A class of stochastic hybrid systems with state-dependent switching noise

In this paper, we develop theoretical results based on a proposed method for modeling switching noise for a class of hybrid systems with piecewise linear partitioned state space, and state-depending switching. We devise a stochastic model of such systems, whose global dynamics is governed by a continuous-time stochastic process. The main result of this paper is that we may identify the realizations of the global dynamics with the solutions of a differential inclusion. Hence, an analysis of switched systems with switching noise can be carried out either based on a non-deterministic method via the differential inclusion, or on a stochastic method via the stochastic process. Furthermore, we describe how to construct intensity plots, which provide a quick overview of the behavior of the system. An example is included to illustrate this.