Stability and L1

In this paper, the problems of stability and L 1 -gain performance analysis for positive delay systems with large delay period are investigated. The maximum allowed delay bound is expanded. Under the limitations of frequency and length rate of the large delay period, the sufficient conditions guaranteeing stability of the considered system are obtained and the weighted L 1 -gain performance analysis is established. Detailed proofs are presented by using co-positive Lyapunov–Krasovskii functional candidates with large delay integral terms and the switching method; where the switching method involves transforming the original system into a positive switched delay system. All the obtained conditions can be solved via linear matrix inequalities. Finally, the validity of the proposed results is illustrated by a numerical example