Title :
Stability and quadratic Lyapunov functions for nD systems
Author_Institution :
ESAT-SISTA, K.U. Leuven, Leuven
Abstract :
We discuss some ideas and preliminary results on the stability of nD systems described by linear constant coefficient PDE´s. The stability concept used is Lscr2-stability and Lscr2-asymptotic stability, with time as a distinguished variable. For scalar equations, stability conditions are derived, including methods to make these conditions into LMI´s in the system parameters. These conditions are interpreted in terms of Lyapunov functions for systems involving many independent variables. Several open problems for multivariable nD systems are formulated.
Keywords :
Lyapunov methods; asymptotic stability; linear matrix inequalities; multivariable systems; LMI; asymptotic stability; independent variables; linear constant coefficient; multivariable systems; quadratic Lyapunov functions; scalar equations; Controllability; Functional analysis; Lyapunov method; Mathematics; Observability; Partial differential equations; Polynomials; Stability; Symmetric matrices; LMI’s; Lyapunov functions; PDE’s; nD systems; quadratic differential forms; stability;
Conference_Titel :
Multidimensional (nD) Systems, 2007 International Workshop on
Conference_Location :
Aveiro
Print_ISBN :
978-1-4244-1111-5
Electronic_ISBN :
978-1-4244-1112-2
DOI :
10.1109/NDS.2007.4509541
