<< obsv

Control System functions

ord2 >>

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obsvf

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Compute observability staircase form.

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Syntax

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

[Abar, Bbar, Cbar, T, k] = obsvf(A, B, C, tol)

Input argument

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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

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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

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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

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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

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obsv, ctrbf.

History

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Version	Description
1.0.0	initial version

Author

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Allan CORNET