Robust Stability and Stabilization Conditions for Nonlinear Networked Control Systems With Network-Induced Delay via T–S Fuzzy Model

Abstract

Robust stability and stabilization problems for a class of discrete-time nonlinear systems are studied in this article. The control signal is transmitted to the nonlinear systems through a lossy communication channel in which time-varying network-induced delay occurs. A Takagi–Sugeno (T–S) fuzzy model is used to represent the nonlinear systems. Using membership function boundary information, a novel membership-function-dependent (MFD) analysis approach is presented. Unlike most previous results, the proposed MFD analysis approach does not need to increase the number of slack variables to reduce conservatism. Combining auxiliary matrices and this approach, we propose some new fuzzy Lyapunov–Krasovskii functionals (FLKFs) that do not require the restrictions of positive definiteness imposed on Lyapunov matrices. Using the FLKF and MFD analysis approach, a sufficient condition in the form of linear matrix inequalities (LMIs) is developed to guarantee the stability of T–S fuzzy time-varying delay systems. Based on the results for stability, less conservative stabilization conditions are also derived. Finally, numerical examples show that less conservative results can be obtained by the proposed approach. The inverted pendulum system with state delay or network-induced delay is also studied to verify the effectiveness of the suggested approach.