Title :
On the existence of a common quadratic Lyapunov function for two stable second order LTI discrete-time systems
Author :
Akar, Mehmet ; Narendra, Kumpati S.
Author_Institution :
Dept. of Electr. Eng., Yale Univ., New Haven, CT, USA
Abstract :
In this paper, necessary and sufficient conditions for the existence of a common quadratic Lyapunov function for two stable second order discrete-time systems are derived. These are expressed in terms of the Schur stability of the matrix pencils. Methods for determining whether the conditions are satisfied can be carried out algebraically or by using root-loci. Work is currently in progress on the extension of the results to higher order systems
Keywords :
Lyapunov methods; discrete time systems; eigenvalues and eigenfunctions; matrix algebra; Schur stability; common quadratic Lyapunov function; matrix pencils; necessary and sufficient conditions; stable second order LTI discrete-time systems; Artificial intelligence; Control theory; Linear systems; Lyapunov method; Nonlinear dynamical systems; Stability; Sufficient conditions; Switches; Switching systems; Time varying systems;
Conference_Titel :
American Control Conference, 2001. Proceedings of the 2001
Conference_Location :
Arlington, VA
Print_ISBN :
0-7803-6495-3
DOI :
10.1109/ACC.2001.946255
