A relaxed binary quadratic function negative-determination lemma and its application to neutral systems with interval time-varying delays and nonlinear disturbances

This paper considers the stability problem of neutral systems with interval time-varying delays and nonlinear disturbances. Firstly, an augmented vector containing two double integral terms is introduced into the Lyapunov-Krasovskii functional (LKF). In this case, a binary quadratic function with discrete and neutral delay arises in the time derivative. To gain the negativity condition of such function, by taking full advantage of the idea of partial differential of the binary quadratic function and Taylor's formula, a relaxed binary quadratic function negative-determination lemma with two adjustable parameters is proposed, which contains the existing lemmas as its special cases and shows the great potential of reducing conservatism for the case where the tangent slope at the endpoint is far from zero. Then, based on the improved lemma, more relaxing stability criteria have been obtained via an augmented LKF. Finally, two classic numerical examples are given to attest the effectiveness and strengths of the obtained stability criteria.