The generalized S- and σ-inverse – a comparative case study for right- and left-invertible plants

• Published in: Bulletin of the Polish Academy of Sciences: Technical Sciences
• Main Authors: P. Majewski, W.P. Hunek
• Format: Article
• Language: English
• Published: Polish Academy of Sciences 2020-12-01
• Subjects: nonunique right/left inverses; nonsquare polynomial matrices; inverse theory; robustification of processes; practical implementation
• Online Access: https://journals.pan.pl/Content/118377/PDF/27_D1517-1523_01630_Bpast.No.68-6_29.12.20_OK.pdf
• ISSN: 2300-1917

In this paper, an advanced study covering the comparison between two classes of generalized inverses is conducted. Two sets of instances, strictly derived from the recently introduced nonunique S- and σ-inverse, are analyzed, especially in terms of degrees of freedom-oriented interchangeable application in different engineering tasks. Henceforth, the respective collections of right and left inverses can be combined in order to achieve a complex tool for robustification of a plethora of real processes. The great potential of two S- and σ-inverse, in particular in robust control and signal recovery as well as complex optimal tasks, is confirmed in the manuscript and supported by the recently carried out research investigations.