikhailov criterion to linear, time-invariant systems with time delays is discussed. The Mikhailov criterion is a graphical procedure which was initially developed to examine the stability of linear, time-invariant systems with no time delays. For these systems, there are two equivalent formulations of the criterion. Attempting to apply the second formulation when there are time delays in the systems can lead to erroneous results, as shown by an example. However, the first formulation remains valid for time-delayed systems of the retarded type, with the understanding that the Mikhailov curve need not necessarily always rotate in the counterclockwise direction for a stable system. At present, application of the Mikhailov criterion to neutral systems has not been justified.