Output regulation for aperiodic sampled linear delay systems via impulsive feedback
Gildardo Mejía-Álvarez, Horacio García–Vázquez, Bernardino Castillo–Toledo, S. Di Gennaro · International Journal of Systems Science · 2025
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.