Robust L 1 filtering for a nonlinear system described by a Takagi–Sugeno fuzzy model with distributed delay and probabilistic interval delay

This study concentrates on investigating the robust L 1 filtering problem for a nonlinear system described by a Takagi–Sugeno fuzzy model with distributed delay and time-varying delay. The stochastic distribution characteristic of the network-induced delay is considered, and the Bernoulli distributed sequence is utilized to represent the probability distribution of the delay appearing in certain intervals. Firstly, according to parallel distributed compensation, an augmented system with stochastic variable is established. Next, the L 1 performance criterion guaranteeing the mean-square asymptotic stability of the fuzzy filtering error system is formulated, by taking advantage of a novel Lyapunov–Krasovskii function and the integral inequality method. Thirdly, the robust L 1 filtering problem is converted into a convex optimization problem and solved using the linear matrix inequality technique. Finally, the results are provided by numerical simulation to certify the effectiveness of the designed filter.