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 Lyapunov-like functions coupled with the decomposition-aggregation techniques are 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 stochastic structural perturbations. This framework of decomposition and aggregation is ideally suited for reducing the dimensionality problem arising in 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 parameter estimation schemes.