Decentralised variable structure observers for nonlinear time delay systems with unknown interconnections

Decentralised variable structure observers are proposed for a class of nonlinear time delay interconnected systems. The nonlinear interconnections are unknown and time delayed. It is not required that the bounds on the uncertainties in the isolated subsystems are functions of the system outputs. Unlike much of the existing work where the designed observer is an interconnected system, the observers designed in this paper are a set of decoupled dynamics and thus decentralised, which is convenient for practical design. Based on the Lyapunov Razumikhin approach, sufficient conditions are derived such that the corresponding error dynamics are asymptotically stable. The delays are time varying, and there is no limitation on the rate of change of the time delays.