Control of nonlinear chained systems: from the Routh-Hurwitz stability criterion to time-varying exponential stabilizers

We show how any linear feedback that stabilizes the origin of a linear chain of integrators induces a simple, continuous time-varying feedback that exponentially stabilizes the origin of a nonlinear chained-form system. The design method is related to a method developed by M'Closkey and Murray (1997) to transform smooth feedback yielding slow polynomial convergence into continuous homogeneous ones that give exponential convergence.