Adaptive Robust Control for Stochastic Systems With Unknown Interconnections

This article considers the decentralized stabilization problem of stochastic interconnected systems. The considered stochastic systems simultaneously contain unknown interconnections, power integrator dynamics, and time-varying delays. First, both state and output feedback controllers are presented for the stochastic interconnected nonlinear systems. Novel barrier Lyapunov–Krasivskii functions are used for the stability analysis of the proposed method. Second, fuzzy systems are adopted to approximate the complex and unknown dynamics in the systems with guaranteed compact set conditions. Based on barrier functions and switching mechanism, it is strictly proved that all the states will always remain in a compact set. Third, an adaptive compensator is presented to handle the resulting errors from input quantization, which finally renders asymptotic stability of the whole interconnected systems. Simulations are conducted to verify the main results.