Prescribed‐Time Stability Analysis of Control Systems With Hybrid Time‐Varying Delays

ABSTRACT This article investigates the prescribed‐time stability (PS) of complex systems with hybrid time‐varying delays (CSHTD) via a novel control strategy. In order to be more suitable for practical application, the internal delay, the self‐delay, and the neighboring delay of complex systems are distinguished in this article, and these time delays are considered as time‐varying functions. An appropriate control strategy is designed in this study to overcome the effects of the hybrid time‐varying delays. This strategy can make CSHTD achieve stability within any settling time, independent of control parameters and initial conditions. Next, a suitable global Lyapunov function of CSHTD is established, and a sufficient criterion for the PS of CSHTD is given by combining Lyapunov stability theory with Kirchhoff's matrix tree theorem. Finally, the PS of the coupled oscillators model with hybrid time‐varying delays via the control strategy is studied as an application, and the effectiveness of the proposed approach is verified by numerical simulations.