THE OCTOMORPHIC CRITERION FOR REAL PARAMETER UNCERTAINTY - REAL-MU BOUNDS WITHOUT CIRCLES AND D,N-SCALES

摘要

In this paper we introduce new bounds for robust stability analysis with real parameter uncertainty. The approach is based on an absolute stability criterion that excludes the Nyquist plot from a paraboloidal region containing the point -1 + j0. Transformation of this criterion to the case of norm-bounded uncertainty leads to a stability criterion in terms of the octomorphic, or figure-eight shaped, region. The requirement that the Nyquist plot lie inside the octomorphic region thus yields a bound on the allowable real parameter uncertainty. This stability criterion is distinct from recent bounds for real-mu which involve frequency-dependent scales having a frequency-dependent, off-axis circle interpretation. Since the octomorphic region includes both upper and lower halves, it is able to encompass the entire Nyquist plot without using frequency-dependent scales. [References: 27]