functionisControllableSISO

To check a SISO system whether it is controllable

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.

Inputs

Type	Name	Default	Description
StateSpace	ss		State space system

Outputs

Type	Name	Default	Description
Boolean	controllable