Adaptive-observer-based controller for distributed control systems with lipschitz nonlinearities and time delays

Observer-based controller is designed for distributed control systems (DCSs) that have intrinsic time delays in each subsystem. Also, subsystems are coupled among themselves, which give rise to delays in interactions of subsystems. DCSs have some nonlinearities, which satisfy generalized Lipschitz condition and there are some unknown parameters. By choosing an appropriate Lyapunov Krasovskii functional, linear matrix inequality (LMI) based result is derived. Using this result, it is shown that the designed controller stabilizes the system by adapting for unknown parameters and reconstructing system states which are not available at output. The efficacy of the result is demonstrated through an illustrative example.