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DynamicSystems[ObservabilityMatrix] - compute the observability matrix

Calling Sequence

ObservabilityMatrix( sys )

ObservabilityMatrix( Amat, Cmat )

Parameters

sys

-

System; state-space system

Amat

-

Matrix; state-space matrix A

Cmat

-

Matrix; state-space matrix C

Description

• 

The ObservabilityMatrix command computes the observability matrix of a state-space system.

• 

If the parameter sys is a state-space System, then the A and C Matrices are sys:-a and sys:-c, respectively.

• 

If the parameters Amat and Cmat are Matrices, then they are the A and C Matrices, respectively.

• 

The observability matrix has dimensions o*n x n, where n is the number of states (dimension of A) and o is the number of outputs (row dimension of C) It has the form <<C>, <C . A>, <C . A^2>, <C . A^3>, ..., <C . A^(n-1)>>.

Examples

withDynamicSystems&colon;

withLinearAlgebra&colon;

sys1:=StateSpace1s2&plus;s&plus;10&colon;

sys1:-a&comma;sys1:-c

01101&comma;10

(1)

ObservabilityMatrixsys1

1001

(2)

sys2:=StateSpace3&verbar;1&verbar;0&comma;5&verbar;0&verbar;1&comma;3&verbar;0&verbar;0&comma;1&comma;2&comma;3&comma;1&verbar;0&verbar;0&comma;0&colon;

sys2:-a&comma;sys2:-c

310501300&comma;100

(3)

ObservabilityMatrixsys2:-a&comma;sys2:-c

100310431

(4)

sys3:=StateSpaceDiagonalMatrixa1&comma;a2&comma;a3&comma;0&verbar;0&comma;b1&verbar;0&comma;0&verbar;b2&comma;c1&verbar;0&verbar;0&comma;0&verbar;0&verbar;c3&comma;0&verbar;0&comma;0&verbar;0&colon;

sys3:-a&comma;sys3:-c

a1000a2000a3&comma;c10000c3

(5)

ObservabilityMatrixsys3

c10000c3a1c10000a3c3a12c10000a32c3

(6)

See Also

DynamicSystems, DynamicSystems[ControllabilityMatrix], DynamicSystems[Controllable], DynamicSystems[Grammians], DynamicSystems[Observable], DynamicSystems[SSTransformation]


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