This paper investigates the state feedback stabilization problem for a class of impulsive linear time‐varying systems over specified time intervals and piecewise quadratic domains (PQDs). First, concepts related to finite‐time stability and PQDs are given. Second, finite‐time stability analysis over PQDs is implemented, and a variety of stability conditions involving differential linear matrix inequalities are investigated. Then, computationally tractable stability conditions are established for the control design. Finally, an illustrative example is presented to show the effectiveness of the designed state feedback control.