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This paper demonstrates the fundamental vulnerability of networked linear control systems to perfectly undetectable false data injection attacks (FDIAs) based on affine transformations. The work formulates a generalized FDIA framework that coordinates multiplicative and additive data injections targeting both control commands and observables in networked systems. The paper derives mathematical conditions for executing affine transformation based perfectly undetectable attacks (ATPAs) on state-feedback and output-feedback control systems, with attack capabilities varying based on the attacker’s knowledge of plant dynamics and control gains. The paper examines several attack scenarios, including scaling and general affine transformations, and characterizes the range of system knowledge—from minimum to full—required for different attack types. The paper classifies ATPA into four types based on the feedback structure (state or output) and knowledge requirements: those that match plant dynamics without controller knowledge and those that match closed-loop dynamics by exploiting controller information. The paper examines several attack scenarios and shows how carefully ATPAs can create the illusion of normal system operation while the actual system behavior deviates significantly from intended trajectories.