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DynamicSystems

  

Observable

  

determine observability of a state-space system

 

Calling Sequence

Parameters

Options

Description

Examples

Calling Sequence

Observable( sys, opts )

Parameters

sys

-

System; system object to test

opts

-

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

Options

• 

method = staircase or rank

Selects the method used to test for observability. The default is staircase.

Description

• 

The Observable command determines whether sys, a state-space system, is observable.

• 

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

• 

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

• 

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

• 

The rank method constructs the observability matrix of sys using the DynamicSystems[ObservabilityMatrix] command. If the matrix has full rank, the system is observable, otherwise, it is unobservable.

• 

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)

ObservableaSys

true

(2)

ObservableaSys,method=rank

true

(3)

See Also

DynamicSystems

DynamicSystems[ControllabilityMatrix]

DynamicSystems[Controllable]

DynamicSystems[ObservabilityMatrix]

DynamicSystems[SSTransformation]

LinearAlgebra

LinearAlgebra[Rank]

 


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