Absolute
Stability Theory, mu Theory, and State-Space Verification of Frequency-Domain
Conditions: Connections and Implications for
Computation
Absolute
Stability Theory, mu Theory, and State-Space Verification of Frequency-Domain
Conditions: Connections and Implications for
Computation
Y. S. Chou, A. L. Tits and V. Balakrishnan
Technical Report TR 97-23, Institute for Systems Research, University of
Maryland, 1996
Abstract:
The main contribution of the paper is to show the
equivalence between the following two approaches for
obtaining sufficient conditions for the robust stability
of systems with structured uncertainties: (i) apply the
classical absolute stability theory with multipliers; (ii)
use modern mu theory, specifically, the mu upper
bound obtained by Fan, Tits and Doyle [IEEE TAC, Vol. 36,
25-38]. In particular, the relationship between the
stability multipliers used in absolute stability theory
and the scaling matrices used in the cited reference is
explicitly characterized. The development hinges on the
derivation of certain properties of a parameterized family
of complex LMIs (linear matrix inequalities), a result of
independent interest. The derivation also suggests a
general computational framework for checking the
feasibility of a broad class of frequency-dependent
conditions, and in particular yields a sequence of computable
"mixed-mu-norm upper bounds", defined with guaranteed convergence
from above to the supremum over the frequency of the aforementioned
mu-upper bound.
Download
PDF
Bibtex entry