Examples
Examples
Try the starting example
- Discrete state transition matrix A
- [[0.8,0.1],[0,0.9]]
- Discrete input matrix B
- [[1],[0.5]]
- Output matrix C
- [[1,0]]
- Feedthrough matrix D
- [[0]]
- Input sequence rows u[k]
- [[1],[1],[0],[0]]
- Initial state x[0]
- 0,0
- Pre-update state trajectory x[k] (JSON)
- [[0,0],[1,0.5],[1.85,0.95],[1.575,0.855]]
- Output trajectory y[k] (JSON)
- [[0],[1],[1.85],[1.575]]
- Final state x[N] (JSON)
- [1.3455,0.7695]
Try another scenario
- Discrete state transition matrix A
- [[1.8,0.1],[0,0.9]]
- Discrete input matrix B
- [[1],[0.5]]
- Output matrix C
- [[1,0]]
- Feedthrough matrix D
- [[0]]
- Input sequence rows u[k]
- [[1],[1],[0],[0]]
- Initial state x[0]
- [0, 0]
- Pre-update state trajectory x[k] (JSON)
- [[0,0],[1,0.5],[2.85,0.95],[5.225,0.855]]
- Output trajectory y[k] (JSON)
- [[0],[1],[2.85],[5.225]]
- Final state x[N] (JSON)
- [9.4905,0.7695]
Calculation method
Calculation method
Pre-update state trajectory x[k] (JSON)
Supplied discrete linear model: y[k]=Cx[k]+Du[k], then x[k+1]=Ax[k]+Bu[k]; no implicit continuous-time discretization.
Output trajectory y[k] (JSON)
Supplied discrete linear model: y[k]=Cx[k]+Du[k], then x[k+1]=Ax[k]+Bu[k]; no implicit continuous-time discretization.
Final state x[N] (JSON)
Supplied discrete linear model: y[k]=Cx[k]+Du[k], then x[k+1]=Ax[k]+Bu[k]; no implicit continuous-time discretization.
Symbols and units
- a
- Discrete state transition matrix A
- b
- Discrete input matrix B
- c
- Output matrix C
- d
- Feedthrough matrix D
- e
- Input sequence rows u[k]
- f
- Initial state x[0]
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; Supplied discrete linear model: y[k]=Cx[k]+Du[k], then x[k+1]=Ax[k]+Bu[k]; no implicit continuous-time discretization. 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.