state-space-linearization SKILL.md skillA
state-space-linearization from benchflow-ai/benchflow is an agent skill: a SKILL.md folder an AI agent loads when a task calls for it.
mdr add benchflow-ai/benchflow/state-space-linearization@git:20260610.e2a435fPins git:20260610.e2a435f in mdr.lock. Pin the fingerprint instead.
- Audit grade
- A, 17 of 17 checks passed
- Kind
- SKILL.md skill
- Repository
- benchflow-ai/benchflow
- Path
tests/fixtures/skillsbench_slice/r2r-mpc-control/environment/skills/state-space-linearization/SKILL.md- Versions recorded
- 1
- Latest version
- git:20260610.e2a435f, committed Jun 10, 2026
- Size
- 1,018 bytes
- Repository stars
- 359
- License
- Apache-2.0
Linearizing nonlinear dynamics around operating points for control design.
Collected from public GitHub. Every version is saved exactly as it was and never changes. Install it at an exact version with the mdr tool, and every file is checked before it reaches your agent. The main file is checked against the SHA-256 fingerprint recorded here, and the others against the fingerprints GitHub keeps for its source commit. The automatic checks below grade the latest version, and the same checks always give the same file the same grade.
What the file says
# State-Space Linearization
## Jacobian Computation
For nonlinear dynamics dx/dt = f(x, u), linearize around (x_ref, u_ref):
```
A = ∂f/∂x |_{x_ref} (n×n matrix)
B = ∂f/∂u |_{x_ref} (n×m matrix)
```
## Discretization
For discrete-time control with timestep dt:
**Euler method** (simple, first-order accurate):
```python
A_d = I + dt * A_c
B_d = dt * B_c
```
**Matrix exponential** (exact for LTI):
```python
A_d = expm(A_c * dt)
B_d = inv(A_c) @ (A_d - I) @ B_c
```
## For R2R Systems
The Jacobian depends on current tensions and velocities. Key partial derivatives:
```python
∂(dT_i/dt)/∂T_i = -v_i / L
∂(dT_i/dt)/∂v_i = EA/L - T_i/L
∂(dv_i/dt)/∂T_i = -R²/J
∂(dv_i/dt)/∂u_i = R/J
```
## Tips
- Linearize around the reference operating point
- Update linearization if operating point changes significantly
- Check stability via eigenvalue analysisRead the whole file at its exact version.
How to install
mdr add benchflow-ai/benchflow/state-space-linearization@sha256:1cd18b96f4f55ff0The line at the top of this page pins the label git:20260610.e2a435f, which is what most people want. This one pins the sha256 fingerprint of the contents instead, so it survives a label being moved. Either way the exact version is written to mdr.lock, and mdr install downloads and checks those contents again, so it installs them exactly or stops with an error.
[](https://markdownregistry.com/a/art_zpgpjv2iw4us2wh7)
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Versions
The registry has recorded 1 version of this file, committed on Jun 10, 2026.
Audit of the latest version
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Source
benchflow-ai/benchflow · 359 stars · license Apache-2.0 · pushed 2026-10-30 · branch main
API
GET https://markdownregistry.com/api/v1/artifacts/art_zpgpjv2iw4us2wh7 GET https://markdownregistry.com/api/v1/resolve?ref=benchflow-ai/benchflow/state-space-linearization GET https://markdownregistry.com/api/v1/blob/1cd18b96f4f55ff004aa92c0acbf0cab2744032c94a42d750ce749055038835b
Your AI assistant does the legwork. You hear about the deals worth your word. Hand yours the standing instructions at modelranch.com and it joins the network that reads files like this one.
Guides: the SKILL.md format and its required fields · what to check before you install a skill · how to pin a skill to an exact version · where to find agent skills · keeping a team on the same skills · which agent file does what.