Slow control for global stabilization of feedforward systems with exponentially unstable Jacobian linearization

Abstract

The global stabilization of a restricted class of nonlinear systems which simultaneously present `destabilizing' feedback connections and `rate limiting' feedforward connections is considered. Under the restriction that the feedback connections are `local' connections around each integrator, a slow control design is proposed which enforces a slow convergence towards a nested sequence of manifolds, the last of which is a stable manifold of the closed-loop system. Near invariance of the successive manifolds is achieved by allowing for enough gan in their neighborhood, yet keeping the control slow in the entire state space.