This paper considers weakly and strongly input-to-state stability (ISS) of a discrete-time time-varying delayed system with synchronous impulses and switches. By employing the uniformly asymptotically stable function and mode-dependent dwell time conditions, ISS criteria are derived using the Krasovskii and Razumikhin techniques. The time differences of the Krasovskii functionals or the Razumikhin functions can be mode-dependent and time-varying, which release constraints of some existing results. As subsequent results, we apply the derived ISS criteria to the multi-agent systems (MASs). Finally, two examples considering the quasi-consensus of MASs are given to verify the established results.

In this brief, the quasi-consensus issue is examined for fractional-order multi-agent systems (FROMASs) subject to both mixed delays and external disturbances, employing an impulsive pinning control (IPC) strategy. Unlike mainstream pinning strategies with fixed nodes or static rules, a dynamic pinning mechanism based on consensus error distances is proposed, which adaptively adjusts the set of pinned nodes at each impulsive instant. By integrating the Razumikhin method, Lyapunov stability theory, and the comparison system approach, sufficient conditions for achieving quasi-consensus of FROMASs are established. Moreover, the convergence bound of consensus errors is quantitatively estimated and shown to be explicitly determined by the intensity of external disturbances. This paper organically integrates the dynamic node pinning mechanism, FRO impulsive control, and Razumikhin stability analysis. It effectively handles mixed delays and external disturbances while significantly reducing control costs. Finally, numerical simulations show that the synchronization errors are strictly bounded within the threshold $M=13.6372$, which effectively validates both the proposed control scheme and the theoretical analysis.