Delay-dependent stability approach for nonlinear descriptor mixed time-varying delays systems

In this paper, the asymptotical stability analysis problem of nonlinear neutral systems with mixed time-varying delays is investigated. By using the Lyapunov-Krasovskii type of descriptor functional, including the triple integral inequalities and free weighting matrix technique, a less conservative delay-decomposition stability criterion is formulated. The main contribution of the proposed method is to transform the original system to an equivalent descriptor form. The lower and upper bounds of integral terms of each delay interval are divided, according to each Lyapunov-Krasovskii functional, into two equidistant subintervals. In order to reduce the conservatism, a new delay-dependent stability condition is derived in terms of Linear Matrix Inequalities (LMIs) technique. Finally, a numerical example illustrates the effectiveness of the proposed stability analysis approach.