Connection between almost everywhere stability of an ODE and advection PDE

Author

Rajaram, Rajeev ; Vaidya, Umesh ; Fardad, Makan

Author_Institution

Shepherd Univ., Shepherdstown

fYear

2007

fDate

12-14 Dec. 2007

Firstpage

5880

Lastpage

5885

Abstract

A result on the necessary and sufficient conditions for almost everywhere stability of an invariant set in continuous-time dynamical systems is presented. It is shown that the existence of a Lyapunov density is equivalent to the almost everywhere stability of an invariant set. Furthermore, such a density can be obtained as the positive solution of a linear partial differential equation analogous to the positive solution of Lyapunov equation for stable linear systems.

Keywords

Lyapunov matrix equations; continuous time systems; invariance; linear differential equations; partial differential equations; set theory; stability; Lyapunov density; Lyapunov equation; ODE; advection PDE; almost everywhere stability; continuous-time dynamical systems; invariant set; linear partial differential equation; necessary and sufficient conditions; stable linear systems; Control systems; Density functional theory; Density measurement; Differential equations; Lyapunov method; Partial differential equations; Stability; Sufficient conditions; Time measurement; USA Councils;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 2007 46th IEEE Conference on

Conference_Location

New Orleans, LA

ISSN

0191-2216

Print_ISBN

978-1-4244-1497-0

Electronic_ISBN

0191-2216

Type

conf

DOI

10.1109/CDC.2007.4434827

Filename

4434827