On impulsive algebraic multiplicities of linear time-invariant singular systems under feedback

Impulsive algebraic multiplicities of linear time-invariant singular systems under output feedback or decentralized output feedback are characterized in terms of system matrices directly. The multiplicities describe the number of impulsive modes that can be eliminated and indicate the number of finite poles that can be assigned by the respective feedback. These characterizations also lead to new regularizability conditions for singular systems.