Delay-dependent stability analysis of nonlinear truck-trailer systems based on non-fragile memory sampled-data via fuzzy control

In this paper, the problem of a truck-trailer reversing to a given position at any initial position is studied, which is the optimal control of the nonlinear system in mathematical model. We describe this system by means of the T-S fuzzy rule and extend the system to general fuzzy time-varying delay systems. Non-fragile controller is designed for the time-varying delay T-S fuzzy systems on the basis of aperiodic memory sampling control. An improved time-delay-dependent Lyapunov–Krasovskii functional (LKF) is proposed, which covers all the information of the sampling interval and the time-delay information in the system and controller, which greatly reduces the conservativeness of the results. On this basis, we use the advanced technique of treating integral inequality to estimate the derivative term of Lyapunov function. The weighted matrix introduced in the integral inequality makes our results more flexible, which will be illustrated in the practical examples in the last section. Using the linear matrix inequalities (LMIs) method, a set of sufficient conditions is established to guarantee the system to be stable.