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 in | Circuits, systems, and signal processing Vol. 26; no. 2; pp. 147 - 164 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Cambridge
Springer Nature B.V
01.04.2007
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0278-081X 1531-5878 |
| DOI | 10.1007/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] |
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| 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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| Copyright | Birkhauser Boston 2007 |
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| DOI | 10.1007/s00034-005-1201-9 |
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| Title | Parameter-Dependent Lyapunov Function Method for a Class of Uncertain Nonlinear Systems with Multiple Equilibria |
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