Stability certification of large scale stochastic systems using dissipativity

In this paper, we analyse the stability of large-scale nonlinear stochastic systems, represented as an interconnection of lower-order stochastic subsystems. Stochastic stability in probability and noise-to-state stability are addressed, and sufficient conditions for the latter are provided. The method proposed proves network stability by using appropriate stochastic passivity properties of its subsystems, and the structure of its interactions. Stability properties are established by the diagonal stability of a dissipativity matrix, which incorporates information about the passivity properties of the systems and their interconnection. Next, we derive equilibrium-independent conditions for the verification of the relevant passivity properties of the subsystems. Finally, we illustrate the proposed approach on a class of biological reaction networks.