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 matricesA, B, andC, into the observability staircase form, resulting in transformed matricesAbar, Bbar, and Cbar.

It also provides a similarity transformation matrixT and a vector k.

The length of vectork corresponds to the number of states inA, and each entry ink signifies the number of observable states factored out at each step of the transformation matrix computation.

The non-zero elements ink indicate the number of iterations needed forT calculation, and the sum ofk represents the number of states in Ao, the observable portion ofAbar.

💡 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