A simultaneous canonical form of a pair of matrices and applications involving the weighted Moore–Penrose inverse

Thome, Néstor

doi:10.1016/j.aml.2015.10.012

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A New Left σ-Inverse1

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Cited by 4 publications

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“…Remark 3. It is worth mentioning that the minimum-norm right and least-squares left unique inverses of β(q) in forms of β R 0 (q) and β L 0 (q), respectively, fulfill the four Moore-Penrose conditions [21]- [23].…”

Section: A New Left σ-Inversementioning

confidence: 99%

A New Generalized Θ-Inverse vs. Moore-Penrose Structure: A Comparative Control-Oriented Practical Investigation

Hunek

2021

IEEE Access

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A new non-unique Θ-inverse of non-square polynomial matrices is presented in this paper. It is shown that the above inverse specializes to the unique Moore-Penrose one under several specific assumptions. Due to the existence of some degrees of freedom, the Θ-inverse outperforms the Moore-Penrose inverse in various inverse-related problems covering the multivariable control theory. In many scenarios the former inverse can stabilize a closed-loop plant being unstable by application of the Moore-Penrose formula. Practical and theoretical simulation examples confirm the correctness of the proposed method.

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Section: A New Left σ-Inversementioning

confidence: 99%