Fuzzy mixed H2/H℞ optimized design of decentralized control for nonlinear interconnected dynamic delay systems

Each subsystem of a nonlinear interconnected dynamic delay system (NIDDS) is first approximated by a weighted combination of L transfer function delay systems (TFDSs). The H₂-norm of the difference between the transfer function of the reference model and the closed-loop transfer function of the kth TFDS of subsystem i is then minimized to obtain a suitable frequency response. Because the output disturbance of the kth TFDS, including the interconnections coming from the other subsystems, the approximation error of the ith subsystem, and the interactions resulting from the other TFDSs, is not small and includes various frequencies, the H_infin-norm of the weighted sensitivity function between the output disturbance and its corresponding output of the kth TFDS is simultaneously minimized to attenuate its effect. In addition, an appropriate selection of the weighted function for the sensitivity can reject the specific mode of the output disturbance. Finally, the stability of the overall system is verified by the concept of L₂ ⁿ-stable with finite gain.