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 Vol. 68; no. 6; pp. 1517 - 1523
• Main Authors: Majewski, P, Hunek, W P
• Format: Journal Article
• Language: English
• Published: Warsaw Polish Academy of Sciences 01-12-2020
• Subjects: Case studies; Engineering; inverse theory; nonsquare polynomial matrices; nonunique right/left inverses; practical implementation; Robust control; robustification of processes; Signal reconstruction; Task complexity; Telecommunications systems
• ISSN: 0239-7528; 2300-1917
• DOI: 10.24425/bpasts.2020.135399

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.