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Regional stability of two‐dimensional nonlinear polynomial Fornasini‐Marchesini systems
Author(s) -
Osowsky Jefferson,
de Souza Carlos E.,
Coutinho Daniel
Publication year - 2018
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.4018
Subject(s) - polynomial , mathematics , lyapunov function , nonlinear system , bounded function , equilibrium point , exponential stability , domain (mathematical analysis) , algebraic number , vector valued function , stability (learning theory) , mathematical analysis , computer science , differential equation , physics , quantum mechanics , machine learning
Summary This paper addresses the problem of regional stability analysis of 2‐dimensional nonlinear polynomial systems represented by the Fornasini‐Marchesini second state‐space model. A method based on a polynomial Lyapunov function is proposed to ensure local asymptotic stability and provide an estimate of the domain of attraction of the system zero equilibrium point. The proposed results that build on recursive algebraic representations of the polynomial vector function of the system dynamics and Lyapunov function are tailored via linear matrix inequalities that are required to be satisfied at the vertices of a given bounded convex polyhedral region of the state space. Numerical examples demonstrate the effectiveness of the proposed method.