Modeling and Control of Discrete-Time T-S Fuzzy Systems Subject to Stochastic Packet Dropouts

The aim of this article is to address the modeling and control problems of discrete-time Takagi–Sugeno (T-S) fuzzy systems that are affected by stochastic packet dropouts. To describe the stochastic behavior of packet dropout between the sensor–controller and controller–actuator, a consecutive packet dropout model is employed. By treating consecutive packet dropouts (CPDs) as an extension of the transmission interval, the considered T-S system is transformed into a stochastic system with bounded stochastic input delay. In addition, a novel equivalent model for the closed-loop system is proposed, which captures the nonuniform distribution of the input delay caused by CPDs. Using the obtained equivalent model, it is possible to evaluate the probability distribution of each stochastic input delay value using the formula for total probability. This approach allows us to fully consider the probability information of CPDs in subsequent stability analysis and controller design. Based on this model, delay-probability dependent stability conditions are derived using stochastic Lyapunov functionals, and controller design conditions are also provided. Finally, the correctness and conservatism reduction of the proposed design method are demonstrated using numerical examples of two physical systems described by T-S fuzzy models.