In this paper a nonlinear feedback control law will be constructed for a class of lineal syatcms. To this end a very purticular critctiou funotional is introduocd. involving a certain S·norm of the state x: ||x||s. When ||x||s=0, singular phenomena occur which arc considered in detail. It is shown that optimal arcs may end up with a singular trajectory. This problem is considered for u-dimcnsicnal linear time-dependent systems with vector control. © 1979 Taylor & Francis Group, Ltd.