This paper investigates input-to-state stabilizing control under denial-of-service (DoS) attacks in networked control systems. The goal is to ensure closed-loop stability despite the presence of DoS attacks, which prevent communication over the network. The paper characterizes the frequency and duration of DoS attacks under which input-to-state stability (ISS) can be preserved. A suitable scheduling of transmission times is determined to achieve ISS. The framework is flexible, allowing the designer to choose from various implementation options that balance performance and communication resources. Examples are provided to illustrate the analysis. The paper begins by discussing the increasing importance of cyber-security in networked systems. It highlights the difference between security in cyber-physical systems (CPSs) and general-purpose computing systems, noting that attacks in CPSs can have physical consequences. It then introduces the concept of DoS attacks, which aim to disrupt communication rather than manipulate data. The paper considers a sampled-data control system where the plant-controller communication is networked, and the attacker's objective is to induce instability by denying communication on measurement and control channels. The paper analyzes the system under DoS attacks, where the process evolves in open-loop according to the last transmitted control sample. The problem is to find conditions under which closed-loop stability can be preserved. The paper introduces a class of sampling logics that achieve ISS in the absence of DoS. It then extends this analysis to the presence of DoS attacks, considering the frequency and duration of attacks. The paper shows that the considered framework is flexible enough to allow the designer to choose from several implementation options that can be used to trade-off performance versus communication resources. The paper discusses the implications of DoS attacks on the system's stability and presents a detailed analysis of the conditions under which ISS can be preserved. It introduces a class of DoS signals and provides a main result showing that any control update rule attaining the conditions of Lemma 1 preserves ISS for any DoS signal that satisfies Assumption 1 and 2 with sufficiently large $\tau_D$ and T. The paper also discusses the disturbance-free case, where the analysis simplifies, and provides a corollary showing that the system is globally asymptotically stable (GAS) under these conditions. The paper concludes with a discussion of resilient control logics, including periodic sampling, event-based/periodic sampling, and self-triggering sampling. These logics are designed to adapt to the occurrence of DoS attacks and the closed-loop behavior, ensuring stability and performance. The paper provides examples to illustrate the analysis, including scenarios with sustained DoS attacks and varying periods and duty cycles. The results show that the proposed control strategies are effective in maintaining stability under DoS attacks, even when a significant portion of communication attempts are denied.This paper investigates input-to-state stabilizing control under denial-of-service (DoS) attacks in networked control systems. The goal is to ensure closed-loop stability despite the presence of DoS attacks, which prevent communication over the network. The paper characterizes the frequency and duration of DoS attacks under which input-to-state stability (ISS) can be preserved. A suitable scheduling of transmission times is determined to achieve ISS. The framework is flexible, allowing the designer to choose from various implementation options that balance performance and communication resources. Examples are provided to illustrate the analysis. The paper begins by discussing the increasing importance of cyber-security in networked systems. It highlights the difference between security in cyber-physical systems (CPSs) and general-purpose computing systems, noting that attacks in CPSs can have physical consequences. It then introduces the concept of DoS attacks, which aim to disrupt communication rather than manipulate data. The paper considers a sampled-data control system where the plant-controller communication is networked, and the attacker's objective is to induce instability by denying communication on measurement and control channels. The paper analyzes the system under DoS attacks, where the process evolves in open-loop according to the last transmitted control sample. The problem is to find conditions under which closed-loop stability can be preserved. The paper introduces a class of sampling logics that achieve ISS in the absence of DoS. It then extends this analysis to the presence of DoS attacks, considering the frequency and duration of attacks. The paper shows that the considered framework is flexible enough to allow the designer to choose from several implementation options that can be used to trade-off performance versus communication resources. The paper discusses the implications of DoS attacks on the system's stability and presents a detailed analysis of the conditions under which ISS can be preserved. It introduces a class of DoS signals and provides a main result showing that any control update rule attaining the conditions of Lemma 1 preserves ISS for any DoS signal that satisfies Assumption 1 and 2 with sufficiently large $\tau_D$ and T. The paper also discusses the disturbance-free case, where the analysis simplifies, and provides a corollary showing that the system is globally asymptotically stable (GAS) under these conditions. The paper concludes with a discussion of resilient control logics, including periodic sampling, event-based/periodic sampling, and self-triggering sampling. These logics are designed to adapt to the occurrence of DoS attacks and the closed-loop behavior, ensuring stability and performance. The paper provides examples to illustrate the analysis, including scenarios with sustained DoS attacks and varying periods and duty cycles. The results show that the proposed control strategies are effective in maintaining stability under DoS attacks, even when a significant portion of communication attempts are denied.