Title :
The Positivstellensatz and nonexistence of common quadratic Lyapunov functions
Author :
Davis, John M. ; Eisenbarth, Geoffrey
Author_Institution :
Dept. of Math., Baylor Univ., Waco, TX, USA
Abstract :
We provide an algorithm for establishing the nonexistence of a common quadratic Lyapunov function for switched LTI systems under arbitrary switching. We show that this nonex-istence question is equivalent to the emptiness of an associated semi-algebraic set. The celebrated Positivstellensatz from real algebraic geometry provides a complete characterization of when this set is empty. Finally, we obtain the desired certificates of set emptiness using sum of squares programming.
Keywords :
Lyapunov methods; algebra; set theory; time-varying systems; Positivstellensatz; common quadratic Lyapunov functions; nonexistence; real algebraic geometry; semialgebraic set emptiness; sum of squares programming; switched LTI system; Geometry; Lyapunov methods; Polynomials; Programming; Stability criteria; Switched systems; Switches; Positivstellensatz; common Lyapunov functions; real algebraic geometry; sum of squares; switched systems;
Conference_Titel :
System Theory (SSST), 2011 IEEE 43rd Southeastern Symposium on
Conference_Location :
Auburn, AL
Print_ISBN :
978-1-4244-9594-8
DOI :
10.1109/SSST.2011.5753776
