Exponential stabilization of switched stochastic dynamical networks

A switched stochastic dynamical network (SSDN) model will firstly be formulated in this paper, which considers two mutually independent switching signals including individual node switching and network topology switching. In the proposed SSDN model, the stochastic perturbation is described by multi-dimensional Brownian motion, and the switching signals are arbitrary under the constraint of the average dwell time. A multiple Lyapunov function is utilized to cope with the switching problem. A single controller is then designed for the exponential mean square stabilization for SSDNs. The coupling matrix of the SSDN can be assumed to be irreducible symmetric or irreducible asymmetric. The obtained criteria are given in terms of linear matrix inequalities, which can be solved efficiently by standard software packages. Numerical examples, including small-world and scale-free networks, are exploited to illustrate the effectiveness of the theoretical results. It can be observed from the examples that our results are also applicable to large-scale dynamical networks. © 2009 IOP Publishing Ltd and London Mathematical Society.