AbstractThis paper investigates the robustness of time‐varying linear systems under a large class of complex time‐varying perturbations. Previous results8which were restricted to bounded linear perturbations of output feedback type are generalized to unbounded and nonlinear perturbations of multi‐output feedback type. We establish a lower bound for the stability radius of these systems and show how it may be possible to improve the bound using time‐varying scalar transformations of the state, input and output variables. The results are applied to derive Gershgorin type stability criteria for time‐varying linea