Robust stability analysis of uncertain T‐S fuzzy systems with random time‐varying delay and packet dropouts

Abstract In this study, we explore the robust control for uncertain T‐S fuzzy systems with random time‐varying delay and packet dropouts. The novel fuzzy model is presented to account for the stochastic nature of delays. A new Lyapunov–Krasovskii functional (LKF) is developed upon a delay decomposition technique. Less conservative results are obtained by segmenting the delay interval and considering the probability distribution within each segment. Once the time‐varying delay is known, conservatism is further reduced. We derive two sufficient criteria using reciprocally convex inequalities. A new delay‐derivative dependent method is proposed. Unlike previous research, this approach effectively incorporates delay derivative information to build the system with stochastic time‐varying delay. The superiority of our approach is thoroughly demonstrated by simulations involving three examples as well as a model of truck‐trailer.