Practical stability criteria for large-scale nonlinear stochastic systems by decomposition and aggregation

In this paper, the concept of practical stability is extended for the large -scale stochastic systems of the Ito-Doob type. The concept of vector Lyapu nov-like functions coupled with the decomposition-aggregation techniques ar e utilized to develop a comparison principle and, sufficient conditions are established for various types of practical stability criteria in the p-th mean and in probability of the equilibrium state of the system under the st ochastic structural perturbations. This framework of decomposition and aggr egation is ideally suited for reducing the dimensionality problem arising i n testing large-scale systems for the concepts of convergence and stability . The results provide new stability tests for stochastic processes arising in various decentralized control, extremal regulation., adaptation, and par ameter estimation schemes.