Aiming Control: Residence Probability and (D,T)-Stability

In this paper, the problem of aiming control is formulated and analyzed in terms of the residence probability measure. Specifically, the notion of residence probability in a domain is introduced and its asymptotic expression is derived for linear systems with small, additive white noise. The associated notion of (D,T)-stability, which characterizes the performance of stochastic systems with no equilibrium points, is introduced and investigated. Finally, the controllability of residence probability is studied and the necessary and sufficient conditions for (D,T)-stabilizability are derived. The development is based on the asymptotic large deviations theory.