Calculation of recoverable sets for 2-dimensional systems with input and state constraints

The paper investigates methods to calculate recoverable sets for 2-dimensional linear time-invariant systems with input and state constraints. A state is recoverable if it can be driven to the equilibrium point while respecting the constraints. The recoverable set is the set of all recoverable states. A new computational procedure is introduced to rapidly calculate recoverable sets. Several examples with distinctive characteristics are presented. The results are compared to those of a method which calculates the recoverable set through an exhaustive search of all the reachable points in reverse time. It is demonstrated that the new procedure is far superior in speed.