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The differential Sylvester equation and its symmetric version, the differential Lyapunov equation, appear in different fields of applied mathematics like control theory, system theory, and model order reduction.
A direct solution to the linear variance equation of a time-invariant linear system
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Introduction to Mathematical Systems Theory
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On properties of Sylvester and Lyapunov operators
M. Konstantinov, V. Mehrmann, and P. Petkov · 2000
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Funktionalanalysis
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Optimal Control: An Introduction
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Banach algebras and the general theory of ∗ * -algebras. Vol. 2
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Matrix Riccati Equations in Control and Systems Theory
H. Abou-Kandil, G. Freiling, V. Ionescu, and G. Jank · 2003
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Perturbation Theory for Matrix Equations
M. M. Konstantinov, D. W. Gu, V. Mehrmann, and P. H. Petkov · 2003
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BDF methods for large-scale differential Riccati equations
P. Benner and H. Mena · 2004
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Approximation of Large-Scale Dynamical Systems
A. C. Antoulas · 2005
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A semi-discretized heat transfer model for optimal cooling of steel profiles
P. Benner and J. Saak · 2005
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Numerical Solution of Differential Riccati Equations Arising in Optimal Control of Partial Differential Equations
H. Mena · 2007
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On the benefits of the L D L T LDL^{T} factorization for large-scale differential matrix equation solvers
N. Lang, H. Mena, and J. Saak · 2015
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Towards practical implementations of balanced truncation for LTV systems
N. Lang, J. Saak, and T. Stykel · 2015
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Low-rank second-order splitting of large-scale differential Riccati equations
T. Stillfjord · 2015
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Solving differential matrix equations using Parareal
M. Köhler, N. Lang, and J. Saak · 2016
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Balanced truncation model reduction for linear time-varying systems
N. Lang, J. Saak, and T. Stykel · 2016
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Low rank approximate solutions to large-scale differential matrix Riccati equations
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Functions of matrices: Theory and computation
N. J. Higham · 2008
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Solution of the matrix eigenvalue problem V A + A ∗ V = μ V VA+A^{*}V=\mu V with applications to the study of free linear dynamical systems
L. Kohaupt · 2008
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On the ADI method for Sylvester equations
P. Benner, R.-C. Li, and N. Truhar · 2009
Cited alongside, same era.
Rosenbrock methods for solving Riccati differential equations
P. Benner and H. Mena · 2013
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Finite-time stability and control
F. Amato, R. Ambrosino, M. Ariola, C. Cosentino, and G. De Tommasi · 2014
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Decoupling and Optimization of Differential-Algebraic Equations with Application in Flow Control
J. Heiland · 2014
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Y. Güldoǧan, M. Hached, K. Jbilou, and M. Kurulay · 2017
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Numerical solutions to large-scale differential Lyapunov matrix equations
M. Hached and K. Jbilou · 2017
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A structure preserving Krylov subspace method for large scale differential Riccati equations
A. Koskela and H. Mena · 2017
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Numerical Methods for Large-Scale Linear Time-Varying Control Systems and related Differential Matrix Equations
N. Lang · 2017
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LTV-BT for MATLAB
N. Lang, J. Saak, and T. Stykel · 2017
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Approximate solutions to large nonsymmetric differential Riccati problems
M. Hached and K. Jbilou · 2018
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