Stabilization of unstable systems with input constraints

This article deals with the synthesis of stabilizing controllers for unstable linear systems and feedback linearizable unstable nonlinear systems, and the estimation of closed-loop regions of stability, in the presence of input constraints. The proposed methodology involves reducing the problem of stabilizing a system of arbitrary dimension into one of stabilizing a subsystem of dimension one, such that the stability of the overall system is ensured by guaranteeing the stability of the latter. The desirable features of the proposed methodology are its ease of implementation and its relative nonconservativeness over existing approaches; these are demonstrated by applying the proposed methodology to a chemical reactor example and comparing it with a Lyapunov-based approach.