A symbolic algorithm to compute immersions of polynomial systems into linear ones up to an output injection. (July 2020)

• Record Type: Journal Article
• Authors: Menini, Laura; Possieri, Corrado; Tornambè, Antonio
• Is Part Of: Journal of symbolic computation. Volume 99(2020)
• Page Start: 1
• Page End: 20
• Publication Date: 2020-07
• Subjects: Observer design -- Linear systems up to an output injection -- Embeddings -- Algebraic geometry; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2019.03.001
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: In this paper, a symbolic, algorithmic procedure to compute an immersion that recasts a polynomial system into a linear one up to an output injection is proposed. Such a technique is based on computing, through algebraic geometry methods, the set of all the embeddings of the system and on matching the coefficients of these polynomials with the ones of the embeddings of a linear system up to an output injection. The given algorithm is then relaxed to compute an immersion that recasts a polynomial system into a form that is linear up to a finite order and an output injection and to compute an approximation of the immersion.