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.
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