7.3 Dual System
The function DualSystem returns the system that is dual to the input system. It is useful because observability tests are often implemented as controllability tests of the system dual to the one in question.
Finding the dual system.
This is a system in state-space form.
This is its dual system.
By default, DualSystem assumes that all symbolic entries in state-space representation can be complex. The user may disable this feature by setting the option ComplexVariables to None, in which case the built-in function ComplexExpand will be applied to the result. ComplexVariables accepts also a list of variables which may be complex. In this case, all other variables are assumed to be real valued.
If we assume that none of the symbolic entries are complex, a simpler result is returned.
Finally, here is the dual system if only a1 may be complex.
Option to DualSystem.