Stability analysis of systems with two additive time-varying delay components via the zero-valued equations

In the case of introducing the double integral state into the augmented vector, the time-varying delay square terms in the derivative of the Lyapunov-Krasovskii functional (LKF) usually needs to be treated with some negative-determination lemmas in the existing literatures, which are only sufficient conditions and are conservative to some extent. In this work, by introducing some new augmented variables, some zero-valued equations are proposed to avoid the appearance of these time-varying delay square terms, which have great potential to reduce the conservatism. Then, a stability result in terms of linear matrix inequalities is derived via the presented zero-valued equations. Finally, a representative example is provided to testify the usefulness and meliority of the raised stability criterion.