New delay-dependent robust stability and stabilization for uncertain T-S fuzzy time-delay systems under imperfect premise matching

ZHANG Ze-jian(张泽健) ¹, HUANG Xian-lin(黄显林) ¹, BAN Xiao-jun(班晓军) ¹, Gao Xiao-zhi(高晓智) ²

(1. Department of Control Science and Engineering, Harbin Institute of Technology, Harbin 150001, China
2. Department of Automation and Systems Technology, School of Electrical Engineering,
Aalto University, Aalto 00076, Finland)

Abstract:To alleviate the conservativeness of the stability criterion for Takagi-Sugeno (T-S) fuzzy time-delay systems, a new delay-dependent stability criterion was proposed by introducing a new augmented Lyapunov function with an additional triple-integral term, which was firstly used to derive the stability criterion for T-S fuzzy time-delay systems. By the same approach, the robust stability issue for fuzzy time-delay systems with uncertain parameters was also considered. On the other hand, in order to enhance the design flexibility, a new design approach for uncertain fuzzy time-delay systems under imperfect premise matching was also proposed, which allows the fuzzy controller to employ different membership functions from the fuzzy time-delay model. By the numerical examples, the proposed stability conditions are less conservative in the sense of getting larger allowable time-delay and obtaining smaller feedback control gains. For instance, when the allowable time-delay increases from 7.3 s to 12 s for an uncertain T-S fuzzy control system with time-delay, the norm of the feedback gains decreases from (34.299 2, 38.560 3) to (10.073 3, 11.349 0), respectively. Meanwhile, the effectiveness of the proposed design method was illustrated by the last example with the robustly stable curves of system state under the initial condition of .

Key words:T-S fuzzy systems; time-delay systems; imperfect premise matching; stability; robust stability; linear matrix inequality (LMI); stabilization