Title :
Connection between almost everywhere stability of an ODE and advection PDE
Author :
Rajaram, Rajeev ; Vaidya, Umesh ; Fardad, Makan
Author_Institution :
Shepherd Univ., Shepherdstown
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;
Conference_Titel :
Decision and Control, 2007 46th IEEE Conference on
Conference_Location :
New Orleans, LA
Print_ISBN :
978-1-4244-1497-0
Electronic_ISBN :
0191-2216
DOI :
10.1109/CDC.2007.4434827
