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SUMMARY:Block Scaled Diagonal Dominance for Applications in Control Theory
  and Optimisation - Aivar Sootla\, University of Oxford
DTSTART:20190221T140000Z
DTEND:20190221T150000Z
UID:TALK117778@talks.cam.ac.uk
CONTACT:Alberto Padoan
DESCRIPTION:In this talk\, we present a generalisation of scaled diagonall
 y dominant (SDD) matrices to block partitioned matrices as well as their a
 pplications in control theory and optimisation. Our basic definition of bl
 ock SDD matrices relies on a comparison matrix\, which is formed by comput
 ing particular norms of the blocks in the partitioning. If the comparison 
 matrix is stable then partitioned matrix is stable\, moreover\, there exis
 ts a block-diagonal solution to Lyapunov inequality and the H infinity Ric
 cati inequality. Furthermore\, these solutions can be constructed using th
 e combination of linear algebra and linear programming methods. We then fo
 cus on symmetric matrices and introduce a set of block factor-width-two ma
 trices\, which can also be seen as a generalisation of SDD matrices. Block
  factor-width-two matrices form a proper cone\, which is a subset of posit
 ive semidefinite matrices. We use these cones and their duals to build hie
 rarchies of inner and outer approximations of the cone of positive semidef
 inite matrices. The main feature of these cones is that they enable decomp
 osition of a large semidefinite constraint into a number of smaller semide
 finite constraints. As the main application of this class of matrices\, we
  envision large-scale semidefinite feasibility optimisation programs inclu
 ding the sum-of-squares (SOS) programs. We present numerical examples from
  SOS optimisation showcasing the strengths of this decomposition.
LOCATION:Cambridge University Engineering Department\, Lecture Theatre 6
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