DocumentCode
896385
Title
Conjugate convex Lyapunov functions for dual linear differential inclusions
Author
Goebel, Rafal ; Teel, Andrew R. ; Hu, Tingshu ; Lin, Zongli
Author_Institution
Dept. of Electr. & Comput. Eng., Univ. of California, Santa Barbara, CA, USA
Volume
51
Issue
4
fYear
2006
fDate
4/1/2006 12:00:00 AM
Firstpage
661
Lastpage
666
Abstract
Tools from convex analysis are used to show how stability properties and Lyapunov inequalities translate when passing from a linear differential inclusion (LDI) to its dual. In particular, it is proved that a convex, positive definite function is a Lyapunov function for an LDI if and only if its convex conjugate is a Lyapunov function for the LDIs dual. Examples show how such duality effectively doubles the number of tools available for assessing stability of LDIs.
Keywords
Lyapunov methods; duality (mathematics); stability; Lyapunov inequalities; conjugate convex Lyapunov functions; convex analysis; convex positive definite function; dual linear differential inclusions; stability properties; Linear matrix inequalities; Linear systems; Lyapunov method; Polynomials; Stability analysis; Stability criteria; Sufficient conditions; Symmetric matrices; Convex conjugate functions; Lyapunov functions; duality; linear differential inclusions (LDIs);
fLanguage
English
Journal_Title
Automatic Control, IEEE Transactions on
Publisher
ieee
ISSN
0018-9286
Type
jour
DOI
10.1109/TAC.2006.872764
Filename
1618844
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