Exponential H∞ synchronization of switching fuzzy systems with time-varying delay and impulses

Abstract

This paper studies the problem of exponential H∞ synchronization of switching fuzzy systems with time-varying delay and impulses via maximum, minimum dwell time. The switching fuzzy model has locally Takagi and Sugeno (T–S) fuzzy models and switches them according to states, external variables and/or time. By introducing the concept of maximum, minimum dwell time and a modified two-side direction relation between the number of switchings and the maximum, minimum dwell time, a normal L2 norm bound constraint is derived. By using the matrix decomposition method and reciprocal convex combination, and combining with the Wirtinger-based inequality, which gives a sharper upper bound than the Jensen's inequality, some new sufficient criteria are obtained to guarantee that the error system without impulses and with impulses is globally exponentially stable with an H∞ performance index γ, respectively. Three illustrative examples are provided to show the effectiveness of the results.