Stability analysis of a class of coupled time-varying differential-difference systems with time-delay and sector-type nonlinearities

Abstract

This paper presents novel stability results for a class of nonlinear time-varying coupled delay differential-difference (CDD) systems with sector-type nonlinearities. Using the comparison method for positive systems and suitably constructed Lyapunov-Krasovskii functionals, we derive explicit criteria for both asymptotic and exponential stability of the system’s zero solution. When applied to the class of time-invariant switched CDD systems, these results lead to verifiable stability conditions that both encompass and improve upon previously obtained ones. The proposed framework is further applied to establish new stability results for time-varying neutral-type delay systems with sector-type nonlinearities, as well as for time-varying Lurie systems with nonlinear output feedback controls. The effectiveness of the approach is illustrated through numerical examples.