Linear time-delay systems: the complete type functionals approach

Abstract

[EN] Recent results on Lyapunov-Krasovskii functionals of complete type for linear time-delay systems are presented. The main concepts and results are introduced for the single delay system case, and necessary and sufficient stability conditions expressed in terms of the Lyapunov delay matrix are explained. The use of complete type functionals in analysis and controller design is discussed. The contribution focuses mainly at results of researchers in Mexico.[ES] Se introducen resultados recientes del enfoque de funcionales de Lyapunov-Krasovski de tipo completo para sistemas lineales con retardos. Se explican brevemente los principales conceptos y resultados para el caso de sistemas con un retardo así como las condiciones necesarias y suficientes de estabilidad expresadas en terminos del análogo de la matriz de Lyapunov. Las extensiones  de este tipo de condiciones de estabilidad a otras clases de sistemas con retardos son expuestas brevemente. Tambien se presentan aplicaciones existentes del efoque de funcionales de tipo completo a problemas de analisis y de diseño de controladores. El trabajo se enfoca a contribuciones de investigadores de Mexico a este tema de estudio.Este trabajo ha sido realizado parcialmente gracias al apoyo del Conacyt, México, Proyecto A1-S-24796.Mondié, S.; Gomez, M. (2022). Contribuciones al estudio de sistemas lineales con retardos: el enfoque de funcionales de tipo completo. Revista Iberoamericana de Automática e Informática industrial. 19(4):381-393. https://doi.org/10.4995/riai.2022.16828381393194Alexandrova, I. V., Zhabko, A. P., 2018. A new LKF approach to stability analysis of linear systems with uncertain delays. Automatica 91, 173-178. https://doi.org/10.1016/j.automatica.2018.01.012Arismendi-Valle, H., Melchor-Aguilar, D., 2019. On the Lyapunov matrices for integral delay systems. Int. J. of Systems Science 50 (6), 1190-1201. https://doi.org/10.1080/00207721.2019.1597943Bejarano, F. 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