The Fortran routines for *model and controller reduction* can deal with both stable and unstable continuous- and discrete-time linear multivariable systems using additive or relative error model reduction methods. The main features and options are:

- several model reduction approaches based on additive or relative error model reduction methods:
*Balance & Truncate*(B&T)*Singular perturbation approximation*(SPA)*Hankel norm approximation*(HNA)*Balanced stochastic truncation*(BST), in conjunction with B&T and SPA*Frequency-weighted reduction*in conjunction with B&T, SPA, and HNA- several controller reduction approaches:
*Frequency-weighted reduction*with special stability/performance enforcing weights*Coprime factorization based reduction*of state feedback and observer based controllers, in conjunction with B&T and SPA- enhanced accuracy algorithms using
*square-root*and*balancing-free*approaches to model reduction - reduction of unstable systems by combining the methods for stable systems with stable coprime factorization or additive spectral decomposition techniques
- availability of both, fully documented drivers and computational routines
- the use of structure exploiting algorithms and dedicated linear algebra tools

A list of the implemented Fortran routines with links to the associated .html documentation is given in the following table, where * denotes auxiliary routines:

AB09AD | Balance & Truncate model reduction |

AB09AX | *Balance & Truncate model reduction with state matrix in real Schur form |

AB09BD | Singular perturbation approximation based model reduction |

AB09BX | *Singular perturbation approximation based model reduction with state matrix in real Schur form |

AB09CD | Hankel norm approximation based model reduction |

AB09CX | *Hankel norm approximation based model reduction with state matrix in real Schur form |

AB09DD | Singular perturbation approximation formulas |

AB09ED | Hankel norm approximation based model reduction for the stable part |

AB09FD | Balance & Truncate model reduction of coprime factors |

AB09GD | Singular perturbation approximation of coprime factors |

AB09MD | Balance & Truncate model reduction for the stable part |

AB09ND | Singular perturbation approximation based model reduction for the stable part |

AB09HD | Stochastic Balance & Truncate and Singular perturbation approximation model reduction |

AB09HX | *Stochastic Balance & Truncate and Singular perturbation approximation model reduction with state matrix in real Schur form |

AB09HY | *Cholesky factors of the controllability and observability Grammians |

AB09ID | Frequency-weighted Balance & Truncate and Singular perturbation approximation model reduction |

AB09IX | *Accuracy enhanced balancing related model reduction with state matrix in real Schur form |

AB09IY | *Cholesky factors of the frequency-weighted controllability and observability Grammians |

AB09JD | Frequency-weighted Hankel-norm approximation method with invertible proper weights |

AB09JV | *State-space representation of a projection of a left weighted transfer-function matrix |

AB09JW | *State-space representation of a projection of a right weighted transfer-function matrix |

AB09JX | *Check stability/antistability of finite eigenvalues |

AB09KD | Frequency-weighted Hankel-norm approximation with biproper invertible weights |

AB09KX | *Stable projection of V*G*W or conj(V)*G*conj(W) |

SB16AD | Controller reduction using frequency-weighted Balance & Truncate and Singular perturbation approximation methods with special stability/performance preserving frequency weights |

SB16AY | *Cholesky factors of the frequency-weighted controllability and observability Grammians for controller reduction |

SB16BD | State-feedback/full-order estimator based controller reduction using coprime factorization with Balance & Truncate and Singular perturbation approximation methods |

SB16CD | State-feedback/full-order estimator based controller reduction using frequency-weighted coprime factorization with Balance & Truncate method |

SB16CY | *Cholesky factors of controllability and observability Grammians of coprime factors of a state-feedback controller |

The documentation of all routines is also accessible from the SLICOT Library main index (in case of the drivers, or user-callable routines), or from the SLICOT Supporting Routines index (in case of the auxiliary routines, marked with * in the table above). The SLICOT Supporting Routines index is also accessible from the main Library index.

This email address is being protected from spambots. You need JavaScript enabled to view it. March 12, 2002, Updated This email address is being protected from spambots. You need JavaScript enabled to view it. March 10, 2005; Updated: June 15, 2006