On Index Reduction and Column Regularization for Rectangular Descriptor Systems via Input Feedbacks

Mamoni Paitandi () and Mahendra Kumar Gupta ()
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Mamoni Paitandi: National Institute of Technology Jamshedpur
Mahendra Kumar Gupta: Indian Institute of Technology Bhubaneswar

Indian Journal of Pure and Applied Mathematics, 2025, vol. 56, issue 3, 1090-1101

Abstract: Abstract The index of a rectangular descriptor system indicates the intensity of impulses within its solutions. This article establishes a necessary condition for the existence of an input feedback that can reduce the system’s index to a specific value and simultaneously column-regularize the system. Further, a necessary and sufficient condition is proposed for the existence of an input feedback such that the index of the resulting closed loop system is restricted to at most two, along with column regularization. All conditions have been specified as rank conditions in system matrices. The appropriate feedback matrix is constructed by applying an algorithm that involves orthogonal transformations. Furthermore, the same technique has been refined to reduce the system’s index to a maximum of one whenever possible. The theory presented in the paper is illustrated with numerical and physical examples.

Keywords: Descriptor systems; Impulse reduction; Regularization; Feedback design; Index; 34A09; 93B52; 15A03; 15A24; 93B25 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s13226-025-00824-3

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