The SDA Method for Numerical Solution of Lur'e Equations

TL;DR

This paper presents a new iterative numerical method for solving Lur'e matrix equations, which are important in control theory and model reduction, by leveraging deflating subspaces of matrix pencils.

Contribution

The paper introduces a linear convergence iterative scheme for Lur'e equations based on deflating subspaces, advancing numerical solutions in control applications.

Findings

The method converges linearly to the maximal solution.

It effectively computes solutions relevant to control and model reduction.

The approach is grounded in the theory of matrix pencils and deflating subspaces.

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.