The regulator problem for linear discrete‐time delay systems with origin on the boundary of the domain of constraints on the control: Independent of delay case

Abstract This paper investigates the linear constrained regulation problem for discrete‐time delay systems and uncertain discrete‐time delay systems. The control input is assumed to be subject to asymmetric constraints. The novelty of the proposed approach lies in the consideration of cases where the origin of the control input is situated on the boundary of the constraint set, a situation frequently encountered in real‐world systems. We use the concept of positive invariance to establish delay‐independent conditions, formulated as linear programs, for designing a state feedback law that ensures constraint satisfaction and asymptotic stability of the closed‐loop system. A numerical example is presented to demonstrate the effectiveness of the proposed methodology.