Abstract:
This paper develops Lyapunov and converse Lyapunov theorems for stochastic semistable nonlinear dynamical systems. Semistability is the property whereby the solutions of ...Show MoreMetadata
Abstract:
This paper develops Lyapunov and converse Lyapunov theorems for stochastic semistable nonlinear dynamical systems. Semistability is the property whereby the solutions of a stochastic dynamical system almost surely converge to (not necessarily isolated) Lyapunov stable in probability equilibrium points determined by the system initial conditions. Specifically, we provide necessary and sufficient Lyapunov conditions for stochastic semistability and show that stochastic semistability implies the existence of a continuous Lyapunov function whose infinitesimal generator decreases along the dynamical system trajectories and is such that the Lyapunov function satisfies inequalities involving the average distance to the set of equilibria.
Published in: 2016 IEEE 55th Conference on Decision and Control (CDC)
Date of Conference: 12-14 December 2016
Date Added to IEEE Xplore: 29 December 2016
ISBN Information: