Continuous-Time Stability of Networked Cyber-Physical Systems Under Denial-of-Service Attacks: A Lyapunov–LMI Framework with Sample-and-Hold Control

Abstract

Cyber-physical systems (CPSs) increasingly rely on shared communication networks to close feedback loops, which exposes the control layer to denial-of-service (DoS) attacks that intermittently block sensing and actuation updates. This paper develops a continuous-time stability framework for linearized CPSs operating under DoS by combining a sampleddata networked control model with deterministic constraints on DoS activation frequency and denial duration. Under a zero-order-hold implementation, the closed loop evolves as a timevarying sampled-data system driven by the sequence of successful update instants. We derive an explicit upper bound on the inter-success time and establish a Lyapunov/contractivity-based sufficient condition that guarantees global exponential stability for all admissible DoS patterns. A nominal stabilizing state-feedback gain is obtained via a quadratic Lyapunov LMI, and the DoS-resilience certificate is verified on a finite grid over the admissible interupdate interval. Simulations on a Jacobian-linearized autonomous-vehicle model (used only for illustration) demonstrate that the proposed ZOH-hold implementation preserves regulation under bursty DoS, while a naive controldropout strategy exhibits degraded transients.