Constructing Lyapunov–Krasovskii functionals for some classes of switched positive systems with infinite delay

The problem of absolute stability is investigated for a switched positive Persidskii system with infinite delay. With the aid of a special construction of Lyapunov–Krasovskii functional, sufficient conditions of absolute stability are derived. These conditions are formulated in terms of the existence of a positive solution for an auxiliary system of linear algebraic inequalities. It is shown that a similar construction of Lyapunov–Krasovskii functional can be used for the permanence analysis for a Lotka–Volterra model of popolation dynamics.