Output regulation for aperiodic sampled linear delay systems via impulsive feedback

In this work, we address the robust output regulation problem for linear systems with state delays and aperiodic discrete-time output measurements through the design of an error-feedback impulsive controller. The proposed scheme is shown to be robust against constant parametric uncertainties and constant delays affecting the dynamics of sampled-data systems, ensuring reliable performance under these challenging conditions. This is achieved by implementing a dynamic controller incorporating an immersion for the steady-state input and an adequate gain design for stabilisation. The solvability conditions are presented in terms of delay-independent linear matrix inequalities, forming the basis for the design of the stabilising controller, while necessary and sufficient conditions are provided for the existence of a regulator. A comprehensive procedure for constructing the controller is given as a series of feasibility problems, assuming such solutions exist. The closed-loop stability and regulation conditions offered by the controller are demonstrated through a rigorous mathematical approach, providing guarantees that the closed-loop system is globally uniformly asymptotically stable with respect to a class of sampling sequences. Our methodology provides a solution to a complex control problem while also offering a systematic approach to managing delays and uncertainties in linear systems. The effectiveness of the proposed controller is illustrated through a numerical example, highlighting its performance and robustness under the specified conditions.