New method for stability of systems with time-varying delay via improved free-matrix-based integral inequality

摘要

This paper concerns the stability problem of systems with time-varying delay. A single integral of the second-order derivative is introduced to Lyapunov-Krasovskii functional for considering more delay-cross relationships. The improved free-matrix-based integral inequality is used to estimate the derivative of double integral of the second-order derivative. Some less conservative stability criteria for systems with time-varying delay are deduced in terms of linear matrix inequalities. Finally, a example is provided to demonstrate validity and superiority of the proposed method.