Trajectory sensitivity reduction through exponentially stable feedback

Trajectory sensitivity with respect to small random perturbations in initial state and plant parameters is investigated. An upper bound on the maximal spread around the nominal trajectory at time t for a probability level p is established in the paper. If a sufficiently high degree of exponential stability is attained by additional feedback, the modified system has a lower upper bound compared to that for the system without additional feedback. Moreover, when a deterministic observer is employed, the upper bound is increased but it is still lower than that corresponding to the system without additional feedback and without an observer.