Mixed H2 /H∞ optimization with discrete smith predictor for fuzzy decentralized control of nonlinear interconnected discrete dynamic systems with large delay

Each subsystem of a nonlinear interconnected discrete dynamic delayed system is approximated by a weighted combination of L pulse transfer function delayed systems (PTFDS). To deal with large time-delay of the controlled system with acceptable performance, a two-degree-of-freedom control is designed. At beginning, the H₂ - norm of the difference between the transfer function of a reference model and the closed-loop transfer function of the jth PTFDS of subsystem i is minimized to obtain a suitable frequency response. In addition, the H_∞ - norm of the weighted sensitivity function between the output disturbance and its corresponding output of the jth PTFDS is simultaneously minimized to reduce its effect. In summary, the proposed control not only accomplishes the above mentioned optimizations but also attenuates the effect of time delay. Furthermore the comparisons between with and without discrete Smith predictor are presented. The main contributions of this paper are three folds. First, the large nominal time-delay is compensated by a discrete Smith predictor. Secondly, the proposed control can achieve the suitable response of the closed loop system with the attenuation of output disturbance and time varying delay. Thirdly, an observer is not needed and the discrete controller is more suitable for the implementation.