Residence time control of systems subject to measurement noise

The residence time control problem is considered for linear systems that are subject to both input and measurement noise disturbances. It is shown that the maximal residence time is bounded, and an upper bound is derived. Necessary and sufficient conditions for the existence of controllers that achieve the upper bound are derived and design techniques for residence time controllers are considered. Connections with optimal output feedback control are explored. It is concluded that even if a system is strongly residence time-controllable, i.e. any residence time is achievable by a state feedback control law, any amount of measurement noise will result in a bounded residence time. Therefore, measurement noise has greater limiting effect than input noise on the achievable residence time