Examples
Examples
Try the starting example
- Discrete state matrix A
- [[0.9,0.1],[0,0.8]]
- Discrete input matrix B
- [[0.1],[0]]
- Sample interval (seconds)
- 0.1
- Forward-Euler approximate continuous A (JSON)
- [[-1,1],[0,-2]]
- Forward-Euler approximate continuous B (JSON)
- [[1],[0]]
Try another scenario
- Discrete state matrix A
- [[1.9,0.1],[0,0.8]]
- Discrete input matrix B
- [[0.1],[0]]
- Sample interval (seconds)
- 0.1
- Forward-Euler approximate continuous A (JSON)
- [[9,1],[0,-2]]
- Forward-Euler approximate continuous B (JSON)
- [[1],[0]]
Calculation method
Calculation method
Forward-Euler approximate continuous A (JSON)
Invert forward-Euler approximation: Ac≈(Ad−I)/Ts, Bc≈Bd/Ts; explicitly not exact matrix-logarithm conversion.
Forward-Euler approximate continuous B (JSON)
Invert forward-Euler approximation: Ac≈(Ad−I)/Ts, Bc≈Bd/Ts; explicitly not exact matrix-logarithm conversion.
Symbols and units
- a
- Discrete state matrix A
- b
- Discrete input matrix B
- c
- Sample interval (seconds)
Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.
Assumptions & limits
Assumptions & limits
- User-supplied measurements and assumptions; Invert forward-Euler approximation: Ac≈(Ad−I)/Ts, Bc≈Bd/Ts; explicitly not exact matrix-logarithm conversion. Supported limits: Finite numeric values bounded to 1e9 magnitude; lists and tables contain 1–100 records unless a stricter bound is stated. Inputs use the units shown. Lists explicitly paired by a method must have matching lengths; independent polynomial coefficient vectors may differ. Respect stated physical, interpolation, policy and computational domain limits.
Are these inputs private?
These calculations run in your browser. A shared link contains the values you choose to share. Only questions submitted to the separate AI finder are sent to OpenAI.
Further reading
Background reading; this does not imply endorsement or independent review of SumFizz.