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

• Published in: Circuits, systems, and signal processing Vol. 26; no. 2; pp. 147 - 164
• Main Authors: Duan, Zhisheng, Wang, Jinzhi, Huang, Lin
• Format: Journal Article
• Language: English
• Published: Cambridge Springer Nature B.V 01.04.2007
• Subjects: Design; Engineering; Nonlinear systems
• ISSN: 0278-081X; 1531-5878
• DOI: 10.1007/s00034-005-1201-9

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]