Control constraints, abnormality and improved performance by periodic control

Second-order conditions for steady-state optimality and nonoptimality in a periodic control problem are presented. The main result is a generalization of the ?? test, a second-order sufficient condition for improved performance by periodic control. Earlier results are generalized in two distinct ways: 1) the control constraint set is only assumed convex (and hence possibly nonopen) thus allowing the optimal steady-state control to be an element of the control constraint set boundary and 2) auxiliary normality conditions are eliminated.