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
IEEE Trans. Aut. Contr., AC-44(5):906-913,
May 1999
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, based on which bisection schemes can be
devised to reliably compute several quantities of interest
for robust control.
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