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DynamicSystems

  

ControllabilityMatrix

  

compute the controllability matrix

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

ControllabilityMatrix( sys )

ControllabilityMatrix( Amat, Bmat )

Parameters

sys

-

System(ss); state-space system

Amat

-

Matrix; state-space Matrix A

Bmat

-

Matrix; state-space Matrix B

Description

• 

The ControllabilityMatrix command computes the controllability matrix of a state-space system.

• 

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

• 

If the parameters Amat and Bmat are Matrices, then they are the A and B Matrices, respectively.

• 

The controllability matrix has dimensions n x n*m, where n is the number of states (dimension of A) and m is the number of inputs (column dimension of B). It has the form << B | A . B | A^2 . B | A^3 . B | ... | A^(n-1) . B >>.

Examples

withDynamicSystems&colon;

withLinearAlgebra&colon;

sys1StateSpace1s2&plus;s&plus;10&colon;

ControllabilityMatrixsys1

0111

(1)

sys2StateSpace3&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;

ControllabilityMatrixsys2:-a&comma;sys2:-b

111222333

(2)

sys3StateSpaceDiagonalMatrixa1&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:-b

a1000a2000a3&comma;00b100b2

(3)

ControllabilityMatrixsys3

000000b10a2b10a22b100b20a3b20a32b2

(4)

See Also

DynamicSystems

DynamicSystems[Controllable]

DynamicSystems[Grammians]

DynamicSystems[ObservabilityMatrix]

DynamicSystems[Observable]

DynamicSystems[SSTransformation]

 


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