Controllability and observability of linear time varying singular systems

Controllability and observability of analytically solvable linear time varying singular systems are considered. Our analysis includes the possible impulsive zero-input response. Based on the definitions of controllability and observability naturally extended from the ones adopted in the time-invariant setting, sufficient and necessary conditions for these two properties are derived. Furthermore, according to the specific definitions of these concepts used here, the authors show that the dual relationship between controllability and observability does not hold.