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.
Wang, X., Saberi, A., Stoorvogel, A. A., Roy, S., & Sannuti, P. (2009). Computation of the recoverable region and stabilisation problem in the recoverable region for discrete-time systems. International journal of control, 82(10), 1870-1881. [10.1080/00207170902802984]. https://doi.org/10.1080/00207170902802984