Solución de la ecuación algebraica de Riccati
DOI:
https://doi.org/10.29105/cienciauanl27.127-5Keywords:
ecuación algebraica de Riccati, matriz por bloques, valores propios, vectores propios, diagonalizaciónAbstract
En este trabajo se obtiene un conjunto de soluciones para la ecuación algebraica de Riccati (ARE), la cual es expresada en términos de los coeficientes de la ecuación original sin necesidad de conocer una de las soluciones para, a partir de ésta, obtener la segunda, como se hace en el caso de la ecuación de Bernoulli. Las soluciones son obtenidas partiendo de una matriz simétrica S por bloques, formada con los coeficientes de la ARE. Las soluciones de la ARE son obtenidas partiendo del cálculo de los valores propios de S y aplicando los principios de ortogonalidad en una base de un módulo sobre el anillo 
. Este procedimiento supone condiciones de simetría en los coeficientes de la ARE y se considera que la diagonalización de la matriz por bloques S siempre es posible. La metodología propuesta se muestra en dos ejemplos.
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