The SDA Method for Numerical Solution of Lur'e Equations

2011/01/06 by Federico Poloni, Poloni, Federico, Timo Reis +1
Computer Science · Engineering · Physics and Astronomy · #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Matrix Theory and Algorithms #Model Reduction and Neural Networks #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1101.1231

openalex publication_date 2011/01/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce a numerical method for the numerical solution of the so-called Lur'e matrix equations that arise in balancing-related model reduction and linear-quadratic infinite time horizon optimal control. Based on the fact that the set of solutions can be characterized in terms of deflating subspaces of even matrix pencils, an iterative scheme is derived that converges linearly to the maximal solution.

Citations

• Dissipative dynamical systems Part II: Linear systems with quadratic supply rates

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