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. Hamadi, M. A.; Jbilou, K.; Ratnani, A.: A model reduction method in large scale dynamical systems using an extended-rational block Arnoldi method (2022)
  2. Huang, Guang-Xin; Chen, Qi-Xing; Yin, Feng: Preconditioned TBiCOR and TCORS algorithms for solving the Sylvester tensor equation (2022)
  3. Saberi-Movahed, Farid; Tajaddini, Azita; Heyouni, Mohammed; Elbouyahyaoui, Lakhdar: Some iterative approaches for Sylvester tensor equations. II: A tensor format of simpler variant of GCRO-based methods (2022)
  4. Zulfiqar, Umair; Sreeram, Victor; Ahmad, Mian Ilyas; Du, Xin: Frequency-weighted (\mathcalH_2)-optimal model order reduction via oblique projection (2022)
  5. Li, Dongping; Zhang, Xiuying; Liu, Renyun: Exponential integrators for large-scale stiff Riccati differential equations (2021)
  6. Benner, Peter; Heinkenschloss, Matthias; Saak, Jens; Weichelt, Heiko K.: Efficient solution of large-scale algebraic Riccati equations associated with index-2 DAEs via the inexact low-rank Newton-ADI method (2020)
  7. Bentbib, A. H.; El-Halouy, S.; Sadek, El M.: Krylov subspace projection method for Sylvester tensor equation with low rank right-hand side (2020)
  8. Kaouane, Y.: A tangential method for the balanced truncation in model reduction (2020)
  9. Sadek, El. Mostafa; Bentbib, Abdeslem Hafid; Sadek, Lakhlifa; Talibi Alaoui, Hamad: Global extended Krylov subspace methods for large-scale differential Sylvester matrix equations (2020)
  10. Sadek, Lakhlifa; Talibi, Alaoui Hamad: The extended block Arnoldi method for solving generalized differential Sylvester equations (2020)
  11. Xie, Yajun; Yin, Minhua; Ren, Limin: Krylov subspace methods of Hessenberg based for algebraic Riccati equation (2020)
  12. Bentbib, A. H.; Jbilou, K.; Kaouane, Y.: An adaptive block tangential method for multi-input multi-output dynamical systems (2019)
  13. Jbilou, K.; Kaouane, Y.: A tangential block Lanczos method for model reduction of large-scale first and second order dynamical systems (2019)
  14. Pulch, Roland: Stability preservation in Galerkin-type projection-based model order reduction (2019)
  15. Pulch, Roland; Narayan, Akil: Balanced truncation for model order reduction of linear dynamical systems with quadratic outputs (2019)
  16. Abidi, O.; Jbilou, K.: Balanced truncation-rational Krylov methods for model reduction in large scale dynamical systems (2018)
  17. Addam, Mohamed; Elbouyahyaoui, Lakhdar; Heyouni, Mohammed: On Hessenberg type methods for low-rank Lyapunov matrix equations (2018)
  18. Barkouki, H.; Bentbib, A. H.; Heyouni, Mohammed; Jbilou, K.: An extended nonsymmetric block Lanczos method for model reduction in large scale dynamical systems (2018)
  19. Benner, Peter; Bujanović, Zvonimir; Kürschner, Patrick; Saak, Jens: RADI: a low-rank ADI-type algorithm for large scale algebraic Riccati equations (2018)
  20. Benner, Peter; Mena, Hermann: Numerical solution of the infinite-dimensional LQR problem and the associated Riccati differential equations (2018)

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