How do I install the State Space Analysis skill?

Run npx skillmds@latest add ashfordeou/state-space-analysis in your terminal (requires Node.js), paste this page's agent-chat prompt into Claude, Cursor, or any MCP-connected agent, or download the SKILL.md file and copy it into your agent's skills directory.

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Which AI agents work with State Space Analysis?

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Is State Space Analysis free to use?

Yes. Installing skills from SkillMD is free. This skill is licensed under Apache-2.

Who published State Space Analysis?

ashfordeOU (@ashfordeou) published this skill. Their other Agent Skills are listed on their SkillMD profile.

State Space Analysis by ashfordeou — Agent Skill

Name: State Space Analysis
Author: ashfordeOU

State Space Analysis

Use when you must analyze a linear time-invariant system in state space: form the controllability and observability matrices, decide controllability and observability from their ranks, compute the 2x2 eigenvalue stability verdict, build the state transition matrix by the Cayley-Hamilton method, and produce the controller or observer canonical forms. Applies to flight control and GNC state-space models written as x_dot = A x + B u with output y = C x. Produces the controllability and observability verdicts, the stability verdict, the transition matrix at a time t, and the canonical form realizations that feed control law design. Trigger: state space, controllability, observability, state transition matrix, eigenvalues, stability, canonical form, linear system, A matrix, B matrix, C matrix.

ashfordeOU 217b88f 3 files · 25.8 KB Updated Sep 17, 2026

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State Space Analysis (gnc-autonomy/control/state-space-analysis)

Use when the task is analyzing a linear time-invariant state space model: controllability and observability checks, stability from the A matrix, the state transition matrix, and canonical form realizations.

Domain quick reference

A linear time-invariant system is x_dot = A x + B u, y = C x with n states, m inputs, p outputs.
Controllability: the pair (A, B) is controllable when the controllability matrix [B, AB, ..., A^(n-1)B] has full row rank n.
Observability: the pair (A, C) is observable when the observability matrix [C; CA; ...; CA^(n-1)] has full column rank n.
Stability: a continuous-time system is stable when every eigenvalue of A has a strictly negative real part.
State transition matrix: Phi(t) = e^(A t) propagates the state as x(t) = Phi(t) x(0); for 2x2 systems the Cayley-Hamilton expansion gives Phi(t) = alpha0(t) I + alpha1(t) A.
Controller canonical form realizes the transfer function denominator coefficients in the last row of A; observer canonical form places them in the last column. Both are similarity transforms of (A, B, C).

Workflow

Check the matrix dimensions (square A, conformable B and C).
Compute the controllability and observability matrices and their ranks; decide controllability and observability.
Compute the eigenvalues of A (2x2 closed form) and the stability verdict.
Build the state transition matrix at the requested time by the Cayley-Hamilton expansion for a 2x2 system.
Produce the controller and observer canonical form realizations.
Optionally assemble the full analysis report with all verdicts.

Pitfalls

Declaring controllability from a matrix whose rank was computed with a too-loose tolerance (rank is a numerical decision).
A transition matrix that does not reduce to I at t = 0.
Mixing the controller and observer canonical form conventions (denominator row vs column placement).
Applying a continuous-time stability test to a discrete system without first mapping the eigenvalues to the unit circle.

Behavior contract (gate 3)

The state space logic is exercised by the gate 3 contract test: scripts/test_state_space.py against scripts/state_space_logic.py (stdlib unittest, offline). Run:

python3 scripts/test_state_space.py

---name: state-space-analysisdescription: Use when you must analyze a linear time-invariant system in state space: form the controllability and observability matrices, decide controllability and observability from their ranks, compute the 2x2 eigenvalue stability verdict, build the state transition matrix by the Cayley-Hamilton method, and produce the controller or observer canonical forms. Applies to flight control and GNC state-space models written as x_dot = A x + B u with output y = C x. Produces the controllability and observability verdicts, the stability verdict, the transition matrix at a time t, and the canonical form realizations that feed control law design. Trigger: state space, controllability, observability, state transition matrix, eigenvalues, stability, canonical form, linear system, A matrix, B matrix, C matrix.license: Apache-2.0---# State Space Analysis (gnc-autonomy/control/state-space-analysis)Use when the task is analyzing a linear time-invariant state spacemodel: controllability and observability checks, stability from theA matrix, the state transition matrix, and canonical formrealizations.## Domain quick reference- A linear time-invariant system is x_dot = A x + B u, y = C x with n states, m inputs, p outputs.- Controllability: the pair (A, B) is controllable when the controllability matrix [B, AB, ..., A^(n-1)B] has full row rank n.- Observability: the pair (A, C) is observable when the observability matrix [C; CA; ...; CA^(n-1)] has full column rank n.- Stability: a continuous-time system is stable when every eigenvalue of A has a strictly negative real part.- State transition matrix: Phi(t) = e^(A t) propagates the state as x(t) = Phi(t) x(0); for 2x2 systems the Cayley-Hamilton expansion gives Phi(t) = alpha0(t) I + alpha1(t) A.- Controller canonical form realizes the transfer function denominator coefficients in the last row of A; observer canonical form places them in the last column. Both are similarity transforms of (A, B, C).## Workflow1. Check the matrix dimensions (square A, conformable B and C).2. Compute the controllability and observability matrices and their ranks; decide controllability and observability.3. Compute the eigenvalues of A (2x2 closed form) and the stability verdict.4. Build the state transition matrix at the requested time by the Cayley-Hamilton expansion for a 2x2 system.5. Produce the controller and observer canonical form realizations.6. Optionally assemble the full analysis report with all verdicts.## Pitfalls- Declaring controllability from a matrix whose rank was computed with a too-loose tolerance (rank is a numerical decision).- A transition matrix that does not reduce to I at t = 0.- Mixing the controller and observer canonical form conventions (denominator row vs column placement).- Applying a continuous-time stability test to a discrete system without first mapping the eigenvalues to the unit circle.## Behavior contract (gate 3)The state space logic is exercised by the gate 3 contract test:scripts/test_state_space.py against scripts/state_space_logic.py(stdlib unittest, offline). Run: python3 scripts/test_state_space.py

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