Adaptive sliding mode observer–based decentralized control design for linear systems with unknown interconnections

In this study, a class of linear interconnected systems with unknown interconnections between subsystems is considered. Primarily, an observer is designed to reconstruct an equivalent of unknown interconnections that are considered uncertain. A decentralized controller will be thereafter designed to keep the stability of the original system when the estimated system is at risk of instability due to the lack of information on interconnections. To design a decentralized observer and to estimate states of each subsystem, without knowing the relations between subsystems, a combination of Luenberger observer along with the adaptive sliding mode technique is used. Because the interconnected system might generally be unstable, a state feedback controller is used to stabilize each subsystem using estimated states together with the output of other subsystems. The stability of the system and the convergence of the discrepancy between real states and that of estimated are guaranteed, gaining the Lyapunov theory. Simulation results signify that the proposed decentralized controller based on a new adaptive sliding mode observer is highly efficient for linear interconnected systems with unknown interconnections.