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Decentralized computation for robust stability analysis of large state-space systems using Polya's theorem

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2 Author(s)
Kamyar, R. ; Dept. of Mech., Mater. & Aerosp. Eng., Illinois Inst. of Technol., Chicago, IL, USA ; Peet, M.M.

In this paper, we propose a parallel algorithm to solve large robust stability problems. We apply Polya's theorem to a parameter-dependent version of the Lyapunov inequality to obtain a set of coupled linear matrix inequality conditions. We show that a common implementation of a primal-dual interior-point method for solving this LMI has a block diagonal structure which is preserved at each iteration. By exploiting this property, we create a highly scalable cluster-computing implementation of our algorithm for robust stability analysis of systems with large state-space. Numerical tests confirm the scalability of the algorithm.

Published in:

American Control Conference (ACC), 2012

Date of Conference:

27-29 June 2012