Event-triggered fuzzy control of nonlinear systems with its application to inverted pendulum systems

This paper is concerned with the event-triggered fuzzy control design and its application to an inverted pendulum system. First, all of the introduced time-varying delay information from the inverted pendulum system and event-triggered mechanism is considered in the stability analysis. The interval of the time-varying delay is then divided into l nonuniform subintervals by utilizing an improved delay-partitioning technique. Information on each subinterval is processed by employing a reciprocally convex method. The proposed delay-dependent stability condition of the inverted pendulum system is determined to be considerably less conservative than the existing results in the literature, and the reduction in the conservativeness becomes progressively noticeable as the delay partitioning number l becomes progressively thinner. Moreover, by employing the parallel distributed compensation law, conditions sufficient for the resulting fuzzy controller and the event-triggering fuzzy controller are presented for the nonlinear inverted pendulum system. Finally, the advantages and effectiveness of the proposed design schemes are demonstrated by three simulation examples.