Multi-Mode Multi-Dimensional Systems with Poissonian Sequencing

Abstract

The dynamics of hybrid systems with mode dynamics of different dimensions is described. The first part gives some deterministic examples of such multi-mode multi-dimensional $(M^3D)$ systems. The second part considers such models under sequential switching at random times. More specifically, the backward Kolmogorov equation is derived, and Lie-algebraic methods are used in the case where the modes are linear. For Poissonian switched equi-dimensional modes, the diffusion limit and its implication in vibrational stability are studied. The motion of a pebble on an elevator belt is given as an example.