[Abar, Bbar, Cbar, T, k] = ctrbf(A, B, C)
[Abar, Bbar, Cbar, T, k] = ctrbf(A, B, C, tol)
| Parameter | Description |
|---|---|
| A | State matrix: Nx-by-Nx matrix |
| B | Input-to-state matrix: Nx-by-Nu matrix |
| C | Output-to-state matrix: Ny-by-Nx matrix |
| tol | scalar real (tolerance). |
| Parameter | Description |
|---|---|
| Abar | Observability staircase state matrix. |
| Bbar | Observability staircase input matrix. |
| Cbar | Observability staircase output matrix. |
| T | Similarity transform matrix. |
| k | Vector: number of observable states. |
ctrbf(A, B, C) decomposes the given state-space system, defined by matrices A, B, and C, into the controllability staircase form.
This results in transformed matrices Abar, Bbar, and Cbar, along with a similarity transformation matrix T and a vector k.
The length of vector k is equal to the order of the system represented by A, and each entry in k denotes the number of controllable states factored out at each step of the transformation matrix computation.
The non-zero elements in k indicate the number of iterations required for T calculation, and the sum of k corresponds to the number of states in Ac, the controllable portion of Abar.
A = [-1.5 -0.5; 1 0];
B = [0.5; 0];
C = [0 1];
[Abar, Bbar, Cbar, T, k] = ctrbf(A, B, C)| Version | Description |
|---|---|
| 1.0.0 | initial version |