Stabilization of nonlinear processes with input constraints

This work deals with nonlinear processes which, in the absence of input con straints, can be locally stabilized by a linearizing static state feedback law. Such systems, under unconstrained linearizing control laws, possess a cascaded structure between a (asymptotically or exponentially) stable nonli near subsystem and an exponentially stable linear subsystem, which allows f or a straightforward stability analysis. In the presence of input constrain ts, however, this cascaded structure breaks down to an interconnection betw een two nonlinear subsystems; analyzing the stability of such interconnecti ons is a rather cumbersome task, that typically results in conservative est imates of regions of stability. In this article, we present an analysis fra mework for the local stabilization of such processes and the estimation of regions of closed-loop stability in the presence of input constraints. The proposed approach entails: (i) specifying a region in state-space where the closed-loop system behaves effectively as a cascade and asymptotic stabili ty can be guaranteed in the presence of constraints, provided that the stat es of the system remain in this region for all times; and (ii) constructing invariant sets within this region that qualify as regions of closed-loop s tability. A detailed case study is carried out on a polymerization reactor example and the desirable features of the proposed methodology are aptly il lustrated. (C) 2000 Elsevier Science Ltd. All rights reserved.