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.

Krishnamurthy et al. investigated the adaptive output feedback control for prescribed-time stability (PTS) of nonlinear uncertain systems on $[0,T)$, where $T>0$. However, there are special constraints on system structure, and the PTS issue is considered on a finite interval $[0,T)$. For systems without required constraints, the existing adaptive output feedback control seems not to be applicable; the PTS issue on $[0,\mathrm{\infty })$ is more practical than that on $[0,T)$. Motivated by the above, an improved observer and controller were proposed to achieve PTS for nonlinearly uncertain systems with lower-triangular linear growth condition on uncertainties. Compared with the existing work, we emphasized the subsequent contributions: 1) Relax the original structure constraint of objective system; 2) achieve PTS on $[T,\mathrm{\infty })$; and 3) keep the proposed controller bounded. The effectiveness of the controller was verified by numerical simulations across varying initial conditions and prescribed times.