Ma. Rotea et al., SYSTEMS WITH STRUCTURED UNCERTAINTY - RELATIONS BETWEEN QUADRATIC ANDROBUST STABILITY, IEEE transactions on automatic control, 38(5), 1993, pp. 799-803
Citations number
12
Categorie Soggetti
Controlo Theory & Cybernetics","Computer Applications & Cybernetics","Engineering, Eletrical & Electronic
The purpose of this note is to investigate the relation between the no
tions of robust stability and quadratic stability for uncertain system
s with structured uncertainty due to both real and complex parameter v
ariations. We present examples which demonstrate that for systems cont
aining at least two uncertain blocks, the notions of robust stability
for complex parameter variations and quadratic stability for real para
meter variations are not equivalent; in fact neither implies the other
. A byproduct of these examples is that, for this class of systems, qu
adratic stability for real perturbations need not imply quadratic stab
ility for complex perturbations. This is in stark contrast with the si
tuation in the case of unstructured uncertainty, for which it is known
that quadratic stability for either real or complex perturbations is
equivalent to robust stability for complex perturbations, and thus equ
ivalent to a small gain condition on the transfer matrix that the pert
urbation experiences.