Calculation of recoverable sets for systems with input and state constraints

The paper investigates two methods to calculate recoverable sets for continuous-time, linear time-invariant systems subjected to input and state constraints. A state is said to be recoverable if it can be driven to the equilibrium point while respecting the constraints. The recoverable set is the set of all the recoverable states. The first computational method discussed in the paper is based on the equivalence between recoverability and the existence of a time-optimal control law. The second method uses short-cuts that are applicable to two-dimensional systems and reduce the number of computations by about an order of magnitude. Several examples with distinctive characteristics are presented.