obsvf
Compute observability staircase form.
Syntax
- [Abar, Bbar, Cbar, T, k] = obsvf(A, B, C)
- [Abar, Bbar, Cbar, T, k] = obsvf(A, B, C, tol)
Input argument
- 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).
Output argument
- 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.
Description
obsvf(A, B, C) decomposes the given state-space system, characterized by matrices A, B, and C, into the observability staircase form, resulting in transformed matrices Abar, Bbar, and Cbar.
It also provides a similarity transformation matrix T and a vector k.
The length of vector k corresponds to the number of states in A, and each entry in k signifies the number of observable states factored out at each step of the transformation matrix computation.
The non-zero elements in k indicate the number of iterations needed for T calculation, and the sum of k represents the number of states in Ao, the observable portion of Abar.
Example
A = [-1.5 -0.5; 1 0];
B = [0.5; 0];
C = [0 1];
[Abar, Bbar, Cbar, T, k] = obsvf(A, B, C)
See also
History
Version | Description |
---|---|
1.0.0 | initial version |
Author
Allan CORNET