Abstract: In this paper, the problems of robust stability and robust stabilization for uncertain generalized systems are considered. The concepts of 'generalized quadratic stability' and 'generalized quadratic stabilizability' for uncertain generalized systems are proposed. In terms of matrix inequalities, necessary and sufficient conditions under which the considered system is robustly stable and robustly stabilizable are derived respectively. Furthermore, the robust stabilizing state feedback control law can be designed by finding a solution to a given matrix inequality.