Parameter-Dependent Lyapunov Function Method for a Class of Uncertain Nonlinear Systems with Multiple Equilibria

First, a new linear matrix inequality (LMI) characterization of extended strict positive realness is presented for linear continuous-time systems. Then a class of nonlinear systems with multiple equilibria subject to polytopic uncertainty is addressed by the parameter-dependent Lyapunov function met...

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Published inCircuits, systems, and signal processing Vol. 26; no. 2; pp. 147 - 164
Main Authors Duan, Zhisheng, Wang, Jinzhi, Huang, Lin
Format Journal Article
LanguageEnglish
Published Cambridge Springer Nature B.V 01.04.2007
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ISSN0278-081X
1531-5878
DOI10.1007/s00034-005-1201-9

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Abstract First, a new linear matrix inequality (LMI) characterization of extended strict positive realness is presented for linear continuous-time systems. Then a class of nonlinear systems with multiple equilibria subject to polytopic uncertainty is addressed by the parameter-dependent Lyapunov function method. New sufficient conditions for global convergence are presented. This allows the Lyapunov function to be parameter dependent. Furthermore, an LMI-based controller design method is also given, and reduced-order controllers can be designed by performing a structural constraint on the introduced slack variables. Several numerical examples are included to demonstrate the applicability of the proposed method. [PUBLICATION ABSTRACT]
AbstractList First, a new linear matrix inequality (LMI) characterization of extended strict positive realness is presented for linear continuous-time systems. Then a class of nonlinear systems with multiple equilibria subject to polytopic uncertainty is addressed by the parameter-dependent Lyapunov function method. New sufficient conditions for global convergence are presented. This allows the Lyapunov function to be parameter dependent. Furthermore, an LMI-based controller design method is also given, and reduced-order controllers can be designed by performing a structural constraint on the introduced slack variables. Several numerical examples are included to demonstrate the applicability of the proposed method. [PUBLICATION ABSTRACT]
Author Wang, Jinzhi
Huang, Lin
Duan, Zhisheng
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Snippet First, a new linear matrix inequality (LMI) characterization of extended strict positive realness is presented for linear continuous-time systems. Then a class...
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SubjectTerms Design
Engineering
Nonlinear systems
Title Parameter-Dependent Lyapunov Function Method for a Class of Uncertain Nonlinear Systems with Multiple Equilibria
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