lti

Planned, wave 3: linear time-invariant models, their algebra, responses and margins.

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

What it will provide

Model types: transfer function, zero-pole-gain, state space and frequency-response data.
Model algebra: series, parallel and feedback connections.
Poles, zeros, DC gain and minimal realisation.
Time response (step, impulse, arbitrary input, initial condition), exact for LTI models through the matrix exponential.
Frequency response, Nyquist encirclements, root locus and stability margins.

It needs the non-symmetric eigenvalue solver, QZ and expm that go-ndarray’s linalg does not yet provide.

References

Subject	Reference
frequency response	Laub, “Efficient multivariable frequency response computations”, IEEE TAC 26(2), 1981, doi:10.1109/TAC.1981.1102602: Hessenberg reduction, then one solve per frequency
matrix exponential	Al-Mohy and Higham, SIAM J. Matrix Anal. Appl. 31(3), 2009, doi:10.1137/09074721X
stability margins	Skogestad and Postlethwaite, Multivariable Feedback Control, 2nd ed., Wiley 2005
textbook examples	Franklin, Powell and Emami-Naeini, Feedback Control of Dynamic Systems, 8th ed., Pearson 2019

How it will be validated

Area	Criterion
poles and zeros	relative error against the reference after sorting, with the conditioning accounted for
frequency response	complex relative error per point against python-control, reported in ULPs of the response
`expm`	relative error against a high-precision reference, norm-wise
time response	agreement with the `expm`-based exact solution; an ODE-based path is judged with a tolerance

Reference implementations: python-control (BSD-3-Clause; the API template), SciPy’s scipy.signal, and Octave’s control package as an oracle only, since it is GPL. Every item also needs unit tests at 100% coverage and a performance table against the reference, no slower than it on one core.

Created on October 23, 2026 by tannevaled

Modified on October 23, 2026 by tannevaled