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In this study, the authors investigate the control problem of switched singular systems aiming to compress their inconsistent state jumps when switch occurs between two different singular subsystems. The proposed hybrid impulsive controller consists of a feedback controller and an impulsive controller. With introduction of the impulsive controller, the state at each switching instant for the closed-loop system can be changed. Based on the given controller structure, some sufficient conditions are derived under which the closed-loop system is admissible (regular, impulse free and stable) and such a controller has the capability of eliminating or minimising the instantaneous state jumps at switching instants. The validity and advantage of the proposed hybrid impulsive controller are illustrated using two examples.