Delay-dependent robust and reliable fuzzy hyperbolic decentralized control for uncertain nonlinear interconnected systems

This paper develops the delay-dependent robust and reliable H ∞ fuzzy hyperbolic control for nonlinear large-scale interconnected systems with parameter uncertainties. Firstly, the modeling method of fuzzy hyperbolic model (FHM) is given for the general large-scale interconnected systems. The main advantages of using FHM over T–S fuzzy model are that neither premise structure identification nor completeness design of premise variables space is needed. Therefore the required computational effort is less than that of using T–S fuzzy model, especially when a lot of fuzzy rules are needed to model complex nonlinear systems. Then according to the Lyapunov direct method and the decentralized control theory of large-scale interconnected systems, linear matrix inequality (LMI)-based conditions with some free weighting matrices are derived, which guarantee the closed-loop interconnected systems to be robustly stable with the H ∞ performance even in the presence of some possible actuator failures. Moreover, precise failure parameters of actuators are not required, and the only requirements are the lower and upper bounds of failure parameters. The restriction that the derivative of the time-varying delay is smaller than one is removed. Therefore, the results obtained are less conservative. Three simulation examples are provided to show the effectiveness of the proposed approach.