The SDA Method for Numerical Solution of Lur'e Equations
arXiv:1101.12314 citationsh-index: 24
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Provides a new numerical tool for solving a specific class of matrix equations relevant to control theory and model reduction.
The paper introduces a numerical method for solving Lur'e matrix equations, which arise in model reduction and optimal control. The method converges linearly to the maximal solution.
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.