Stability and Stabilization of T–S Fuzzy Systems With a Periodic Variable Delay via Monotone Delay-Interval-Based Functional

The stability and stabilization problems for T–S fuzzy systems with a periodic variable delay are analyzed in this article. First, an improved delay-dependent reciprocally convex inequality is presented to deal with the periodic variable delay, which contains some existing results. Second, according to the monotonicity of the delay interval, the interval of each period is divided into a monotonically increasing interval and a monotonically decreasing interval, and different looped functionals are constructed on the two intervals. A new monotone delay-interval-based functional is presented to introduce more delay information and system state information on the basis of augmented functional and looped functional methods. Then, a generalized memory controller is designed to assure robust stabilization of the system by considering the variable delay and its bounds, which is more general than conventional controllers. Finally, some examples are shown to elaborate on the feasibility and validity of the obtained results.