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DynamicSystems

 Controllable
 determine controllability of a state-space system

 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

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