Introduction to Stability of switched stochastic nonlinear systems
Hybrid systems are digital real-time systems which are embedded in analog environment. Analog part of the hybrid system is described with differential equations and discrete part of the hybrid systems is an event driven dynamics which can be described using concept from discrete event systems (Cassandras & Lafortune, 2008) and (Tabuada, 2009). In this paper we will consider the switched systems which can be viewed as higher-level abstraction of hybrid systems (Liberzon, 2003) and (Sun & Ge, 2005).We model each subsystem of a switched system by differential equation. There are two ways for analysis of stability of switched deterministic systems. The first one is a construction of common Lyapunov function. Find the common Lyapunov functions is a difficult task (Narendra & Balakrishnan, 1994). The second one utilizes multiple Lyapunov functions for analysis of switched systems (Branicky, 1998). In this paper we will consider a stability of switched stochastic systems. We assume that (i) there is no jump in the state at switching instants and (ii) there is no Zeno behaviour, i.e. there is finite number of switches…
