Here, by integrating continuous control and dynamic event-triggered impulsive control (DETIC) based on a piecewise function ratio framework, a hybrid control strategy is developed to solve prescribed-time stabilization (PTS) for nonlinear systems. Different from the traditional methods, the designed hybrid control strategy is rooted in DETIC, and the designed triggering mechanism allows the impulsive triggering instants to be dynamically adjusted, with the Zeno behavior being eliminated. The dynamic event-triggered mechanism (DETM) is utilized to determine the instants of impulses, thereby reducing unnecessary control execution and enhancing control efficiency. Moreover, the proposed approach is utilized for the master-slave synchronization of the Lorenz system, and numerical experiments are conducted to demonstrate the practicality and efficiency of the developed hybrid control scheme.

This article addresses the prescribed-time stability (PTS) problem for a class of nonlinear strict-feedback systems subject to unknown disturbances. Herein, a novel backstepping-sliding-mode (BSM) composite control structure is proposed: a dynamic time-varying sliding-mode surface is integrated into the final step of the backstepping design, effectively suppressing matched disturbances and simplifying the implementation complexity. Specifically speaking, 1) for systems with known nonlinear terms, time-varying gains are directly embedded within the backstepping virtual control laws to achieve PTS; 2) for the case of unknown nonlinear terms, by combining adaptive laws with the BSM framework, the controlled system is guaranteed to converge within the prescribed-time and maintain globally stability thereafter. Moreover, the prescribed time $T_p$ is designer-prespecified and does not depend on initial conditions or controller gains. Finally, two numerical simulation examples validate the convergence performance and robustness of the proposed approaches.

Researchers have reported on prescribed-time stability (PTS) for delay systems, but they do not take into account the significant impulses phenomenon and focus on only single delay. To tackle these two aspects, we aimed to investigate PTS issues for nonlinear impulsive systems with multiple time-varying delays and uncertainties. By the Lyapunov-Krasovskii functional method, PTS criteria were established for multi-delay systems. Specifically speaking, an adaptive control strategy was proposed for multi-delay systems to achieve PTS through the integrated design of time-varying delay compensation and uncertainty handling, which could ensure system states and control inputs to precisely converge to the origin within the prescribed time frame. Furthermore, the proposed method significantly enhanced the system's robustness against time-varying delays and uncertainties, thus overcoming the limitations of traditional methods in terms of convergence time and disturbance rejection capability. Finally, a simulation result was given to verify the feasibility and effectiveness of the proposed method.

To present, there has been much research on prescribed-time stability (PTS) of uncertain systems, but the significant impulse factor has not been considered. Therefore, in this paper, the stability control problem of a class of impulsive systems with uncertainties within the prescribed time was studied by the Lyapunov functional approach. The comparison lemma was utilized and iteration was carried out for each impulsive interval to prove the PTS theorem for general impulsive systems with uncertainties. In addition, a time-varying adaptive controller in combination with the backstepping method was constructed for PTS of special impulsive strict-feedback systems with uncertainties, breaking through the dependence of traditional methods on uncertain parameters. Finally, a simulation example was used to verify the effectiveness and feasibility of the proposed method.

We explored the prescribed-time stability (PTSt) of impulsive piecewise smooth differential systems (IPSDS) based on the Lyapunov theory and set-valued analysis technology, allowing flexibility in selecting the settling time as desired. Furthermore, by developing a feedback controller, we employed the theoretical results to evaluate the synchronization behavior of impulsive piecewise-smooth network systems (IPSNS) within a prescribed time frame and obtained novel criteria to guarantee the synchronization objective. A numerical example was presented to validate the accuracy of the results.