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
fDate :
4/1/2006 12:00:00 AM
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);
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.2006.872764
