In this paper, new properties of the cascade between a multi-input multi-output linear time-invariant system, referred to in the following as the original system, and an inner system are dealt with. In particular, attention is devoted to the relationship between the Hankel singular values and characteristic values of the cascade system and those of the original one, proving that, if the inner system has gain greater than or equal to one, then the first n Hankel singular values (characteristic values) of the cascade system are greater than or equal to those of the original system. The results are then applied to derive a new property of minimum phase systems.

Cascading with Inner Systems: Hankel Singular Values and Characteristic Values

Buscarino, Arturo;Fortuna, Luigi;Frasca, Mattia;Nunnari, Giuseppe
2020-01-01

Abstract

In this paper, new properties of the cascade between a multi-input multi-output linear time-invariant system, referred to in the following as the original system, and an inner system are dealt with. In particular, attention is devoted to the relationship between the Hankel singular values and characteristic values of the cascade system and those of the original one, proving that, if the inner system has gain greater than or equal to one, then the first n Hankel singular values (characteristic values) of the cascade system are greater than or equal to those of the original system. The results are then applied to derive a new property of minimum phase systems.
Linear systems; Eigenvalues and eigenfunctions; MIMO communication; Computational modeling; Symmetric matrices; Control systems; Machine-to-machine communications; All-pass systems; characteristic values; Hankel singular values; inner systems; linear time-invariant (LTI) systems
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11769/364967
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