design

Planned, wave 3: Riccati and Lyapunov equations, LQR and LQG, pole placement and discretisation.

Status: planned (wave 3). No code exists. The package name is provisional.

What it will provide

Continuous and discrete algebraic Riccati equations (CARE, DARE).
Lyapunov and Sylvester equations.
LQR, LQG and Kalman gains.
Pole placement for multi-input systems.
Discretisation (c2d): zero-order hold, first-order hold, Tustin and matched.

It depends on lti and on Schur reordering, QZ and expm in go-ndarray’s linalg.

References

Subject	Reference
CARE and DARE	Laub, “A Schur method for solving algebraic Riccati equations”, IEEE TAC 24(6), 1979, doi:10.1109/TAC.1979.1102178
Riccati refinement	Kleinman, IEEE TAC 13(1), 1968, doi:10.1109/TAC.1968.1098829
Sylvester and Lyapunov	Bartels and Stewart, CACM 15(9), 1972, doi:10.1145/361573.361582; Hammarling, IMA J. Numer. Anal. 2(3), 1982, doi:10.1093/imanum/2.3.303
exact zero-order hold	Van Loan, IEEE TAC 23(3), 1978, doi:10.1109/TAC.1978.1101743
pole placement	Kautsky, Nichols and Van Dooren, Int. J. Control 41(5), 1985, doi:10.1080/0020718508961188

How it will be validated

Area	Criterion
Riccati and Lyapunov	relative residual below 1e3·n·eps, a solution symmetric to one ulp, closed-loop poles in the left half-plane; the worst residual over the benchmark set and the median ratio against SLICOT and SciPy are reported
`c2d`	relative error against a high-precision reference, 10·eps norm-wise

Reference implementations: SLICOT-Reference (BSD-3-Clause in the repository; each routine’s header is to be checked, and the commit recorded, before any port), SciPy (solve_continuous_are, place_poles), python-control and Octave’s control package as oracles. The SLICOT benchmark collections and COMPleib are the corpora. Every item also needs unit tests at 100% coverage and a performance table against the reference.

Created on October 23, 2026 by tannevaled

Modified on October 23, 2026 by tannevaled