$H_{\infty }$ Fuzzy Control of Nonlinear Systems Under Unreliable Communication Links

This paper investigates the problem of $H_{\infty }$ fuzzy control of nonlinear systems under unreliable communication links. The nonlinear plant is represented by a Takagi--Sugeno (T--S) fuzzy model, and the control strategy takes the form of parallel distributed compensation. The communication links existing between the plant and controller are assumed to be imperfect (that is, data packet dropouts occur intermittently, which appear typically in a network environment), and stochastic variables satisfying the Bernoulli random binary distribution are utilized to model the unreliable communication links. Attention is focused on the design of $H_{\infty }$ controllers such that the closed-loop system is stochastically stable and preserves a guaranteed $H_{\infty }$ performance. Two approaches are developed to solve this problem, based on the quadratic Lyapunov function and the basis-dependent Lyapunov function, respectively. Several examples are provided to illustrate the usefulness and applicability of the developed theoretical results.