Mikhailov Stability Criterion for Time-delayed Systems

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 developed to examine the stability of linear, time-invariant systems with no time delays. Two equivalent formulations of the criterion are discussed. Results indicate that the first formulation remains valid for time-delayed systems of the retared type, with the understanding that the Mikhailov curve need not necessarily always rotate in the counterclockwise direction for a stable system. Erroneous results in the second formulation are formed when there are time delays in the systems.