State estimation of linear dynamical systems under bounded control

The problem of estimation of all possible states that a linear system under bounded control may take (namely, the reachable or attainable set) is addressed. A number of previously developed Lyapunov techniques for estimating the reachable set of ann-dimensional linear system are extended and compared. The techniques produce over-estimates in the form ofn-dimensional ellipsoids. Illustrative examples are solved.This work was supported by the Natural Sciences and Engineering Research Council of Canada, Operating Grant Nos. A-0621 and A-4080, and by Research Personnel Support from the Dean of Science, Memorial University of Newfoundland, Canada.