The construction of the set of stable states for constrained systems with open-loop unstable plants

Control in the presence of hard control and state constraints, and open-loop unstable plants, is addressed. A methodology for the construction of a set of stable states of a tracking control system is presented. A saturation avoidance control strategy is employed, and the exogenous reference signal is modified nonlinearly so that the controlled process state is constrained to a positively invariant set. Stability is guaranteed for all initial states in this set. The said set is an arbitrarily close approximation of the maximal statically admissible set. Characterization of this set is an important stepping stone in the synthesis of tracking controllers