Robust H∞ fuzzy control of discrete nonlinear networked control systems: A SOS approach

The paper presents a methodology for designing a robust mode delay dependent H∞ controller for nonlinear discrete-time networked control systems (NCSs). The nonlinear systems are modelled by a Takagi-Sugeno fuzzy model, and network induced delays between sensors and controllers are modelled by a finite state Markov process. The fuzzy controller׳s membership functions are allowed to be different from the plant׳s membership functions, and also the controller׳s premise variables are allowed to be the delayed plant׳s premise variables to accommodate the fact that the plant׳s premise variables are transmitted via the network. To reduce the conservatism of the controller design, the membership functions of the plant and the fuzzy controller are incorporated into the controller design. Based on the Sum Of Square (SOS) approach, sufficient conditions for the existence of the controller are derived in terms of SOS inequalities, which are then solved by YALMIP. Comparisons between the proposed design methodology and the existing controller designs are made using a numerical example.