Hierarchical stability conditions of systems with time-varying delay

This paper studies the stability problem of time-varying delay systems. Firstly, By con-structing a delay-product Lyapunov-Krasovskii functional, a stability criterion is estab-lished, where the advantages of convexity properties are being exploited. This stability cri-terion in terms of linear matrix inequality (LMI) can be checked exactly using an improved negativity condition of quadratic polynomials. It is demonstrated in the numeric examples that the proposed method can greatly reduce the conservativeness without leading to in-crease the number of decision variables. (c) 2021 Elsevier Inc. All rights reserved. Time delays, known as a source of oscillation and instability for most practical systems, has received massive attentions in the past few decades [1?9] . As stability is a basic requirement for a control system, seeking maximal region of the delay has become a hot topic. Lyapunov approach is extensively adopted in the stability analysis of time-varying delay (TVD) systems. Based on the framework of Lyapunov-Krasovskii functional (LKF) and linear matrix inequality (LMI), many approaches have been proposed to reduce the conservativeness of stability analysis, for example, model transformation [10] , integral inequality techniques [11?13] and free-weighting matrix approach [14] . As is well known, the conservativeness of Lyapunov approach comes from the following two aspects: the choice of LKF