Stability analysis of linear systems with two delays of overlapping ranges

In this paper, a delay-dependent stability criterion is derived for linear time-delay systems with two constant delays having overlapping ranges. This overlapping feature of the delays is exploited in delay-dependent analysis of the system using Lyapunov–Krasovskii approach. The developed treatment of the delays reduces conservatism in analysis compared to the approaches treating the delays individually. Numerical examples are used to demonstrate the less conservativeness of the derived criterion.