LYAPACK A MATLAB Toolbox for Large Lyapunov and Riccati Equations, Model Reduction Problems, and Linear–Quadratic Optimal Control Problems Users ’ Guide (Version 1.0). Control theory is one of the most rapidly developing disciplines of mathematics and engineering in the second half of the 20th century. In the past decade, implementations of numerically robust algorithms for many types of dense problems in control theory have become available in software packages, such as SLICOT [7]. However, little research has been done on efficient numerical methods for control problems related to large sparse or structured dynamical systems before 1990. In the last few years, quite a number of approaches for several types of large control problems have been proposed, but, at present, it is often not clear, which of them are the more promising ones. It is needless to say that there is little software for large control problems available. In this situation, the author took the opportunity to implement the software package LYAPACK (“Lyapunov Package”), which covers one particular approach to a class of large problems in control theory. An efficient ADI-based solver for large Lyapunov equations is the “workhorse ” of LYAPACK, which also contains implementations of two model reduction methods and modifications of the Newton method for the solution of large Riccati equations and linear-quadratic optimal control problems. ..

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  1. Abidi, O.; Jbilou, K.: Balanced truncation-rational Krylov methods for model reduction in large scale dynamical systems (2018)
  2. Addam, Mohamed; Elbouyahyaoui, Lakhdar; Heyouni, Mohammed: On Hessenberg type methods for low-rank Lyapunov matrix equations (2018)
  3. Barkouki, H.; Bentbib, A. H.; Heyouni, Mohammed; Jbilou, K.: An extended nonsymmetric block Lanczos method for model reduction in large scale dynamical systems (2018)
  4. Benner, Peter; Bujanović, Zvonimir; Kürschner, Patrick; Saak, Jens: RADI: a low-rank ADI-type algorithm for large scale algebraic Riccati equations (2018)
  5. Benner, Peter; Mena, Hermann: Numerical solution of the infinite-dimensional LQR problem and the associated Riccati differential equations (2018)
  6. Bentbib, A. H.; Jbilou, Khalide; Kaouane, Yassine: A computational global tangential Krylov subspace method for model reduction of large-scale MIMO dynamical systems (2018)
  7. Mena, Hermann; Ostermann, Alexander; Pfurtscheller, Lena-Maria; Piazzola, Chiara: Numerical low-rank approximation of matrix differential equations (2018)
  8. Barkouki, H.; Bentbib, A. H.; Jbilou, K.: A matrix rational Lanczos method for model reduction in large-scale first- and second-order dynamical systems. (2017)
  9. Bentbib, Abdeslem Hafid; Jbilou, Khalide; Sadek, El Mostafa: On some extended block Krylov based methods for large scale nonsymmetric Stein matrix equations (2017)
  10. Barkouki, Houda; Bentbib, A. H.; Jbilou, K.: An adaptive rational block Lanczos-type algorithm for model reduction of large scale dynamical systems (2016)
  11. Bouhamidi, A.; Hached, M.; Jbilou, K.: A preconditioned block Arnoldi method for large scale Lyapunov and algebraic Riccati equations (2016)
  12. Braun, Philipp; Hernández, Erwin; Kalise, Dante: Reduced-order LQG control of a Timoshenko beam model (2016)
  13. Massoudi, Arash; Opmeer, Mark R.; Reis, Timo: Analysis of an iteration method for the algebraic Riccati equation (2016)
  14. Mehrmann, Volker; Poloni, Federico: An inverse-free ADI algorithm for computing Lagrangian invariant subspaces. (2016)
  15. Simoncini, V.: Computational methods for linear matrix equations (2016)
  16. Bänsch, Eberhard; Benner, Peter; Saak, Jens; Weichelt, Heiko K.: Riccati-based boundary feedback stabilization of incompressible Navier-Stokes flows (2015)
  17. Lang, Norman; Mena, Hermann; Saak, Jens: On the benefits of the (L D L^T) factorization for large-scale differential matrix equation solvers (2015)
  18. Lin, Yiding; Simoncini, Valeria: A new subspace iteration method for the algebraic Riccati equation. (2015)
  19. Benner, P.; Saak, J.; Schieweck, F.; Skrzypacz, P.; Weichelt, H. K.: A non-conforming composite quadrilateral finite element pair for feedback stabilization of the Stokes equations (2014)
  20. Druskin, V.; Simoncini, V.; Zaslavsky, M.: Adaptive tangential interpolation in rational Krylov subspaces for MIMO dynamical systems (2014)

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