Stability of Systems Subjected to Zero Ergodic Mean Disturbances

This paper considers the stability of systems subjected to zero ergodic mean disturbances. We first consider the stability of averaged systems and give an example showing that exponential stability does not imply averaged stability. Next a sufficient condition is established for a class of averaged systems to be stable. Using this result, we study the stability of systems subjected to zero ergodic mean disturbances, and obtain conditions guaranteeing convergence to an attractive set.