Revisiting classical cross-gramian definition for model order reduction of linear time-invariant systems

Resumen: This paper presents, under the perspective of balancing-reducing linear systems via Hankel singular values, a proposition that is aimed to offer a plain relationship among controllability and observability gramians, and the classical cross-gramian for a certain class of systems: from defining the cross-gramian as the solution of Sylvester’s equation, and the controllability and observability gramians as solutions of the Lyapunov’s algebraic equation, which is a particular case of Sylvester’s equation, the established proposition provides a condensed starting point to redifuse and repopularize, among the control systems community, the usage of the cross-gramian for model order reduction of linear time-invariant dynamical systems.

¿Cómo citar?

Fernando Aaron Ortiz-Ricardez & Luis Alvarez-Icaza. Revisiting classical cross-gramian definition for model order reduction of linear time-invariant systems. Memorias del Congreso Nacional de Control Automático, pp. 1-5, 2020.

Palabras clave

Linear control systems, Singular value decomposition, Educational aids

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