Theory of residence time control by output feedback

The problem of residence time control of a stochastic system by observer-based output feedback is formulated and solved for the case of linear systems with small additive input noise. Both noiseless and noisy measurements are considered. In the noiseless measurements case, it is shown that the fundamental bounds on the achievable residence time depend on the nonminimum-phase zeros of the system. In the noisy measurements case, the achievable residence time is shown to be always bounded, and an estimate of the bound is given. Controller design techniques are presented. The development is based on the asymptotic large deviations theory