Stability analysis for some classes of nonlinear systems with distributed delay

Under study is the stability of Persidskii systems with distributed delay. We assume that the sector-type functions on the right-hand sides of the system are essentially nonlinear. Also, we propose some original construction of the Lyapunov–Krasovskii functional of use in deriving new asymptotic stability conditions of the zero solution. The approach is applied to the stability analysis of the Lurie indirect control system and a mechanical system with essentially nonlinear positional forces. Using some development of the averaging method, we obtain the conditions that guarantee stability under nonstationary perturbations with zero mean values for the systems under study.