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arXiv · 1810.05033

Lyapunov matrix equation $A^HX+XA+C=O_r$ with $A$ a Jordan matrix

Dan Comănescu
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Abstract

A Lyapunov matrix equation can be converted, by using the Jordan decomposition theorem for matrices, into an equivalent Lyapunov matrix equation where the matrix is a Jordan matrix. The Lyapunov matrix equation with Jordan matrix can be reduced to a system of Sylvester-Lyapunov type matrix equations. We completely solve the Sylvester-Lyapunov type matrix equations corresponding to the Jordan block matrices of the initial matrix.

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Dan Comănescu. 2018-10-10. Lyapunov matrix equation $A^HX+XA+C=O_r$ with $A$ a Jordan matrix. https://arxiv.org/abs/1810.05033

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