Decentralized adaptive robust control for a class of large-scale systems including delayed state perturbations in the interconnections

The problem of decentralized stabilization is considered for a class of large-scale time-varying systems with delayed state perturbations in the interconnections. In this note, the upper bounds of the uncertainties in the interconnections are assumed to be unknown. The adaptation laws are proposed to estimate such unknown bounds, and by making use of their updated values, a class of decentralized memoryless state feedback controllers is constructed. Based on Lyapunov stability theory and Lyapunov-Krasovskii functional, it is shown that the solutions to the resulting adaptive closed-loop large-scale time-delay system can be guaranteed to be uniformly ultimately bounded. Finally, a numerical example is given to demonstrate the validity of the results.