A note on invertibility and relative degree of MIMO LTI systems. (June 2022)

• Record Type: Journal Article
• Authors: Kadam, Sujay D.; Palanthandalam-Madapusi, Harish J.
• Is Part Of: IFAC journal of systems and control. Volume 20(2022)
• Publication Date: 2022-06
• Subjects: Invertibility -- System inversion -- Relative degree; Automatic control -- Periodicals; Relay control systems -- Periodicals; Embedded computer systems -- Periodicals; Feedback control systems -- Periodicals; Artificial intelligence -- Periodicals; Artificial intelligence; Automatic control; Embedded computer systems; Feedback control systems; Relay control systems; Electronic journals; Periodicals; 629.89
• DOI: 10.1016/j.ifacsc.2022.100193
• Languages: English
• ISSNs: 2468-6018

Abstract

Abstract: The property of system invertibility is important both from a theoretical standpoint and an important consideration in left and right inversion problems that deal with input estimation and tracking control respectively. Nuances associated with the notion of relative degree in multi-input, multi-output (MIMO) systems on account of input–output delays pose challenges in system inversion problems and are more acute in the case of non-square systems. In this note, using the LTI discrete-time MIMO systems framework, we review existing notions of relative degree and develop new definitions and generalizations for relative degree to help address some of the gaps in system inversion problems. In doing so, we also show through simple but elegant results that existence of well-defined relative degree for an LTI MIMO system implies its invertibility. Furthermore, we also highlight the utility of these ideas in practical tracking control and input estimation situations and problems.