An LMI optimization approach to Lyapunov stability analysis for linear time-invariant systems

Author

Wang, Jianhong ; Li, Xun ; Ge, Yaping ; Jia, Guangfeng

Author_Institution

Sch. of Sci., Nantong Univ., Nantong

fYear

2008

fDate

2-4 July 2008

Firstpage

3044

Lastpage

3048

Abstract

Theorem of alternatives based on the separation theorems are proposed to provide systematic and unified proofs of necessary and sufficient conditions for solvability of Lyapunov inequality on P. As an application of the theorem of alternatives, we investigate the conditions for the existence of feasible solutions to Lyapunov inequality on P and obtain a restatement of the celebrated Lyapunov stability theorem for linear time-invariant systems. Furthermore, the effectiveness of the proposed method is illustrated by a numerical example.

Keywords

Lyapunov methods; linear matrix inequalities; linear systems; optimisation; stability; LMI optimization approach; Lyapunov inequality; Lyapunov stability analysis; linear time-invariant systems; separation theorems; Control theory; Educational institutions; Lagrangian functions; Linear feedback control systems; Linear matrix inequalities; Lyapunov method; Optimal control; Robust control; Sufficient conditions; Vectors; LMI optimization; Linear matrix inequality; Linear time-invariant systems; Lyapunov stability; Theorem of alternatives;

fLanguage

English

Publisher

ieee

Conference_Titel

Control and Decision Conference, 2008. CCDC 2008. Chinese

Conference_Location

Yantai, Shandong

Print_ISBN

978-1-4244-1733-9

Electronic_ISBN

978-1-4244-1734-6

Type

conf

DOI

10.1109/CCDC.2008.4597885

Filename

4597885