On the existence of diagonal Lyapunov-Krasovskii functionals for a class of nonlinear positive time-delay systems

This work investigates the absolute stability problem for positive Persidskii systems with delay. Righthand sides of these systems are linear combinations of nonlinearities of a sector type. A special construction of diagonal Lyapunov-Krasovskii functionals is proposed and a criterion for the existence of such functionals guaranteeing the absolute stability is derived. Furthermore, sufficient conditions under which a common diagonal Lyapunov-Krasovskii functional can be constructed for a family of time-delay Persidskii systems are obtained. Four examples are presented demonstrating the efficiency of the developed approaches.(c) 2023 Elsevier Ltd. All rights reserved.