Аннотация:An approach is proposed to construct a digital controller stabilizing a continuoustime switched linear interval system with commensurate delays in control under slow switchings.The stabilization approach consistently includes the construction of a switched continuous-time–discrete-time closed-loop system with a digital controller, the transition to its discrete-timemodel represented as a switched discrete-time linear interval system with modes of variousorders, simultaneous stabilization of the subsystems of the resulting discrete-time model, and the calculation of the delay time ensuring the stability of the original switched system closed by the controller found.Keywords: switched interval system, switching signal, stability, feedback, stabilization, delays in control