On controllability of linear stochastic systems

Abstract

Several concepts of controllability for partially observable stochastic systems (complete controllability, approximate controllability, controllability) are discussed. It is shown that complete and approximate controllability notions are equivalent, and in turn they are equivalent to the controllability for linear stochastic systems controlled with Gaussian processes. Necessary and sufficient conditions for these concepts of controllability are derived. These criteria reduce to the well known rank condition.