New H_∞ control approaches for interval time-delay systems with disturbances and their applications

In this paper, the H_∞ performance and control problems for linear systems with interval state or input delays and disturbances are investigated. In order to exploit more information on the delay range, the quadruple -integral terms and quadratic forms of triple integrals are introduced into the Lyapunov-Krasovskii functional (LKF). Particularly, an improved integral inequality is developed for estimation of the cross terms in triple-integral type, which displays significant improvement over the Wirtinger inequality. As a result, a less conservative H_∞ performance criterion is derived without requiring many slack variables. Based on the criterion, the H_∞ controller design approaches are obtained. Besides the numerical examples, the applications to the practical systems are also provided to illustrate the effectiveness of the proposed approaches.