The authors consider an interconnected large-scale stochastic system consisting of subsystems given by the following nonlinear stochastic differential equations
where , , are the states of the th subsystem , , is the control of the th subsystem, , are -dimensional standard Wiener processes, , are -dimensional smooth row vector functions with , and , are -dimensional smooth interconnections between the th subsystem and th subsystem with . The interconnections are bounded by strong nonlinear functions that contain first-order and higher-order polynomials as special cases.
The authors present a decentralized control such that the closed-loop interconnected system (1) is globally asymptotically stable in probability for all admissible interconnections. They show that the decentralized global stabilization via both state feedback and output feedback can be solved by a Lyapunov-based recursive design method.