A second variational theory for optimal periodic processes

A sufficiency condition for a periodic process with free period to be a weak local minimum is given. By making detailed use of the properties of the monodromy matrix, the transition matrix calculated over a closed orbit, previous results are corrected, extended, and clarified. A necessary condition for a real valued periodic Riccati matrix to exist is that there be no distinct eigenvalues of the monodromy matrix on the unit circle. For local sufficiency, it is required that no eigenvalues of the monodromy matrix, except a double root at unity, lie on the unit circle.