Abstract. In the development of ideas of B.N. Pshenichnyi, the paper considers a linear differential game with impulse controls. A research technique is proposed, which is based on time extension and oriented to the case where the classical Pontryagin condition does not hold. Sufficient conditions for the finiteness of the guaranteed approach time are obtained. An illustrative example is given.

Keywords: function of the time extension, differential game, impulse control, set-valued mapping, Minkowski’ geometric difference, Pontryagin’s condition.