Abstract
We propose an algorithm for the numerical solution of the Lur'e equations in the bounded real and positive real lemma for stable systems. The algorithm provides approximate solutions in lowrank factored form. We prove that the sequence of approximate solutions is monotonically increasing with respect to definiteness. If the shift parameters are chosen appropriately, the sequence is proven to be convergent to the minimal solution of the Lur'e equations. The algorithm is based on the ideas of the recently developed ADI iteration for algebraic Riccati equations. In particular, the matrices obtained in our iteration express the optimal cost in a certain projected optimal control problem.
Original language  English 

Pages (fromto)  431458 
Number of pages  28 
Journal  Numerische Mathematik 
Volume  135 
Issue number  2 
Early online date  29 Apr 2016 
DOIs  
Publication status  Published  1 Feb 2017 
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Profiles

Mark Opmeer
 Department of Mathematical Sciences  Senior Lecturer
 EPSRC Centre for Doctoral Training in Statistical Applied Mathematics (SAMBa)
Person: Research & Teaching