Delay-dependent Stability Criteria for Linear Systems with Two Additive Time-varying Delays

This paper studies the stability problem of linear systems with two additive time-varying delays. Firstly, a modified Lyapunov-Krasovskii functional (LKF) is constructed involving the delay-dependent non-integral items and some augmented single-integral items. Secondly, based on the improved LKF, a stability criterion is derived via the generalized free-matrix-based inequality application, which is less conservative than some recent existing ones. Thirdly, a generalized refinement of allowable delay set removed some impossible delay subsets is proposed to further reduce the conservatism of the stability criterion. Finally, a numerical example and an application of the load frequency control for a single area power system are presented to show the effectiveness of the proposed approach.