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This paper discusses the asymptotic stability of nonlinearly perturbed dynamical systems. A suitable delay-dependent Lyapunov–Krasovskii functional (LKF) including triple integral terms has been formulated in the way that the proposed time-varying dynamical model is asymptotically stable. Using the method of integral inequality, new sufficient stability conditions have been accomplished by way of linear matrix inequalities (LMIs). Furthermore, the novel stability conditions are utilized with many standard practical control system such as power system (PS) with one-area load frequency control (LFC) and two-area LFC, DC motor system and heat exchanger model. Also, the maximum allowable delay bounds (MADBs) are acquired, and it is compared through the time-domain simulations.