Stabilization of a Switched System with Commensurate Delays under Slow Switchings

An approach is proposed to constructing a digital controller that stabilizes acontinuous-time switched linear system with commensurate delays in control under slowswitchings. The approach to stabilization consistently includes the construction of a switchedcontinuous–discrete-time closed-loop system with a digital controller, the transition to itsdiscrete-time model, represented in the form of a switched system with modes of different orders,simultaneous stabilization of the subsystems of the resulting discrete-time model, and calculationof a delay time that ensures the stability of the original switched system closed by the controllerfound.