state-space-linearization
It computes linear approximations of nonlinear models to assist in the design of stable controllers.
Install
mkdir -p .claude/skills/state-space-linearization && curl -L -o skill.zip "https://agentskills.codes/api/skills/download/1413" && unzip -o skill.zip -d .claude/skills/state-space-linearization && rm skill.zipInstalls to .claude/skills/state-space-linearization
Activation
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Linearizing nonlinear dynamics around operating points for control design.Key capabilities
- →Compute Jacobian matrices for nonlinear dynamics
- →Discretize systems using Euler method
- →Discretize systems using matrix exponential
- →Analyze stability via eigenvalue analysis
How it works
The skill calculates the Jacobian of nonlinear dynamics around a specific operating point and provides methods to discretize the resulting linear system.
Inputs & outputs
When to use state-space-linearization
- →Control system design for nonlinear models
- →Simplifying complex dynamic simulations
- →Stability analysis of operating points
About this skill
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):
A_d = I + dt * A_c
B_d = dt * B_c
Matrix exponential (exact for LTI):
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:
∂(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 analysis
When not to use it
- →Linearizing systems that are not near a reference operating point
Limitations
- →Linearization accuracy degrades far from the reference point
How it compares
It automates the derivation of partial derivatives for complex dynamic models compared to manual symbolic differentiation.
Compared to similar skills
state-space-linearization side by side with the closest alternatives in the catalog.
| Skill | Installs | Updated | Safety | Difficulty |
|---|---|---|---|---|
| state-space-linearization (this skill) | 3 | 6mo | No flags | Advanced |
| quant-analyst | 103 | 2mo | No flags | Advanced |
| umap-learn | 6 | 2mo | Review | Intermediate |
| embedding-strategies | 8 | 2mo | No flags | Intermediate |
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