Algorithms to Compute the Largest Invariant Set Contained in an Algebraic Set for Continuous-Time and Discrete-Time Nonlinear Systems

作     者：Laura Menini Corrado Possieri Antonio Tornambè Laura Menini;Corrado Possieri;Antonio Tornambè

作者机构：Dipartimento di Ingegneria IndustrialeUniversitàdi Roma Tor VergataRoma 00133Italy Istituto di Analisi dei Sistemi ed Informatica“A.Ruberti”Consiglio Nazionale delle Ricerche(IASI-CNR)Roma 00185Italy Dipartimento di Ingegneria Civile e Ingegneria InformaticaUniversitàdi Roma Tor VergataRoma 00133Italy 

出 版 物：《IEEE/CAA Journal of Automatica Sinica》 (自动化学报（英文版）)

年 卷 期：2020年第7卷第1期

页      面：57-69页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主　　题：Asymptotic stability discrete-time systems invariance nonlinear systems 

摘      要：In this paper, some computational tools are proposed to determine the largest invariant set, with respect to either a continuous-time or a discrete-time system, that is contained in an algebraic set. In particular, it is shown that if the vector field governing the dynamics of the system is polynomial and the considered analytic set is a variety, then algorithms from algebraic geometry can be used to solve the considered problem. Examples of applications of the method(spanning from the characterization of the stability to the computation of the zero dynamics) are given all throughout the paper.