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.

[1]  John Lygeros,et al.  Towars a Theory of Stochastic Hybrid Systems , 2000, HSCC.

[2]  Anders Rantzer,et al.  Piecewise linear quadratic optimal control , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[3]  John Lygeros,et al.  Toward a General Theory of Stochastic Hybrid Systems , 2006 .

[4]  Anders Rantzer,et al.  Computation of piecewise quadratic Lyapunov functions for hybrid systems , 1997, 1997 European Control Conference (ECC).

[5]  Daniel Liberzon,et al.  Switching in Systems and Control , 2003, Systems & Control: Foundations & Applications.

[6]  S. Sastry,et al.  Towars a Theory of Stochastic Hybrid Systems , 2000, HSCC.

[7]  J. Hespanha.  Modelling and analysis of stochastic hybrid systems , 2006 .

[8]  G. Smirnov.  Introduction to the Theory of Differential Inclusions , 2002 .

[9]  S. Lalley.  RENEWAL THEORY , 2014 .

[10]  Manuela L. Bujorianu,et al.  Extended Stochastic Hybrid Systems and Their Reachability Problem , 2004, HSCC.

[11]  John Lygeros,et al.  Stochastic Hybrid Systems: A Powerful Framework for Complex, Large Scale Applications , 2010, Eur. J. Control.

[12]  S. Pettersson,et al.  Stability and robustness for hybrid systems , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[13]  J. Leth,et al.  On formalism and stability of switched systems , 2012, Journal of Control Theory and Applications.