Improved Stability of Time-Delayed Linear Systems Based on Delay-Interval-Dependent LKFs

The Lyapunov-Krasovsky function(LKF) approach has been widely used to obtain delay-dependent stability results for linear systems with time-varying delays. This approach consists in selecting an LKF and deriving linear matrix inequality (LMI) conditions that guarantee the negativity of its time derivative. It is reasonable to expect that using different LKFs for different delay intervals can lead to improved results. Recently, a few stability results utilizing this idea have been reported. This paper proposes a new method for selecting an LKF based on this approach and presents an LMI condition that guarantees system stability. Finally, the effectiveness of the proposed results is demonstrated through two well-known examples.