SLICOT Control Theory Library

C11 translation of SLICOT (Subroutine Library In COntrol Theory) with Python bindings.

Naming Convention

Routines follow XX##YY pattern:

•XX - 2-letter category prefix (AB, SB, MB, etc.)
•## - 2-digit subcategory number
•YY - variant suffix (MD=real, MZ=complex, ND=multi-input, etc.)

Looking Up Routine Details

To get detailed documentation for any SLICOT routine, use Python's help function:

python

import slicot
help(slicot.sb02md)  # Full docstring with params, returns, examples

Category Quick Reference

Prefix	Domain	Key Functions
AB	Analysis	Controllability, observability, zeros, model reduction
AG	Analysis (Generalized)	Descriptor system analysis
SB	Synthesis	Riccati, Lyapunov, pole placement, H-inf, LQR/LQG
SG	Synthesis (Generalized)	Descriptor Riccati, Lyapunov
MB	Matrix	QR, SVD, eigenvalues, Hessenberg, Schur
MC	Matrix Construction	Polynomial operations
MA	Matrix Auxiliary	Helper matrix operations
MD	Matrix Decomposition	Advanced decompositions
TB	Transform (State-space)	Similarity, minimal realization, balancing
TC	Transform (Polynomial)	Coprime factorization, TF↔SS
TD	Transform (Data)	Transfer function manipulation
TF	Transform (Frequency)	Frequency response
TG	Transform (Descriptor)	Descriptor systems, staircase forms
IB	Identification	MOESP, N4SID subspace methods
NF	Nonlinear Filter	Nonlinear estimation
FB	Filter	Kalman filtering
FD	Filter Design	IIR/digital filter design
DE	Data Exchange	FFT, data conversion
BB, BD, DF, DG, DK	Utility	Basic ops, block diagonal, validation
UD, UE	Utility	Triangular, update/extract

Task-to-Routine Lookup

Controller Design

Task	Routine	Description
LQR (continuous)	`sb02md`	Solve continuous ARE for optimal gain
LQR (discrete)	`sb02md`	Solve discrete ARE (DICO='D')
LQG	`sb02md` + `fb01qd`	ARE + Kalman filter
Pole placement	`sb01bd`	Multi-input eigenvalue assignment
Eigenstructure	`sb01dd`	Eigenvector assignment
H-infinity	`sb10ad`	Continuous H-inf controller
H-infinity (discrete)	`sb10dd`	Discrete H-inf controller
Deadbeat	`sb06nd`	Finite settling time

System Analysis

Task	Routine	Description
Controllability	`ab01nd`	Multi-input controllable realization
Observability	`ab01od`	Staircase form reduction
System zeros	`ab08nd`	Transmission zeros
Stability check	`ab09jx`	Stable/antistable decomposition
H-infinity norm	`ab13md`	Compute ‖G‖∞
H2 norm	`ab13bd`	Compute ‖G‖₂
Hankel norm	`ab13ad`	Compute Hankel singular values

Model Reduction

Task	Routine	Description
Balanced truncation	`ab09ad`	Hankel-norm approximation
Balanced stochastic	`ab09bd`	Stochastic balancing
Frequency-weighted	`ab09cd`	Weighted balanced reduction
Singular perturbation	`ab09md`	Frequency-weighted SPA
Coprime factorization	`ab09fd`	Normalized coprime factors
Hankel MDA	`ab09hd`	Hankel minimum degree

Matrix Equations

Equation	Routine	Description
Riccati (ARE)	`sb02md`	A'X + XA - XGX + Q = 0
Lyapunov	`sb03md`	A'X + XA + Q = 0
Sylvester	`sb04md`	AX + XB = C
Generalized Lyapunov	`sg03ad`	A'XE + E'XA + Q = 0

System Transformation

Task	Routine	Description
Continuous ↔ Discrete	`ab04md`	Bilinear transformation
State-space ↔ Transfer	`tb04ad`	SS to transfer function
Minimal realization	`tb01pd`	Remove uncontrollable/unobservable

System Identification

Task	Routine	Description
Order estimation	`ib01ad`	MOESP/N4SID preprocessing
Matrix estimation	`ib01bd`	A, B, C, D from data
Kalman gain	`ib01bd`	With JOBCK='K'

Common Patterns

Array Order

All arrays use Fortran column-major order:

python

import numpy as np
A = np.array([[1, 2], [3, 4]], dtype=float, order='F')

In-Place Array Modification Warning

IMPORTANT: SLICOT functions may modify input arrays in-place. Always pass copies if you need to preserve originals:

python

# BAD - A, B, C, D may be corrupted after call
A_d, B_d, C_d, D_d, info = ab04md('C', A, B, C, D, alpha=1.0, beta=2.0/dt)

# GOOD - originals preserved
A_d, B_d, C_d, D_d, info = ab04md('C', A.copy(), B.copy(), C.copy(), D.copy(), alpha=1.0, beta=2.0/dt)

This applies to most SLICOT routines including ab04md, sb02md, tb05ad, etc.

Info Codes

•info = 0 → Success
•info < 0 → Parameter -info is invalid
•info > 0 → Algorithm-specific warning/error

DICO Parameter

•'C' → Continuous-time system
•'D' → Discrete-time system

JOB Parameter

•'A' → All computations
•'B' → B-related only
•'C' → C-related only
•'N' → None/minimal

UPLO Parameter (Symmetric Matrices)

•'U' → Upper triangle stored
•'L' → Lower triangle stored

Type Aliases

Type	Size	Fortran Equivalent
`i32`	32-bit int	INTEGER
`i64`	64-bit int	INTEGER*8
`f64`	64-bit float	DOUBLE PRECISION
`c128`	128-bit complex	COMPLEX*16

Subcategory Numbers

Common patterns in the 2-digit number:

•01-03 → Realization, reduction, canonical forms
•04-05 → Transformation, interconnection
•06-07 → Feedback, inverse
•08 → Zeros, poles analysis
•09 → Model reduction
•10 → H-infinity, robust control
•13 → Norms (H2, H-inf, Hankel)

Example: Finding the Right Routine

Task: Design LQR for continuous system with state Q and input R weights

•Need Riccati solver → SB prefix (synthesis)
•Algebraic equation → sb02 subcategory
•Real matrices → MD suffix
•Answer: sb02md with DICO='C'

Task: Identify system from I/O data

•System identification → IB prefix
•Subspace method → ib01 subcategory
•First call ib01ad (preprocessing + order)
•Then call ib01bd (matrix estimation)

Resources

•Routine Details: Use help(slicot.routine_name) in Python to get full docstring with parameters, return values, and examples
•Tests: tests/python/test_*.py (usage examples)

See references/ for detailed category info, workflows, and quick reference tables.