Leap Effects among Robust Root Trajectories
The set of closed-loop eigenvalues in the presence of the worst uncertainty is termed robust root trajectory. The open-loop gain or some other system parameter is changed monotonically. The admissible uncertainties are considered along their envelope. The worst uncertainty is denoted as that one where a specified function of the eigenvalues leads to the maximum disadvantageous effect on the closed-loop stability performance. Leaps in the dynamic behavior occur even for infinitesimally small changes in the gain parameter when system uncertainties are considered that are located especially at their bounds.
continuous-time and discrete-time linear time-invariant systems generalized vector norm root loci uncertainty envelope unstructured uncertainty