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

obsv, ctrbf.

🕔 History

Version	📄 Description
1.0.0	initial version