This can happen and is completely expected.
Transfer functions are defined as the relationship between inputs and outputs, whereas state-space models contain two separate relationships: inputs to states and states to outputs.
For this reason, a single transfer function can be expressed as an infinite combination of state-space realizations. While your two state-space models look different, they should contain the same system dynamics.
This is part of the reason why people often convert state-space models into different canonical forms, such as modal, observability, etc. This ensures that you always get the same structure for state-space realizations.
- Sebastian
