On controlled-invariance and stabilization of time-delay systems

A non-conservative synthesis approach for discrete-time linear time-delay systems is presented, induced by a relaxed notion of invariance, namely, controlled (k, λ)-D-contractiveness. We characterize two particular families of controlled (k, λ)-contractive sets in the augmented state space of the corresponding delay-free system and establish their relationship to controlled (k, λ)-D-contractive sets of the time-delay system. The required computations for both the controller synthesis and controller implementation are carried in the state space of the time-delay system, making the method scalable with respect to the maximum delay.