This note continues an investigation by the authors of minimizing the transient response of a linear system as measured by nonquadratic penalty functions, in particular, penalty functions which have linear growth. First, this note shows that the optimal state feedback which minimizes the transient response in the case of no exogenous inputs also minimizes the induced l(1) norm in case exogenous inputs are present. Second, it considers the case of constrained systems and derives bounds which establish the stability and performance of receding horizon control laws. Finally, this note illustrates the results for scheduling of reliable manufacturing systems.