Accessory minimum problem of optimal periodic processes

This paper presents a new approach for analyzing the accessory minimum problem of optimal periodic process. A stability preserving transformation is introduced which produces an LTI equivalent system to the periodic Hamiltonian. A linear matrix inequality (LMI) related to the equivalent system is then established. Since the Hamiltonian system of an optimal periodic process has the property that its monodromy matrix has a pair of coupled unit eigenvalues with the primary eigenvector along the extremal periodic trajectory, the matrix inequality is of a form that is similar to that of a singular linear quadratic problem. It is expected that investigating properties of this LMI will shed light to and enrich the second variation theory for optimal periodic processes