Event‐triggered output quantization control for asynchronously switched interval type‐2 fuzzy systems

Abstract

This article considers exponential stabilization (ES) of switched interval type‐2 (SIT2) fuzzy systems with asynchronous switching control. The SIT2 fuzzy system switches from one mode to another according to transition probabilities (TPs). A general SIT2 fuzzy quantized event‐triggered output controller (QETOC) is designed to save the communication resources. The QETOC employs distinctive membership functions from those of the IT2 fuzzy model and switches with mode‐pendent switching delay, which is more practical than asynchronously switched control techniques with a common switching delay and control schemes without TP. By designing discretized multiple Lyapunov function (DMLF) and using convex combination technique, sufficient conditions formulated by linear matrix inequalities (LMIs) are obtained to ensure that the DMLF does not ‘jump high’ at the moment of switching, and hence the conservatism of obtained results is significantly reduced since no additional dwell time is needed for the stabilization. It is discovered that the SIT2 fuzzy system is not necessary to be unstable on mismatched intervals, and it can be unstable on matched intervals. The advantages of theoretical analysis are verified by numerical simulations, and the classical assumption that each subsystem is unstable on mismatched intervals is conservative for control design.