.Modelica_LinearSystems2.StateSpace.Internal.isControllableSISO

Information

This function is to calculate whether a SISO state space system is controllable or not. Therefore, it is transformed to lower controller Hessenberg form

               | *    *     0   ...  0 |               | 0 |
               | .    .     .    .   . |               | . |
 Q*A*Q ' = H = | *   ...   ...   *   0 |,    Q*b = q = | . |,   c*Q = ( *, ..., * )
               | *   ...   ...   *   * |               | 0 |
               | *   ...   ...   *   * |               | * |

Note, that

rank(b, A*b, ..., A^n-1*b) = rank(q, H*q, ..., H^n-1*q)

and that

(q, H*q, ..., H^n-1*q)

is a lower triangular matrix and has full rank if and only if none of the elements in the diagonal is zero. That is, that neither qn or hi,i+1, i = 1,..., n-1 may be zero.

Interface

encapsulated function isControllableSISO
  import Modelica_LinearSystems2;
  import Modelica_LinearSystems2.StateSpace;
  input StateSpace ss "State space system";
  output Boolean controllable;
end isControllableSISO;

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