Forced Oscillations and Convex Superposition in Piecewise-Linear Systems - Fleishman, B. A. (SIAM review, 1965)
Several aspects of the theory of forced oscillations of piecewise-linear systems are considered. First of all, the general probelm of determining such periodic solutions is formulated and the principal methods of solving the problem are described briefly. By way of illustration, forced periodic solutions of the simplest kind are determined for a second-order on-off system subject to a sinusoidal external force. Next, piecewise-linear systems are shown to possess a property of convex superposition with respect to any set of responses (to different excitations) which are "synchronous", i.e., are in phase as they switch from one linear branch of the piecewise-linear function to another. Finally, for sets of periodic responses which are "almost synchronous", a conjecture is offered concerning "approximate" superposition; in this connection the example involving the second-order system is reconsidered.