Computation of the recoverable region and stabilisation problem in the recoverable region for discrete-time systems

This paper considers discrete-time linear time-invariant systems subject to input and state constraints. It is shown that the recoverable region (which is the largest domain of attraction that is theoretically achievable) can be semi-globally stabilized by non-linear feedbacks while satisfying the constraints. Moreover, the recoverable region for the given system is constructed by constructing the same however for a reduced order subsystem of the given system. Such a reduction in the order or dimension of the system generally leads to a considerable simplification in the computational effort.