Stabilization of linear conservative dynamical systems using cyclic energy dissipation

In a previous paper we addressed the following problem: Under what conditions can a conservative mechanical circuit consisting of point masses and linear springs be stabilized by adding persistent damping (e.g., using dashpots) at appropriate locations in the circuit? In answering this question, we arrived at a new invariance theorem for linear time-invariant systems (necessary and sufficient conditions for asymptotic stability in the large) which is equivalent to the LaSalle-Barbashin-Krasovskii invariant theorem. This result involves a certain observability condition for linear systems. In the present paper, we extend the above result by asking the more general question: Under what conditions can we stabilize the above conservative dynamical system using intermittent energy dissipation over arbitrary duty cycles.