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DynamicSystems

  

Controllable

  

determine controllability of a state-space system

 

Calling Sequence

Parameters

Options

Description

Examples

Calling Sequence

Controllable( sys, opts )

Parameters

sys

-

System(ss); system object to test

opts

-

(optional) equation(s) of the form option = value; specify options for the Controllable command

Options

• 

method = staircase or rank

Selects the method used for testing controllability. The default is staircase.

Description

• 

The Controllable command determines whether sys, a state-space system, is controllable.

• 

If sys is controllable, true is returned, otherwise false is returned.

• 

Two methods, selected by the method option, are available for determining controllability.

• 

The staircase method applies the controllable staircase transform to the A and B Matrices of sys. If the state matrix of the resulting controllable subsystem has the same dimension as A, the system is controllable, otherwise it is uncontrollable.

• 

The rank method constructs the controllability matrix of sys system using the DynamicSystems[ControllabilityMatrix] command. If the matrix has full rank, the system is controllable, otherwise, it is uncontrollable.

• 

An error occurs if sys is not a state-space system.

Examples

withDynamicSystems:

aSysStateSpace1,2|3,4,2,3,1,0|0,1,0,0:

aSys:-a,aSys:-b,aSys:-c

1324,23,1001

(1)

ControllableaSys

true

(2)

ControllableaSys,method=rank

true

(3)

See Also

DynamicSystems

DynamicSystems[ControllabilityMatrix]

DynamicSystems[ObservabilityMatrix]

DynamicSystems[Observable]

DynamicSystems[SSTransformation]

LinearAlgebra

LinearAlgebra[Rank]

 


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