Regional stability of two-dimensional nonlinear polynomial Fornasini-Marchesini systems
Jefferson Osowsky
Department of Underwater Acoustic, Instituto de Estudos do Mar Almirante Paulo Moreira, Brazilian Navy, Arraial do Cabo, Brazil
Search for more papers by this authorCorresponding Author
Carlos E. de Souza
Department of Mathematical and Computational Methods, Laboratório Nacional de Computação Científica, Petrópolis, Brazil
Correspondence
Carlos E. de Souza, Department of Mathematical and Computational Methods, Laboratório Nacional de Computação Científica, Petrópolis-RJ 25651-075, Brazil.
Email: [email protected]
Search for more papers by this authorDaniel Coutinho
Department of Automation and Systems, Universidade Federal de Santa Catarina, Florianópolis, Brazil
Search for more papers by this authorJefferson Osowsky
Department of Underwater Acoustic, Instituto de Estudos do Mar Almirante Paulo Moreira, Brazilian Navy, Arraial do Cabo, Brazil
Search for more papers by this authorCorresponding Author
Carlos E. de Souza
Department of Mathematical and Computational Methods, Laboratório Nacional de Computação Científica, Petrópolis, Brazil
Correspondence
Carlos E. de Souza, Department of Mathematical and Computational Methods, Laboratório Nacional de Computação Científica, Petrópolis-RJ 25651-075, Brazil.
Email: [email protected]
Search for more papers by this authorDaniel Coutinho
Department of Automation and Systems, Universidade Federal de Santa Catarina, Florianópolis, Brazil
Search for more papers by this authorSummary
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.
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