Robust stability of linear systems with interval time-varying delay via HPLKFs

The delay-dependent stability problem for systems with time-delay varying in an interval is addressed through a new method of homogeneous polynomial forms. Based on Lyapunov-Krasovskii theory and homogeneous polynomial forms, appropriate homogeneous polynomial Lyapunov-Krasovskii functional (HPLKF) is introduced to establish some improved criteria of the stability interval. A tighter upper bound of the derivative is estimated, which has an advantage over some existing ones in the literature due to the fact that it involves extended matrix and is less conservative, which is established theoretically. Finally, two illustrative numerical examples are given to demonstrate the advantages and applicabilities of the proposed results.