ctrbf

Compute controllability staircase form.

📝 Syntax

• [Abar, Bbar, Cbar, T, k] = ctrbf(A, B, C)

• [Abar, Bbar, Cbar, T, k] = ctrbf(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

ctrbf(A, B, C) decomposes the given state-space system, defined by matricesA, B, andC, into the controllability staircase form.

This results in transformed matrices Abar,Bbar, andCbar, along with a similarity transformation matrixT and a vector k.

The length of vectork is equal to the order of the system represented byA, and each entry ink denotes the number of controllable states factored out at each step of the transformation matrix computation.

The non-zero elements ink indicate the number of iterations required forT calculation, and the sum ofk corresponds to the number of states inAc, the controllable portion of Abar.

💡 Example

A = [-1.5  -0.5; 1     0];
B = [0.5; 0];
C = [0   1];
[Abar, Bbar, Cbar, T, k] = ctrbf(A, B, C)

🔗 See also

ctrb.

🕔 History

Version	📄 Description
1.0.0	initial version