Common errors on using convex modelling and linear matrix inequalities for nonlinear control

Jorge Luis Álvarez-Urias; Víctor Estrada-Manzo; Miguel Ángel Bernal-Reza

doi:10.29057/icbi.v11i21.10855

Jorge Luis Álvarez-Urias Instituto Tecnológico de Sonora https://orcid.org/0000-0001-6439-6049
Víctor Estrada-Manzo Universidad Politécnica de Pachuca https://orcid.org/0000-0002-2902-8424
Miguel Ángel Bernal-Reza Instituto Tecnológico de Sonora https://orcid.org/0000-0003-3488-6180

DOI: https://doi.org/10.29057/icbi.v11i21.10855

Palabras clave: Desigualdades Matriciales Lineales, Método Directo de Lyapunov, Modelo Convexo, Control no Lineal, Dominio de atracción

Resumen

Este trabajo analiza los errores comunes al usar el modelado convexo y las desigualdades matriciales lineales para el control no lineal, una metodología que se ha vuelto cada vez más popular debido a su sistematicidad e implementabilidad numérica. Los ejemplos sobre problemas comunes son tomados de literatura existente: se clasifican, discuten y se dan consejos para prevenirlos. El modelado convexo se emplea en la variación de parámetros lineales, los modelos Takagi-Sugeno y otras estructuras convexas para subsumir o reescribir un sistema no lineal para el análisis o diseño a través del método directo de Lyapunov. La convexidad juega un papel central al permitir que un conjunto finito de condiciones en forma de desigualdades matriciales lineales sea suficiente para la tarea correspondiente. A diferencia de otras metodologías no lineales, ésta produce expresiones que se asemejan a resultados lineales, lo que hace que sea más fácil de comprender y, a menudo, induce errores sútiles.

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