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CATEGORIES:CUED Control Group Seminars
SUMMARY:Robustness and model reduction of dominant systems
- Alberto Padoan\, University of Cambridge
DTSTART;TZID=Europe/London:20181206T140000
DTEND;TZID=Europe/London:20181206T150000
UID:TALK112213AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/112213
DESCRIPTION:The talk presents a quantitative robustness analys
is framework geared towards the analysis and desig
n of systems that switch and oscillate. This is mo
tivated by the fact that\, while such phenomena ar
e ubiquitous in nature and in engineering\, model
reduction methods are not well developed for behav
iours away from equilibria. Our framework addresse
s this need by extending recent advances on p-domi
nance theory and p-dissipativity theory\, which ai
m at generalising stability theory and dissipativi
ty theory for the analysis of systems with low-dim
ensional attractors. We first prove a robust Nyqui
st theorem for p-dominance. Then we discuss a gene
ralisation of balanced truncation to linear domina
nt systems. From a mathematical viewpoint\, balanc
ed truncation requires the simultaneous diagonalis
ation of the reachability and observability gramia
ns\, which are positive definite matrices. Within
our framework\, the positivity constraint on the r
eachability and observability gramians is relaxed
to a fixed inertia constraint: one negative eigenv
alue is considered in the study of switches and tw
o negative eigenvalues are considered in the study
of oscillators. The proposed framework is illustr
ated by means of a textbook electro-mechanical exa
mple.
LOCATION:Cambridge University Engineering Department\, Lect
ure Theatre 6
CONTACT:Alberto Padoan
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