Title :
A sufficient condition for the existence of a common Lyapunov function for two second order linear systems
Author :
Shorten, R.N. ; Narendra, K.S.
Author_Institution :
Center for Syst. Sci., Yale Univ., New Haven, CT, USA
Abstract :
A sufficient condition for the existence of a common Lyapunov function for two stable linear second order systems x=Aix, A i∈{Al, A2} is presented, namely that the matrix pencil A1+γA2 have distinct negative eigenvalues for all γ∈(0,∞). The implications of this result for the stability of more general switching systems are briefly discussed
Keywords :
Lyapunov methods; asymptotic stability; eigenvalues and eigenfunctions; linear systems; matrix algebra; Lyapunov function; asymptotic stability; matrix pencil; negative eigenvalues; second order linear systems; sufficient condition; switching systems; Asymptotic stability; Eigenvalues and eigenfunctions; Equations; Interconnected systems; Linear systems; Lyapunov method; Sufficient conditions; Switching systems; Symmetric matrices; Time varying systems;
Conference_Titel :
Decision and Control, 1997., Proceedings of the 36th IEEE Conference on
Conference_Location :
San Diego, CA
Print_ISBN :
0-7803-4187-2
DOI :
10.1109/CDC.1997.652394
