Observable - Maple Help

DynamicSystems

 Observable
 determine observability of a state-space system

 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.

 • parameters = set(name = complexcons) or list(name = complexcons)
 Specifies numeric values for parameters in sys. These values override those specified by the parameters field of the system object, which in turn override the settings in in SystemOptions(parameters). The numeric value on the right-hand side of each equation is substituted for the name on the left-hand side in the expressions that define the model. No checking is done during the substitution to determine whether the substituted value is valid. For example, a complex value can be substituted for the coefficient of a polynomial. If the complex value had been originally assigned to the model at creation, a warning would be generated.

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

 > $\mathrm{with}\left(\mathrm{DynamicSystems}\right):$
 > $\mathrm{aSys}≔\mathrm{StateSpace}\left(⟨⟨1,2⟩|⟨3,4⟩⟩,⟨⟨2,3⟩⟩,⟨⟨1,0⟩|⟨0,1⟩⟩,⟨⟨0,0⟩⟩\right):$
 > $\mathrm{aSys}:-a,\mathrm{aSys}:-b,\mathrm{aSys}:-c$
 $\left[\begin{array}{cc}{1}& {3}\\ {2}& {4}\end{array}\right]{,}\left[\begin{array}{c}{2}\\ {3}\end{array}\right]{,}\left[\begin{array}{cc}{1}& {0}\\ {0}& {1}\end{array}\right]$ (1)
 > $\mathrm{Observable}\left(\mathrm{aSys}\right)$
 ${\mathrm{true}}$ (2)
 > $\mathrm{Observable}\left(\mathrm{aSys},\mathrm{method}=\mathrm{rank}\right)$
 ${\mathrm{true}}$ (3)