Robust decentralized adaptive control for interconnected systems with time delays

The problem of robust stabilization for a class of time-varying nonlinear large-scale systems subject to multiple time-varying delays in the interconnections is considered. The interconnections satisfy the match condition, and are bounded by nonlinear functions that may contain a high-order polynomial with a time delay. Without the knowledge of these bounds, we present adaptive state feedback controllers that are continuous and independent of time delays. Based on the Lyapunov stability theorem, we prove that the controllers can render the closed loop systems uniformly ultimately bounded stable. We also apply the result to constructing adaptive feedback controllers to stabilize a class of interconnected systems whose nominal systems are linear. Finally, several examples are given to show the potential of the proposed techniques.