Title :
On explicit steady-state solutions of Fokker-Planck equations for a class of nonlinear feedback systems
Author :
Brockett, Roger W. ; Liberzon, Daniel
Author_Institution :
Div. of Eng. & Appl. Sci., Harvard Univ., Cambridge, MA, USA
Abstract :
We study the question of existence of steady-state probability distributions for systems perturbed by white noise. We describe a class of nonlinear feedback systems for which an explicit formula for the steady-state probability density can be found. These systems include what has been called monotemperaturic systems in earlier work. We also establish relationships between the steady-state probability densities and Liapunov functions for the corresponding deterministic systems
Keywords :
Fokker-Planck equation; Lyapunov methods; feedback; nonlinear systems; probability; thermodynamics; white noise; Fokker-Planck equations; Liapunov functions; deterministic systems; explicit steady-state solutions; monotemperaturic systems; nonlinear feedback systems; steady-state probability density; steady-state probability distributions; white noise; Eigenvalues and eigenfunctions; Feedback; Laboratories; Linear systems; Nonlinear equations; Nonlinear systems; Probability distribution; Steady-state; Stochastic systems; White noise;
Conference_Titel :
American Control Conference, 1998. Proceedings of the 1998
Conference_Location :
Philadelphia, PA
Print_ISBN :
0-7803-4530-4
DOI :
10.1109/ACC.1998.694672
