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.

Automated summary

This paper investigates the absolute stability problem for positive Persidskii systems with delay, proposes a special construction method for diagonal Lyapunov-Krasovskii functionals, and derives a criterion for the existence of such functionals guaranteeing the absolute stability, as well as obtaining sufficient conditions for a family of time-delay Persidskii systems to construct a common diagonal Lyapunov-Krasovskii functional. The efficiency of the developed approaches is demonstrated through four examples.