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SUMMARY:Robustness and model reduction of dominant systems - Alberto Padoa
 n\, University of Cambridge
DTSTART:20181206T140000Z
DTEND:20181206T150000Z
UID:TALK112213@talks.cam.ac.uk
CONTACT:Alberto Padoan
DESCRIPTION:The talk presents a quantitative robustness analysis framework
  geared towards the analysis and design of systems that switch and oscilla
 te. This is motivated by the fact that\, while such phenomena are ubiquito
 us in nature and in engineering\, model reduction methods are not well dev
 eloped for behaviours away from equilibria. Our framework addresses this n
 eed by extending recent advances on p-dominance theory and p-dissipativity
  theory\, which aim at generalising stability theory and dissipativity the
 ory for the analysis of systems with low-dimensional attractors. We first 
 prove a robust Nyquist theorem for p-dominance. Then we discuss a generali
 sation of balanced truncation to linear dominant systems. From a mathemati
 cal viewpoint\, balanced truncation requires the simultaneous diagonalisat
 ion of the reachability and observability gramians\, which are positive de
 finite matrices. Within our framework\, the positivity constraint on the r
 eachability and observability gramians is relaxed to a fixed inertia const
 raint: one negative eigenvalue is considered in the study of switches and 
 two negative eigenvalues are considered in the study of oscillators. The p
 roposed framework is illustrated by means of a textbook electro-mechanical
  example.
LOCATION:Cambridge University Engineering Department\, Lecture Theatre 6
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