A software package for the solution of generalized algebraic Riccati equations. The generalized eigenvalue problem provides a powerful framework for the solution of quite general forms of algebraic Riccati equations arising in both continuous-and discrete-time applications. This general form is derived from control and filtering problems for systems in generalized (or implicit or descriptor) state space form. A software package called RICPACK has been developed to solve such Riccati equations by means of deflating subspaces for certain associated Hamiltonian or symplectic generalized eigenvalue problems. Utilizing an embedding technique, the package also calculates a solution even in cases where all cost or covariance matrices are singular or ill-conditioned with respect to inversion. Cross-weighting or correlated noise is handled directly. Both system-theoretic balancing and Ward’s balancing for the generalized eigenvalue problem are available to improve condition and accuracy. Condition estimates for the solution are also calculated. An iterative improvement calculation via Sylvester equations is available and can be used to generate new solutions for ”small” changes in the model. An interactive driver with numerous convenient default options has also been written. A numerical example is shown.

References in zbMATH (referenced in 65 articles )

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  1. Kirrinnis, P.: Fast algorithms for the Sylvester equation (AX-XB^T=C) (2001)
  2. Hansson, A.; Hagander, P.: How to decompose semi-definite discrete-time algebraic Riccati equations (1999)
  3. Kim, Sang Woo; Park, Poo Gyeon: Matrix bounds of the discrete ARE solution (1999)
  4. Sun, Ji-guang: Sensitivity analysis of the discrete-time algebraic Riccati equation (1998)
  5. Varga, A.: Computation of normalized coprime factorizations of rational matrices (1998)
  6. Benner, Peter; Faßbender, Heike: An implicitly restarted symplectic Lanczos method for the Hamiltonian eigenvalue problem (1997)
  7. Benner, Peter; Mehrmann, Volker; Xu, Hongguo: A new method for computing the stable invariant subspace of a real Hamiltonian matrix (1997)
  8. Sun, Ji-guang: Backward error for the discrete-time algebraic Riccati equation (1997)
  9. Zečević, Aleksandar I.; Šiljak, Dragoslav D.: Solution of Lyapunov and Riccati equations in a multiprocessor environment (1997)
  10. Chattergy, Rahul; Syrmos, Vassilis L.; Misra, Pradeep: Finite modeling of parabolic equations using Galerkin methods and inverse matrix approximations (1996)
  11. Katayama, Tohru: ((J,J’))-spectral factorization and conjugation for discrete-time descriptor system (1996)
  12. Vandenberghe, Lieven; Boyd, Stephen: A primal-dual potential reduction method for problems involving matrix inequalities (1995)
  13. Clements, D. J.: Rational spectral factorization using state-space methods (1993)
  14. Aliev, F. A.; Bordyug, B. A.; Larin, V. B.: Discrete generalized algebraic Riccati equations and polynomial matrix factorization (1992)
  15. Chen, Y. H.: Decentralized robust control design for large-scale systems: The uncertainty is time-varying (1992)
  16. Kenney, Charles; Laub, Alan J.; Wette, Matt: Error bounds for Newton refinement of solutions to algebraic Riccati equations (1990)
  17. Ballesteros, F.; de Arriaga, F.: Optimal control of power systems and the Riccati equation (1989)
  18. Clements, D. J.; Glover, K.: Spectral factorization via Hermitian pencils (1989)
  19. Jódar, Lucas; Navarro, E.: On the generalized Riccati matrix differential equation. Exact, approximate solutions and error estimate (1989)
  20. Kenney, Charles; Laub, Alan J.; Jonckheere, Edmond A.: Positive and negative solutions of dual Riccati equations by matrix sign function iteration (1989)