Novel stability analysis for time-delay systems via two new lemmas and genetic algorithm

This paper studies the stability problem of time-delay systems and proposes three new methods. First, A new negative definite lemma with two parameters (2-parameter NNDL) for quadratic functions is put forward. It can be used to handle linear matrix inequalities (LMIs) containing time-delay square terms in system stability analysis. Different from previous studies that have no or only one adjustable parameter, this lemma include two adjustable parameters, leading to better estimation performance. Second, aiming at these two adjustable parameters, a genetic algorithm is proposed to select the optimal two parameters, so as to obtain the optimal stability results. Third, a new Lyapunov function is proposed, which introduces free matrices into the quadratic form of Lyapunov function. It helps to reduce the conservatism of LMIs. Moreover, no scaling is needed after differentiating this structure, that is, no inequality estimation is required, which makes the final LMI estimation tighter. Finally, simulation results verify the effectiveness of the three proposed methods.