Control of linear dynamic systems with set constrained disturbances

A linear dynamic system with input and observation uncertainties is studied. The uncertainties are constrained to be contained in specified sets. No probabilistic structure is assumed. The problem of keeping the state of the system in a specified region is investigated. Necessary and sufficient conditions for a solution to the problem and an algorithm that constructs the control are derived for open-loop and closed-loop control laws. The algorithm is also approximated by a bounding ellipsoid algorithm. Two special control laws, linear and "linear-plus-dead-band," are studied, and the regions that contain the state and control are characterized. Ellipsoids that bound the state and control are also derived, and a simple example of linear and linear-plus-dead-band control laws is presented.