A generalized multiple-integral inequality based on free matrices: Application to stability analysis of time-varying delay systems

Abstract

© 2022 Elsevier Inc.This study proposed a novel generalized multiple-integral inequality based on free matrices in a quadratic form of an augmented vector stacked with a state and its derivative, with generalization realized in terms of both the integration and bounding orders. Further, additional cross information on the two entries of the augmented vector was considered using structured free matrices. Consequently, the proposed generalized multiple-integral inequality guaranteed tight bounds with various existing multiple-integral inequalities included as special cases. Moreover, it was observed that higher the orders of the generalized multiple-integral inequalities and Lyapunov–Krasovskii functions, less conservative the stability criterion obtained. Furthermore, three recognized numerical simulations were presented to confirm the improved effectiveness of the stability criterion derived through the proposed generalized multiple-integral inequality than in previous studies.