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

Laura Menini; Corrado Possieri; Antonio Tornambè

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

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cqvip: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.

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《自动化学报：英文版》 |2020年第1期|P.57-69|共13页
作者
Laura Menini; Corrado Possieri; Antonio Tornambè;
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作者单位

Dipartimento di Ingegneria Industriale Universitàdi Roma Tor Vergata Roma 00133 Italy;

Istituto di Analisi dei Sistemi ed Informatica“A.Ruberti ”Consiglio Nazionale delle Ricerche(IASI-CNR) Roma 00185 Italy;

Dipartimento di Ingegneria Civile e Ingegneria Informatica Universitàdi Roma Tor Vergata Roma 00133 Italy;

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正文语种 chi
中图分类数学分析;
关键词
Index Terms—Asymptotic stability; discrete-time systems; invariance; nonlinear systems.;

机译：索引词-渐近稳定性;离散时间系统;不变性;非线性系统;

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

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