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 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.

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

Author

Allan CORNET