Stability and quadratic Lyapunov functions for nD systems

Author

Willems, Jan C.

Author_Institution

ESAT-SISTA, K.U. Leuven, Leuven

fYear

2007

fDate

27-29 June 2007

Firstpage

41

Lastpage

45

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;

fLanguage

English

Publisher

ieee

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

Type

conf

DOI

10.1109/NDS.2007.4509541

Filename

4509541