Tham khảo tài liệu 'air traffic control part 3', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 2 Stability of switched stochastic nonlinear systems Vojislav Filipovic and Novak Nedic Mechanical Engineering Kraljevo Serbia 1. Introduction 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 . there is finite number of switches on every bounded interval of time. The situation with jump in the state of x at the switching instants is considered in Guan et. al. 2005 and Li et al. 2005 . In recent years the stochastic hybrid systems become hot research topic. There are a few approaches to the problem. In the stochastic setting we have jump diffusion as the solution of stochastic differential equation driven by Levy process which is a linear combination of time Brownian motion and pure jump process Oksendal Sulem 2005 . Close to deterministic hybrid systems is the concept of Piecewise deterministic Markov processes Davis 1993 and Stochastic hybrid systems Hu et al. 2000 . The most important difference among the models lies in where the randomness is introduced Pola et al.
