A HYPERBOLIC PDE DESCRIBING THE EVOLUTION OF A CLASS OF RANDOMLY SWITCHED DELAY SYSTEMS AND STOCHASTIC STABILIZATION

The class of alternating stochastic systems is considered. These are described by a linear system, with parameters switching randomly between two known values (i.e., an alternating system). The hyperbolic backward equations are obtained. For alternating systems, the functional partial differential equation is explicitly computed, and its diffusion limit is derived. The latter sheds light on the stability of the system. In addition, applications to vibrational stabilizability are discussed. We also make some connections with white noise analysis.